muhammad elias - core · mc mass flow rate of hot water at inlet of the evaporator kg.s-1. mw mass...

STUDY OF HEAT AND MASS TRANSFER IN A FALLING FILM

EVAPORATION PROCESS

MUHAMMAD ELIAS

NATIONAL UNIVERSITY OF SINGAPORE

2004.

STUDY OF HEAT AND MASS TRANSFER IN A FALLING FILM

EVAPORATION PROCESS

By

MUHAMMAD ELIAS

B.Sc. (Eng.) (BUET, Dhaka)

A THESIS SUBMITTED FOR THE DEGREE OF MASTER IN ENGINEERING

DEPARTMENT OF MECHANICAL ENGINEERING

NATIONAL UNIVERSITY OF SINGAPORE

2004.

ACKNOWLEDGEMENTS

The author would like to express his sincere appreciation, gratitude and heartiest

thanks to his supervisors Associate Professor M.N.A. Hawlader and Professor N.E.

Wijeysundera for their encouragement and invaluable guidance during the pursuit of

this research work. Their invaluable advice and constructive criticism have been

always enlightening and inspiring.

The author expresses his special thanks to Dr. Md. Raisul Islam and Mr. See Kai Zin

for their help in different discussion for the completion of the project. The author

wishes to express his sincere thanks to the technical staff of the Thermal Process Lab

1, specially Mr. Yeo Khee Ho and Mr. Chew Yew Lin for their help in fabricating the

experimental set-up.

The author is greatly indebted to The National University of Singapore for providing

financial support in the form of Research Scholarship, which enabled him to carry out

this study.

Finally, the author also extends his deepest gratitude and appreciation to his family

members and friends for their invaluable inspiration, support, and encouragement

rendered towards his developments in education.

Above all, author expresses his profound gratitude to the Almighty for enabling him to

achieve this end.

i

Table of Contents

Page

TABLE OF CONTENTS

ACKNOWLEDGEMENTS i

TABLE OF CONTENTS ii

SUMMARY vi

NOMENCLATURE ix

LIST OF FIGURES xiv

LIST OF TABLES xix

CHAPTER 1 INTRODUCTION

1.1 Principles and types of Falling film evaporation process 1

1.2 Features and application of falling film evaporator 3

1.3 Objectives of the Present Study 5

1.4 Scope of the thesis 6

CHAPTER 2 LITERATURE REVIEW

2.1 Falling film evaporation 7

2.1.1 Analysis of Falling Film Evaporation Processes 7

2.1.2 Experimental investigation 10

2.1.2.1 Vertical tube configuration 10

2.1.2.2 Horizontal tube configuration 12

2.1.2.3 Study of Influence of different field variables 14

2.1.3 Numerical study 17

2.2 Falling Film absorption 19

ii

Table of Contents

CHAPTER 3 THE EXPERIMENTS

3.1 Description of the Experimental Set-up 25

3.1.1 Heat Exchanger, distributor and

Evaporation Chamber 26

3.1.2 Solution Bath 31

3.1.3 Hot Water Tank 32

3.1.4 Flow Circuits 32

3.1.5 Air Circulating Fan 33

3.1.6 Air Chamber 34

3.1.7 Insulation and Support Structure 35

3.1.8 Measuring Equipment 36

3.1.9 Data Acquisition System 38

3.2 Experimental Procedure and Experimental data 39

3.2.1 Actual Experimental Investigation of

Evaporation Performance 39

3.2.2 Experimental heat and mass transfer data 40

CHAPTER 4 MATHEMATICAL MODELS

4.1 Physical Arrangement of the evaporator heat exchanger 41

4.2 Detailed Model 44

4.2.1 Assumptions 44

4.2.2 Governing Equations 48

4.2.3 Solution Procedure 53

4.3 Simplified Model for constant mass flow rate of distributed

water 56

iii

Table of Contents

4.3.1 Assumptions 56

4.3.2 Governing Equations 57

4.3.3 Solution Procedure 61

CHAPTER 5 EXPERIMENTAL RESULTS AND DISCUSSION

5.1 Experimental Results and Discussion 65

5.1.1 Calculation procedure 65

5.1.2 Results 69

5.1.3 Effects of different variables on the heat and

mass transfer coefficients 70

5.2 Comparison of the results 83

5.3 Comparison of experimental data with the simulated data 86

5.4 Development of correlations for two regimes 88

5.5 Comparison of the simulated data with different models

from literature 92

CHAPTER 6 NUMERICAL ANALYSIS AND DISCUSSION

6.1 Variation of the field variables with area by detailed model

and simplified model 95

6.2 Numerical comparison of detailed model and Simplified

Model 104

CHAPTER 7 ANALYSIS OF ABSORBERS USING LINEARIZED MODEL

107

CHAPTER 8 CONCLUSIONS 123

iv

Table of Contents

RECOMMENDATIONS 126

REFFERENCES 127

APPENDIX A Calibration of instrumentations 138

APPENDIX B Tabulated data and results 151

APPENDIX C Comparison with basic equation 162

APPENDIX D Property equations 167

APPENDIX E Analysis of Uncertainty 171

APPENDIX F Different Diagrams 180

v

Summary

SUMMARY

Falling film evaporation processes have been used in different industrial plants for a

long time due to some attractive features, such as short contact time, higher heat

transfer coefficient, minimal pressure drop, and small process fluid holdup in

comparison to the flooded tube evaporator. In this study, a horizontal tubular falling

film evaporator has been designed and its performance has been evaluated under

different operating conditions.

The experimental system mainly comprises four major sub-systems assisted by some

auxiliary devices. The main parts are evaporation chamber, solution distribution

system, heating medium, and the air circulating system. A data acquisition system was

used to record and monitor different parameters required for the evaluation of the

process performance. In addition to that, several accessories for safety and for

supporting the system have been implemented. A series of experiments have been

performed to evaluate the performance of the evaporator under different operating

conditions.

A detailed mathematical model and also a simplified one have been developed to

describe the evaporation process. Based on these models, simulation programs have

been developed to predict the thermal performance of the process using Compaq

Visual FORTRAN. The results obtained by two models have been compared and the

reasons for the deviation have been described. In addition, two correlations for the heat

transfer coefficients from tube wall to the bulk solution and from the bulk solution to

the interface have been developed and good agreement was found.

vi

Summary

The overall heat transfer coefficient from heating fluid to the evaporating film of water

was found to vary from 0.7kW/m2K to 1.1kW/m2K for different experimental

conditions for both models. The heat transfer coefficient from the bulk of the film of

water to its interface varies from 2 to 5 kW/m2K based on the flow rates of the solution

for both models. The range of heat and the mass transfer coefficients from film

interface to the air stream were found to vary from 15 to 30 W/m2K and 0.015 to 0.3

kg/m2s, respectively. It was found that, with increase of the bulk film temperature, the

overall heat transfer coefficient from the hot water to the falling film decreases;

whereas, it increases with the increase of the hot water temperature. The mass transfer

coefficients did not vary significantly.

Influence of all important field variables, namely, the temperatures of hot water,

distributed water, air and air-water mixture, flow rate of distributed water, moisture

contents of air and air-water mixture, enthalpies of air and interface etc has been

evaluated from the models and a good agreement was found with the experimental

values. It was found that the temperature of the hot water and the enthalpies of

interface decrease with the flow. In contrast, the temperature of distributed water, air

and air-water mixture, the moisture contents of air and air-vapor mixtures, and

enthalpies of air increase with the flow. The temperature of the air-vapor mixture was

dominated by the temperature of the distributed water rather than that of air.

The whole experimental falling film evaporation was carried out at atmospheric

pressure. The heat and mass transfer processes in the evaporating falling film are

analogous to those in absorption cooling processes in an absorber. Similar heat and

mass transfer equation can be used to describe these two systems. Therefore, data

vii

Summary

obtained of evaporating film may be used in the design of absorbers. In view of this

observation, the models developed for the evaporating system was used to analyze

some published data from absorption experiments. The linearized model used the same

principles for the absorption as the detailed model and simplified model used for

evaporation. Using both the linearized model and the experimental data from the

literature, correlations have been developed for the falling film absorption heat and

mass transfer coefficients. The value of the overall heat transfer coefficients from

solution to tube wall was found to vary from 0.78 to 0.99 kW/m2K and the effective

mass transfer coefficient was found to vary from 0.052 to 0.092 kg/m2s.

viii

Nomenclature

SYMBOL DESCRIPTIO

a Constant in equ

a1 Constant in equ

a2 Constant in equ

A Area,

Ao Total area

b Constant in equ

b1 Constant in equ

b2 Constant in equ

C Specific heat o

cx′ Constant in exp

equation (7.1.4

co′ Constant in exp

equation (7.1.4

Cw specific heat of

Cpm specific heat of

dA incremental are

.wmd incremental ma

cmd.

incremental ma

D diameter of the

Di inner diameter

Do outer diameter

NOMENCLATURE

N UNIT (SI)

ilibrium relationship (7.1.7)

ation (7.1.18) K

ation (7.1.18) K

m2

m2

ilibrium relation (7.1.7) m2

ation. (7.1.19) K-1

ation. (7.1.19)

f hot water kJkg-1K-1

ression for enthalpy in

) kJkg-1.K-1

ression for enthalpy in

) kJkg-1

distributed water kJkg-1

moisture kJkg-1

a m2

ss flow rate of distributed water kgs-1

ss flow rate of hot water kgs-1

tube m

of the tube m

of the tube m

ix

Nomenclature

Difw mass diffusivity of water m2s-1

Ds Diffusivity of lithium bromide solution m2 s-1

f Factor in equation. (7.1.12) m2s-1

g1 Constant defined in (7.1.12)

g2 Constant defined in (7.1.14) Km-2

g3 Constant defined in (7.1.15) m-2

ha heat transfer coefficient from interface to air kWm-2K-1

h* dimensionless heat transfer coefficient, µvhl

hwo heat transfer coefficient from bulk

solution to interface kWm-2K-1

Ha enthalpy of dry air at the inlet of

the evaporator kJ/kg of dry air

H enthalpy kJ.kg-1

Hv enthalpy of vapor kJ.kg-1

is enthalpy kJ.kg-1

ivs enthalpy of absorption kJ.kg-1

Ka mass transfer coefficient of evaporation process kg.m-2.s-1

Kef Effective mass transfer coefficients in absorption

Process kg/m2s

Kw thermal conductivity of tube wall kW.m-2.K-1

kS thermal conductivity of solution kW.m2.K-1

vl viscous length scale, 3.12

⎟⎟⎠

⎞⎜⎜⎝

⎛

gυ

.ma mass flow rate of dry air at inlet of

x

Nomenclature

the evaporator kg.s-1

.cm mass flow rate of hot water at inlet of

the evaporator kg.s-1

.wm mass flow rate of distributed water at inlet

of the evaporator kg.s-1

absM.

total rate of vapor absorption kg.s-1

Re Reynolds number of the film, µΓ4

Rec Reynolds number of the hot water, µπ iDcm.

4

Sc Schmidt number, wDif

ν

T temperature °C

Tw temperature of the distributed water °C

Tif temperature of the vapor-water interface °C

Tc temperature of the hot water °C

U overall heat transfer coefficient from hot water

to distributed water kW.m-2.K-1

X mass fraction of water in lithium bromide solution

Ka kapitza number 3

4

ρσ

µ g

Nui Nusselt number for tube wall to bulk solution, skih δ

Nuo Nusselt number for bulk solution to interface, sk

oh δ

xi

Nomenclature

Pr Prandtl number, αν

Sh Sherwood number, wDif

akρ

δ

Greek Symbols

α thermal diffusivity m2s-1

α1, α2 roots of equation defined in (7.1.18) m-2

β parameter defined in (7.1.16) K-1

θ temperature difference defined in (7.1.8) K

Ψ mass fraction difference defined in (7.1.9)

δ film thickness, m

δA elemental area, m2

δis change of solution enthalpy kJ kg-1

δ change of solution mass flow rate kg s.sm -1

δ vapor absorption/evaporation rate kg.s.

mv -1

δw thickness of the stainless steel tube wall m

Γ mass flow rate of distributed water

per unit length kg.m-1.s-1

µ absolute viscosity of the solution kg.m-1.s-1

ν kinematic viscosity of the solution m2.s-1

κ thermal conductivity of the solution

ρ density kg.m-3

xii

Nomenclature

Subscripts

0 value at A=0

a air

c hot water

co coolant

ef effective

ex Exit

f saturation water

I Tube wall to the bulk solution

io solution to tube wall

if water-vapor interface

in Inlet

l lithium bromide

o interface to bulk solution

s bulk solution

v vapor

w distributed water

wo bulk to interface

xiii

List of Figures

F

F

F

F

F

F

F

F

F

F

F

F

F

F

F

F

F

F

F

F

F

Figure Name of Figure Page

igure 1.1 A typical falling film tubular evaporator 3

igure 3.1 Schematic Diagram of Experimental Set-up 26

igure 3.2 Details of the Experimental Set-up 27

igure 3.3 photograph of heat exchanger 28

igure 3.4 Insulated evaporation chamber 29

igure 3.5 Photograph of the solution bath 31

igure 3.6 Photograph of hot water tank 32

igure 3.7 Photograph of Centrifugal pump 33

igure 3.7 Photograph of air circulation fan 34

igure 3.8 Photograph of variable area flow meter 36

igure 3.9 Photograph of humidity sensor 37

igure 3.10 Photograph of Fluke Hydra data logger 38

igure 4.1 Flow circuits of all fluids included in the system (3D) 42

igure 4.2 Flow circuits of all fluids included in the system (2D) 42

igure 4.3 Temperature profile of distributed water within the film 43

igure 4.4 Distribution of Falling film over the horizontal tube 45

igure 4.5 Geometrical configuration of the flowing film 46

igure 4.5 Air water interactions within the film 46

igure 4.7 Temperature profile across an evaporating turbulent falling film 47

igure 4.8 Geometrical configuration of the control volume 47

igure 4.9 Flow Chart for Calculation of solution properties and coolant temperature using detailed model 55

xiv

List of Figures

Figure 4.10 Flow Chart for Calculation of solution properties and coolant temperature using Simplified model 63

Figure 5.1 Variation of overall heat transfer coefficient from hot water to distributed water, U with inlet temperature of solution at different mass flow rate of solution 71

Figure 5.2 Variation of overall heat transfer coefficient with distributed water inlet temperature at different mass flow rate of hot water 72

Figure 5.3 Variation of overall heat transfer coefficient with the

distributed water flow rate at different inlet temperature of distributed water 73

Figure 5.4 Variation of overall heat transfer coefficient with the inlet temperature of hot water at different mass flow rate of distributed water 74

Figure 5.5 Variation of overall heat transfer coefficient with the Mass flow rate of distributed water at different mass flow rate of hot water 75

Figure 5.6 Variation of overall heat transfer coefficient with the hot water flow rate at different inlet temperature of distributed water 76

Figure 5.7 Variation of overall heat transfer coefficient from hot water to distributed water with the mass flow rate of air 77

Figure 5.8 Variation of mass transfer coefficient Ka, with hot water inlet temperature of hot water at different mass flow rates of distributed water 79

Figure 5.9 Variation of mass transfer coefficient Ka with the inlet temperature of distributed water at different hot water flow rate 80

Figure 5.10 Variation of mass transfer coefficient, Ka with the distributed water flow rate at different inlet temperature of distributed water 80

Figure 5.11 Variation of mass transfer coefficient Ka, with the hot water flow rate at different inlet temperature of distributed water 81

Figure 5.12 Variation of mass transfer coefficient Ka with the mass flow rate of air 82

Figure 5.13 Variation of Nusselt Number from the tube wall to the bulk solution with the solution Reynolds number 83

xv

List of Figures

Figure 5.14 Variation of Nusselt Number from the bulk solution to the interface with the solution Reynolds number 84

Figure 5.15 Average Variation profile of Nusselt Number from the tube wall to the bulk solution with the solution Reynolds number 85 Figure 5.16 Average Variation profile of Nusselt Number from the bulk solution

to the tube wall with the solution Reynolds number 85

Figure 5.17 Comparison of experimental and simulated hot water temperature for two different hot water inlet temperatures 86

Figure 5.18 Graphical comparison of the Nusselt number from tube wall to the bulk solution with the studies of different researchers 93

Figure 5.19 Graphical comparison of the bulk solution to the interface Nusselt number with the studies of different researchers 94

Figure 6.1 Variation of different fluid temperature with area at U=0.71 kW/m2K, ha=0.019 kW/m2K, hwo=3.14 kW/m2K and Ka=0.0189 kg/m2sec 96

Figure 6.2 Variation of hot water temperature with area by simplified model at

different inlet temperature of hot water 97

Figure 6.3 Variation of distributed water temperature with area by simplified at different model inlet temperature of distributed water 98

Figure 6.4 Variation of air temperature with area by detailed model for different inlet temperature of air 99

Figure 6.5 Variation of moisture content of air and air-vapor mixture with area 100

Figure 6.6 Variation of moisture content of air with area by detailed model for different inlet condition of moisture content of air 101

Figure 6.7 Variation of mass flow rate of distributed water with area at different experimental conditions for inlet mass flow rate 0.0295 kg/sec 102

Figure 6.8 Variation of enthalpy of air with area 103

Figure 6.9 Variation of enthalpy of interface with area 103

Figure 6.10 Variation of the temperatures with area at U=0.70 kW/m2K, ha=0.016

kW/m2K, Ka=0.0145 kg/m2K 105

Figure 6.11 Variation of the enthalpy of air with area, by detailed and simplified model 105

xvi

List of Figures

Figure 7.1 Physical models for counter flow absorber 108

Figure 7.2 Variation of Temperature difference,θ with absorber area (a)Tsin=53.6 °C and Tcoin=35.17 °C (b) Tsin=55.0 °C and

(c) Tcoin=35.07 °C (d) Tsin=57.9 °C and Tcoin=34.94 °C. 115

Figure 7.3 Variation of solution, coolant and interface temperature with area, at Tco,in= 35 °C and Ts,in= 53.6 °C. 116

Figure 7.4 Variation of mass fraction difference,ψ with area. (a) Tsin=53.6 °C and Tcoin=35.17 °C (b) Tsin=55.0 °C and Tcoin=35.07 °C (c) Tsin=55.5 °C and Tcoin=35.12 °C. 117

Figure 7.5 Variation of concentration with area, at Tco,in= 35 °C and Ts,in= 53.6 °C. (A) for experimental solution concentration, (B) solution concentration at solution to vapor interface. 117

Figure 7.6 Variation of overall heat transfer coefficients with solution mass flow rate at Ts,in=53.6 ° C and Tco,in= 35 ° C. (U) overall , (Hi) solution to tube wall. (Ho) interface to bulk solution. 118

Figure 7.7 Variation of mass transfer coefficient with solution mass flow rate at Ts,in=53.6 ° C and Tco,in= 35 °C. (Kef) overall and (Ko) interface to bulk solution. 119

Figure 7.8 Variation of film Nusselt Number ( Nu ) with the film Reynolds Number, Re. (a) solution to tube wall (b) interface to bulk solution. 120

Figure 7.9 Variation of film Sherwood Number, Sh with the film Reynolds Number, Re. (a) effective (b) interface to bulk solution 120

Figure A1 Calibration graph for channel 1 140









xvii

List of Figures




Figure A15 Calibration graph for humidity sensors 146

Figure A16. Calibration graph for Hot Water Flow Meter 147

Figure A17 Calibration graph for Distributed Water Flow Meter 148

Figure A18 Calibration graph for lowest speed of fan 149

Figure A19 Calibration graph for 2nd lowest speed of fan 149

Figure A20 Calibration graph for 3rd lowest speed of fan 150

Figure F.1 Isometric View of evaporator heat exchanger 181

Figure F.2 Front view of the experimental setup 182

Figure F.3 Left side view of the experimental setup 183

Figure F.4. Top view of the base plate 184

Figure F.5 Front view of the base plate 184

Figure F.6 Isometric view of the base plate 185

xviii

List of Tables

T

T

T

T

T

T

T

T

T

T

T

T

T

T

T

Number Title Page

able 5.1 Experimental studies on falling film evaporation of water 87

able 5.2 Comparison of the moisture contents of air. 87

able 5.3 Comparison of the enthalpies of air 87

able 5.4 Experimental studies on falling film evaporation of water 93

able 7.1 Range of experimental conditions and variables 114

able 7.2 Effect of index, n 121

able 7.3 Effect of ivs 122

able A.1. Equations of calibration curves of the thermocouples 139

able A.2. Equations of calibration curves of flow meters 147

able A.3. Values of the mass flow rates of air at different fan speed 150

able B.1. Salient data of copper tube evaporator 152

able B.2. Salient data of stainless steel tube absorber 152

able-B.3. Operating conditions of the experiments, falling film Evaporation 153

able-B.4 The results for the heat and mass transfer coefficients 158

able E.1. Uncertainty in the derived parameters for detailed model 176

xix

Chapter-1 Introduction

IN N

Falling film evaporation process

demand of falling film evaporati

industry. As, the surface area

effectiveness of falling film evap

design as well as the developme

process more cost effective.

1.1 Principles and types of F

Evaporation is an operation used

emulsion by boiling off some of

concentration process. The proces

with a more concentrated, but sti

product from the process. In fallin

parallel flow or counter flow. The

to boiling temperature. An even

device in the head of the evapor

partially evaporated. This grav

augmented by the co-current vap

falling film evaporation proces

objectives are always same that

conditioning and refrigeration ap

of heat transfer. On the other ha

CHAPTER 1

TRODUCTIO

es are used widely in industrial applications. The

on is increasing day by day in the food engineering

of the evaporator plays an important role in the

oration process, the improvement in the evaporator

nt of the improved model is essential to make the

alling film evaporation process

to remove a liquid from a solution, suspension, or

the liquid. It is thus a thermal separation, or thermal

s is one that starts with a liquid product and ends up

ll liquid and still pump-able concentrate as the main

g film evaporators, liquid and vapor flow onwards in

liquid to be concentrated or evaporated is preheated

thin film enters the heating tubes via a distribution

ator, flows downward at boiling temperature, and is

ity-induced downward movement is increasingly

or flow. Although depending upon the requirements

ses follow different working principles, the final

is to evaporate some of the working fluid. In air

plication the evaporation process is used as a means

nd, in the food industry where many substances are

Page 1


heat sensitive, the process is a means of mass transfer. Here, a thin film of the product

to be concentrated trickles down inside of heat exchanging tubes and steam condenses

on the outside of the tubes supplying the required energy to the inside of the tubes.

Meanwhile, depending upon the application, the falling film evaporators can be

categorized into two main groups; vertical tube falling film and horizontal spray-film

evaporator having either parallel flow or counter flow arrangements. In a vertical

arrangement, the working fluid where the evaporation will occur is first preheated near

to its saturation temperature. Then, this fluid is fed through the vertical tube from up to

down and is allowed to fall due to gravity. In the mean time, the fluid that supplies

heat energy for evaporation, commonly steam, is fed over the outside surface of the

tube. On the other hand, a in horizontal tube arrangement, the working fluid flows

from one end to the other end of the horizontal tube(s) and the heat supplying fluid

flows over the tube(s). Based on the application, the process may also occur in reverse

arrangement i.e. the working fluid flow over the tube(s) and the heat supplying fluid

flows through the tube.

Page 2


Figure 1.1 A Typical falling film tubular evaporator.

1.2 Features and application of falling film evaporator

Falling film evaporators are found in many industrial applications due to the advantage

of short contact time typically just a few seconds per pass between the process fluid

and the heated surface. It shows high heat transfer coefficients, minimal pressure drop,

A: Product

B: Vapor

C: Concentrate

D: Heating Steam

E: Condensate

1: Head

2: Calandria

3: Calandria, Lower part

4: Mixing Channel

5: Vapor Separator

D

E

B

C

A

1

C

4

5

3

2

Page 3


minimal static heat and small process fluid holdup when compared with flooded-

bundle evaporators. Since there is no liquid pool, the effect of hydrostatic heat on the

heat transfer is eliminated. These characteristics make the falling film evaporator

particularly suitable for heat-sensitive products, and it is today the most frequently

used type of evaporator. In addition, spray evaporators have the advantage of using a

smaller refrigerant charge than flooded evaporator units of equivalent capacity. Falling

film evaporators are highly responsive to alterations of parameters such as energy

supply, vacuum, feed rate, concentrations, etc. When equipped with a well designed

automatic control system they can produce a very consistent concentrated product.

The characteristics of free falling films are of importance in many aspects of thermal

engineering and chemical processes, especially, in heat exchange devices in the

chemical, refrigeration, petroleum refining and food industries. In refrigeration and

heat pump applications, falling film evaporators are very attractive due to the high heat

transfer coefficient with negligible pressure drop. Heat transfer through thin liquid

films has been used in distillation and, desalination processes. Falling film evaporation

on horizontal tubes has also been considered one of the heat transfer processes

appropriate for ocean thermal energy conversion systems. In closed-cycle ocean

thermal energy conversion (OTEC) systems, a horizontal–tube spray-film evaporator

has been proposed to operate at the available small temperature difference. The fact

that falling film evaporators can be operated with small temperature differences makes

it possible to use them in multiple effect configurations or with mechanical vapor

compression systems in modern plants with very low energy consumption. Because of

the low liquid holding volume in this type of unit, the falling film evaporator can be

started up quickly and changed to cleaning mode or another product easily.

Page 4


However, falling film evaporators must be designed very carefully for each operating

condition; sufficient wetting of the heating surface by liquid is extremely important for

trouble-free operation of the plant. If the heating surfaces are not wetted sufficiently,

dry patches and incrustations will occur; at worst, the heating tubes will be completely

clogged. In critical cases, the wetting rate can be increased by extending or dividing

the evaporator effects, keeping the advantages of single pass operation.

1.3 Objective of the Present Study

In this present study, the characteristic behavior of a 24 row horizontal tube evaporator

has been studied carefully. The performance of this evaporator was tested by using the

water as a working fluid that flows over the horizontal tube along with the use of hot

water as the heating medium, flowing through the tubes. In the calculation of heat and

mass transfer coefficients, the approach of using two heat transfer coefficients as

suggested by Grossman (1983) was used. The main objectives of the research are

listed as follows:

• Design and fabrication of an experimental falling film evaporator.

• Formation of the mathematical models for the system

• Development of simulation models.

• Conduct experiments to evaluate the performance of the evaporator.

• Carry a comparison between the experimental and simulated results.

• Development of correlations for the heat and mass transfer coefficients of a

falling film evaporation process by using the concept of the model and the

experimental data.

Page 5


1.4 Scope of the thesis

An introduction to the falling film evaporation process is included in Chapter 1. A

survey of the published literature that is directly related to the evaporation process, as

well as falling film absorption is presented in Chapter 2. In Chapter 3 of this thesis, the

detailed experimental investigation covering the design and construction of the

evaporator rig, the instrumentation and the details of the experiments are presented. A

detailed model considering the variation of mass flow rate of different fluids and a

simplified model for constant mass flow rate of solution, hot water and air have been

developed and presented in Chapter 4. The solution procedure for both of the models

has also been discussed in that chapter. Chapter 5 comprises the experimental results

and discussion, the method of calculation, the effect of different field variables on heat

and mass transfer coefficients, comparison of the two models developed with the

models available in the literature and, finally, the development of correlations for

different regions of the flow. A detailed numerical investigation including the

variations of the all field variables within the different locations of the evaporator have

been discussed in Chapter 6. The analysis of absorber using the linearized model taken

from the literature has been presented in Chapter 7. Finally, Chapter 8 presents

conclusions of the present study and the recommendations for future investigation.

Page 6

Chapter-2 Literature Review

LITE W

The overall efficiency and the e

evaporator depend on the physi

conditions of the experiments. I

process along with the effect of

studies have been undertaken. T

falling film evaporation processe

namely, the theoretical analys

investigation with and without th

horizontal configurations and, fi

compare the model for falling film

using the same principles for falli

literature on falling film absorptio

2.1 Falling Film Evaporatio

The review of important publicat

carefully discussed in the followi

study: theoretical, experimental an

the years of publication.

2.1.1 Analysis of Falling Film Ev

The classical work on the mechan

was presented by Nusselt (1916).

CHAPTER 2

RATURE REVIE

ffectiveness of the evaporation process within the

cal characteristics of the evaporator as well as the

n order to understand the falling film evaporation

different operating variables, reviews of previous

he published literature that is directly related to the

s is reviewed in this Chapter in three major areas

is of the evaporation process, the experimental

e effect of different variables for both vertical and

nally, the numerical studies. In addition to that, to

evaporation developed in Chapter 4 with the model

ng film absorption, a through review of the important

n was carried out.

n

ions on the falling film evaporation process has been

ng section. The analysis covers three major areas of

d numerical, respectively and presented according to

aporation Processes

ics of thin films and heat transfer through these films

His main assumptions were that flow throughout the

Page 7


film is laminar and only gravity forces are acting. On this basis, the velocity

distribution and film thickness could be calculated from Newton’s law of viscosity. In

laminar flow, the heat transfer is by molecular conduction. Thus, the assumption of

laminar flow permitted solving for the heat transfer coefficient, by use of Fourier’s

law, as the ratio of thermal conductivity to the liquid film thickness.

From experimental observation, it was found that Nusselt’s relationships were

conservative for higher flow rates. Colburn (1934) suggested a semi-theoretical

relationship for turbulent flow in the film by assuming the value of the transition

Reynolds number 2000, as it was pipe flow and there was no interfacial shear. Grigull

(1942) attempted to find a transition Reynolds number other than 2000. Rohsenow et

al. (1956) and Seban et al. (1954) took different approaches to apply analogies

between heat and mass transfer based on velocity distribution equations for pipes

flowing full, to the case of film flow. They faced the same problem to assume some

critical Reynolds number or some fixed position in the film at which the transition

between laminar and turbulent flow took place. By estimating a specific resistance of

the liquid film as a function of position from the wall, Chari and Kulkarni (1951)

attempted to modify the original Nusselts relationships to correct for a small amount of

turbulence.

Duckler (1960) developed some new equations for velocity and temperature

distribution in thin vertical films of the same geometry found in the falling-film

evaporators, vertical condenser and film cooling equipment. These equations utilize

the expression proposed by Deissler(1950) for the eddy viscosity and eddy thermal

conductivity near a solid boundary, thus introducing turbulent fluctuations close to the

Page 8


wall. The determination of the film thickness, the local heat transfer coefficient and the

average coefficient over an entire condenser tube had been performed from the

graphical relationships as well as from the external flow rates, the properties of the

fluids and the tube dimensions.

Chun and Seban (1971), had measured and presented the falling film heat transfer

coefficients for water on a vertical plain tube in both laminar and turbulent flow

regimes. For the laminar flow regime, the heat transfer coefficients were estimated

based on the Nusselt film and it’s modification for the effect of capillary waves on the

surface of the film. For the turbulent regime, initiated at some postulated Reynolds

number, theoretical predications like those of Duckler (1960) have been used to

estimate the local heat-transfer coefficient. An empirical equation for predicting the

transition threshold from laminar to turbulent flow and a heat transfer correlation for

evaporation without nucleate boiling occurring in the film were presented by them.

Significant influence of Prandtl number in evaporation heat transfer was found in the

correlation. Thus, the transition Reynolds number for the falling film was expressed as

a function of Prandtl number.

In 1978, Lorenz and Yung developed a combined model for simultaneous film

evaporation and nucleate boiling in liquid films flowing over horizontal plain tubes.

Arshavski et al. (1995) presented an analytical solution for a transient conjugate heat

transfer problem in three domains: a solid wall, an evaporating falling liquid film, and

a flowing gas. The solution is obtained by using Riemann’s integral method for the

evolution of the temperature solution in the vicinity of the dry out front.

Page 9


A mathematical model of evaporation process, with and without interfacial shear stress

due to the vapor flow at the liquid film surface of a laminar falling liquid film on a

vertical plate of constant temperature is presented by Assad et al. (2001). Their results

showed that the interfacial shear stress has a negative effect on the evaporator

performance only for the countercurrent flow.

2.1.2 Experimental Investigation

The experimental investigation on falling film evaporation is discussed in three sub

sections based on the configuration of the evaporators and the factors that influence the

process. The two main configurations; the vertical tube and the horizontal tube and the

influence of mass flow rates of different fluids, liquid feeding system, heat flux and the

dimension of the evaporator were taken into account for discussion.

2.1.2.1 Vertical Tube configuration

Shmerler et al. (1988) performed experiments of free-falling films on a vertical tube

made of stainless steel (25.5 mm outer diameter and 24.6 mm inner diameter). By

using water as the test fluid, they showed that the local heat transfer coefficients,

averaged over the section of the heated length, where the minimum values were seen

to occur, correlated well as a function of Reynolds number and Prandtl number.

Nakayama et al. (1982) measured the falling film heat transfer coefficients for vertical

plates with (1) a Hitachi Thermoexcel-E type of enhanced pool boiling surface (2) a

vertical grooved surface (3) a horizontal grooved surface, with decreasing thermal

performance in that order, respectively, all for R-11. The Thermoexcel-E type of

surface promoted nucleate boiling on the plate, giving better heat transfer coefficients

Page 10


with nucleate boiling in the falling film mode than for pool boiling conditions. The

vertically grooved surface, however, functioned via film evaporation only.

Benzeguir et al. (1991) measured falling film coefficients on the outside of a vertical

tubes (plain, doubly-crosscut grooves, and helically wire-wrapped) for a lithium

bromide-water solution without additives. They found that the grooved tube improved

performance 1.5 times compared to the plain tube while the wire-wrap-ping was less

effective than the grooves.

O-uchi et al.(1991) studied falling film evaporation on vertical tubes (a plain tube and

with 0.3 mm high helical grooves of .5°, 45° and 90° from the horizontal) with an

aqueous solution of nearly pure ethanol. Inclination of the grooves from the vertical

was found to be effective for delaying the onset of dry patches and the breakup of the

liquid film into rivulets.

Chyu and Bergles (1985a) developed a method for predicting falling film coefficients

by zone around a plain tube from top to bottom. Their falling film coefficients for

water were reported for four tubes: Wieland Gewa-T, Hitachi Thermoexcel-E, UOP

High Flux and plain tubes. The optimum type of geometry was found to depend on

whether there was nucleate boiling in the film (favoring the High Flux and

Thermocexcel-E geometrics) or only film evaporation (which favored the Gewa-T’s

fins for thinning the liquid film)

Alhusseini et al. (1998) presented the influence of Prandtl number greater than five in

the heat and mass transfer processes of falling film evaporation. By doing experiments

Page 11


for lower Prandtl number fluid water (Pr=1.73, 3.22 and 4.27), as well as higher

Prandtl number fluid, propylene glycol (Pr=40.2 and 46.6), they established a

correlation for wavy laminar regimes by using both the Reynold and Kapitza numbers.

A semi-empirical correlation for the turbulent region and an asymptotic combination

of the wavy laminar and turbulent coefficients for all Re numbers were proposed by

them.

Asblad et al.(1991) presented an experimental study for the evaporation of a

refrigerant R12 from a vertical tube. The influence of the Prandtl number, length of the

tube, pressure drops and heat flux were examined. Due to the small variation of

Prandtl number in the experimental temperature range for R12 (Pr≈3), the Prandtl

dependency cannot be explained but the dependency of the evaporator length was

established. On finding the dependency on the length, along with the solution

Reynolds number, they proposed a correlation to represent the surface evaporation of

R12 in the same pressure and Reynolds number range which agree 10% with seban

correlation.

2.1.2.2 Horizontal Tube configuration

Fletcher et al. (1974) studied the falling film boiling heat transfer coefficients for the

horizontal tube system. The tests were conducted with a thin-slot water distribution

system for 2.54 and 5.08 cm diameter smooth tubes. The heat transfer coefficients

increased with increasing feed water flow rate and inlet temperature of the solution,

and the tube-wall heat flux. They also found that the heat transfer coefficients were

higher for sea water film than that of the fresh water.

Page 12


In 1976, Danilova et al. conducted the heat transfer tests by using R-12, R-22 and R-

113 evaporating on plain, horizontal tube bundles, including simulated bundles up to

40 rows deep. They presented empirical correlations for vaporization and nucleate

boiling as a function of liquid film Reynolds number, liquid Prandtl number and the

ratio of tube pitch to tube diameter.

Chyu et al. (1982) measured falling film heat transfer coefficients for water on (1) a

horizontal plain tube, (2) a high flux porous coated tube, and (3) a Gewa- T tube. The

high flux tube promoted nucleate boiling but the Gewa-T geometry provided better

performance at low wall superheats, in the absence of nucleate boiling, by promoting

enhanced thin film evaporation (which is similar in many aspects to falling film

condensation on low finned tubes).

In 1980, by investigating vapor-liquid interface and liquid entrainment for vapor cross

flow conditions on plain tube bundles, Yung et al. presented a criterion for transition

from drip to column flow mode form tube to tube. Chen and

Kocamustafaogullari(1989) studied falling film evaporation of water on horizontal

plain tube bundles both experimentally and numerically.

A correlation for horizontal tube falling film evaporation heat transfer coefficient is

presented by Owens (1978) for both laminar and turbulent flow regimes. The influence

of the Reynolds number and the ratio of separation distance between upper and lower

surfaces of two consecutive tubes to the diameter of the tube were taken into account

in the correlation. By using ammonia and water separately, the values of the heat

Page 13


transfer coefficients were calculated that agree nearly with Nusselt’s theoretical

analysis for condensation in the laminar regime.

A controlled systematic study was conducted by Parken et al. (1990) with 2.54 cm and

5.08 cm diameter smooth horizontal plain tube by using a thin slot water distribution

system. They obtained both local and average falling film heat transfer coefficients

around the horizontal tube as a function of angle for both nucleate boiling and film

evaporation regimes. Correlations of average heat transfer coefficients for boiling and

non- boiling conditions were developed and compared.

2.1.2.3 Study of Influence of different field variables

The influence of solution flow rate and inter-tube spacing on falling film heat transfer

on horizontal plain tube bundles for sub cooled liquid without evaporation was

investigated by Mitrovic (1986) for iso-propanol and water. Chyu and Bergles (1987)

presented a discussion about the effects of film flow rate, liquid feed height, and wall

superheat on falling films on horizontal plain tubes.

Rifert et al.( 1992) measured falling film coefficients using water for a plain tube and

longitudinally grooved horizontal tubes of six vertical rows, finding about 1.4-1.9 heat

transfer augmentation factors for the grooves; an empirical correlation was presented

that describes their results.

Fujita and Tsutsui (1994) measured falling film coefficients and drip patterns for a

vertical row of plain, horizontal tubes for R-11 and compared their data to existing

correlations and proposed a new one.

Page 14


Zeng et al. (1994) measured the spray distribution rates and flow rate uniformity on

horizontal tube bundles to investigate the effects of tube surface geometries and tube

bundle pattern. They observed that the plain tube bundles demonstrated more uniform

liquid distribution in the bottom row than the low finned tube bundles, while the

grooved tube bundle performed similar to the plain tube bundle.

Zeng et al. (1995) tested a 19.1 mm diameter plain, stainless steel horizontal tube by

using ammonia at saturation temperature of -23.3 °C to 10 °C. By keeping the mass

flow rate nearly constant they found that the heat transfer coefficient increases linearly

with the increase of heat flux.

Hu and Jacobi (1996a) experimentally investigated the falling film flow pattern by

using three plain horizontal tubes in a vertical row. Among these three tubes the

second one was the test tube, where the solution was fed from the top tube. To obtain

broad range thermo-physical properties, they tested water, ethylene glycol,

water/glycol, oil and alcohol, where the air was allowed to flow over the film up to a

maximum velocity of 15 m/s. The flow pattern was categorized into droplet, droplet-

jet, in-line jet, staggered jet, jet sheet and sheet modes. Transition modes between

sheet mode to jet mode and between jet modes to droplet mode were also tested. The

flow map indicates that when the inertia effects dominate, the flow will take the sheet

mode. Gravity or surface tension dominated flows result in a droplet pattern. The

results provide a deeper understanding of the falling film mode transitions and a useful

tool for designing, operating and modeling heat exchangers. Empirical correlations for

the transition boundaries were also determined in the form of Re vs Ga where Ga is the

Page 15


modified Galileo number (fourth power of the ratio of gravitational force to viscous

force).

Zeng et al. (1998) had extended their experiments on falling film evaporation by using

ammonia on a carbon steel low fin tube and a corrugated tube. A large number of

single-tube tests were run in the temperature range of -23.3 °C to 10 °C. Among

different configurations tested by them, the low finned tube increased the performance

as much as 2.8 times with respect to the prior plain tube tests at high heat fluxes. They

showed that the spray evaporation coefficient increases with spray flow rate at a high

temperature and a low heat flux. The spray evaporation coefficient also increases with

nozzle height and decreases with spray angle at high temperature. The performance of

the corrugated tube is about the same as the plain tube for all saturation temperatures.

The Nu data were correlated as a function of Re, Pr, reduced pressure and heat flux.

To improve the performance of compact heat exchangers, the EHD (electro-

hydrodynamic) enhancement technique has been applied to falling film evaporation by

Yamashita and Yabe (1997). The tests were conducted to determine their suitability for

long-term industrial application. Electrodes were used to create the EHD effect that

increase the falling film evaporation performance on the plain tube by six –fold using

perforated plate electrodes.

The falling film coefficients on the outside of two vertical tubes (one is plain and

another is Wolverine enhanced pool boiling Turbo-B tube) for R-11 were measured by

Chen et al. (1994). They observed that the enhanced surface was particularly beneficial

in retarding film dry out, allowing higher heat fluxes to be sustained up to nearly

Page 16


complete dry out of the film. It means that an enhanced boiling tube can potentially

increase the achievable vaporization fraction of the falling film compared to a plain

tube.

Federov et al. (1997) and Manganaro et al. (1970) proposed that the local heat

exchange between the air stream and the liquid film depends on two related factors.

The sensible convection heat transfer is due to the interfacial temperature gradient on

the airside and the evaporative mass transfer rate on the liquid film side results in

latent heat transfer. They also presented that the transport coefficients are affected by

the buoyancy force for a film Reynolds number smaller than 30,000.

2.1.3 Numerical Study

By using eddy diffusivity models, numerical studies were performed by Shmerler et al.

(1988) to determine heat transfer coefficients in the development region and under

fully developed conditions. The behavior of the experimental data of the early stage of

development region were predicted accurately by the model but failed to predict the

heat transfer coefficient in the development region at lower Prandtl number.

Turbulent convection heat and mass-transfer characteristics in an asymmetrically

heated, wet, vertical, parallel-plate channel have been studied by Fedorov et al. (1997).

Based on the numerical results they showed that heat transfer from the liquid film is

dominated by the transport of latent heat associated with the evaporation of the liquid

film and, at Reynolds number lower than 30,000, the buoyancy aids the flow distorts

the velocity distribution which affects the transport coefficients.

Page 17


Feddaoui, et al. (2003) presented an analysis to estimate the variation of heat and mass

transfer in falling film of water inside a vertical tube. By doing some numerical

calculation, they showed that a better heat transfer results for a higher gas flow

Reynolds number, a higher heat flux or lower inlet water flow rate. The convection of

heat by the flowing film becomes the main mechanism for heat removal from the wall.

The sensible and latent heat exchanges increase in the flow direction for but decreases

with the liquid flow rate. It was revealed from their results that the latent heat

exchange is about five times larger than the sensible heat exchange and a reduction of

mass flow rate of the liquid cause greater film evaporation. For the turbulent forced

convection, the heat transfer is large for a higher Reynolds number of airflow. The

larger film evaporation is found for systems at higher wall heat flux or at higher

Reynolds number, (Re). It was also mentioned that, a reduction in the inlet liquid film

cause a greater film evaporation and the evaporation rate increases in the direction of

liquid film flow. The interfacial temperature and water vapor concentration is higher

for a smaller inlet liquid flow rate.

The Lorenz and Yung (1978) correlation was found to predict their data fairly well. A

three zone model was proposed by them for evaporating laminar falling films. With a

developing flow region, a transition region and developed region while for turbulent

film flow they utilized the universal velocity profile without modification, setting the

eddy conductivity equal to the eddy viscosity. They also observed the flow regimes

experimentally for R-11 at 0.2 MPa.

Page 18


2.2 Falling Film Absorption

The heat and mass transfer processes in the evaporating falling film are analogous to

those in absorption and cooling processes in an absorber. Similar heat and mass

transfer equations can be used to describe these two systems. Therefore, data obtained

from an evaporating film may be used in the design of absorbers. In view of this

observation the models developed for the evaporating system was used to analyze

some published data from absorption experiments. A review of a few important papers

on the absorption system is summarized below.

A model for the non-isothermal absorption of water vapor into a laminar film of

lithium bromide–water flowing down a constant temperature vertical flat plate was

presented by Andberg and Vliet (1983). The general guidelines for the design of

falling film absorbers are listed by them.

Grossman (1983) presented a model to analyze the combined heat and mass transfer

processes in the absorption of gas or vapor into a laminar liquid film. By this model,

the variation of heat and mass transfer coefficients from interface to bulk solution and

bulk solution to tube wall were obtained.

A model for falling film over a vertical tube absorber had been developed by Patnaik

et al. (1993). By using the lithium bromide solution they had shown that, at high

coolant flow rates with the increase of solution flow rate, the mass of vapor absorbed

and heat load increased but, at low coolant flow rates, the influence of solution flow

rate was very small.

Page 19


Min and Choi (1999) proposed that, at low flow rate of the falling film, the surface

tension plays an important role in the flow field. Sabir et al.( 1999) presented a method

for measuring the effect of non absorbable gases on falling film and they found that by

enlarging the absorber surface area the effect of the non absorbable gases can be

reduced.

Matsuda et al. (1994) presented the results for experiments conducted on an absorber

and generator in an absorption refrigeration machine made of a vertical falling-film of

stainless steel column. The working fluids were 40, 50, and 60% based on the wt. of

LiBr aqueous solutions and the pressures were 1.3 kPa and 5.3 kPa. They found that

the absorption rate decreased with the reducing pressure and increasing or remaining

constant the concentration of LiBr in the falling liquid, because the falling film

becomes thicker due to the increased viscosity of the solution.

By conducting the experiment in a horizontal tube falling film absorber with aqueous

solutions of LiBr with and without surfactants, Hoffman(1996) showed that the heat

transfer coefficient decreases with the increasing of viscosity, augmenting surface

tension and the decrease of the solution flow rate. The solution flow rate, temperatures

of the cooling water and of the solution, and the concentration of the solution were

varied by them to develop the correlations of the heat transfer coefficient with the

physical properties of the solution. Two types of tubes were used, one with a plain

surface, the other one with a structured surface to examine the influence of two

surfactants (1-octanol and 2-ethyl-1-hexanol) in various concentrations on the

absorption processes.

From 1996 to 1997 Tsai and Perez-Blanco presented that, under typical operating

condition found in commercial chillers, the theoretically possible maximum mass

Page 20


absorption rate is 0.049kgm2/sec and that, at a mechanically feasible mixing frequency

of 1000 Hz, a mass absorption rate of 0.0256 kg m2/s is possible. The latter rate is

about an order of magnitude larger than that found in commercial chillers.

Kim et al. (1995) showed that for a particular experimental condition, with the increase

of the mass fraction from 0.5 to 15%, the Sherwood number decreases by about 20%.

By using the heat and mass transfer analogy near the surface of the falling film, Chen

and Sun (1997) experimentally measured the heat and mass transfer coefficients as

well as the temperature and concentration of the interface.

Yang and Jou (1998) developed a mathematical model and correlation to study the

effect of waves and non absorbable gases on absorption process in a falling film. Their

correlation can be used to design an absorber. Ameel et al. (1996) presented that, as

the concentration of the non-absorbable gases increases at the interface of the film, the

absorption rates decreases continuously.

Deng and Ma (1999) had conducted experiment on a falling film absorber which was

consisted of 24 rows horizontal smooth tubes, using 60 to 64%(wt basis) LiBr-water as

working fluid. An increase in the spray density increased the mass transfer coefficient

much more than the heat transfer coefficient. They found that the heat transfer

coefficients increase with the increase of the solution concentration. An expression

was developed for the heat transfer coefficient, taking into account the effect of the

inlet solution concentration.

Page 21


Yoon et al. (1999) conducted experiments using bare tube, bumping bare tube, floral

tube, twisted floral tube and a tube with bumps on the surfaces to determine the largest

heat exchange area for improving the performance of an absorber. They found that

floral and twisted floral tubes have 40% higher heat and mass transfer performance

than those with the bare tube conventionally used in an absorber. It was concluded that

the larger wetted area of the floral tubes was responsible for this improvement.

Kim and Kim(1999) conducted experiments on falling film evaporation by using a

knurled tube, a spirally grooved tube, a bare tube and a tube coated with 20

micrometer aluminum particles, and they found that the knurled tube showed the best

performance in heat transfer.

By using a spirally wound fin inside the wall of a circular tube, Schwarzer et al. (1993)

provides a novel design of a falling film heat and mass exchanger. The effect of the

slope of the spiral shaped disc on the film side heat transfer coefficient was observed.

Choudhury et al. (1993) presented a physical model to analyze the absorption

phenomena on the basis of various interactions between the parameters and boundary

conditions involved in actual situations. Nusselt’s equation and continuity equation

were used to describe the solution flow rate, film thickness and velocity field. The

finite difference method with an equilibrium boundary condition at the liquid-vapor

interface was used to solve the energy and the diffusion equations. Their results

showed that, for larger flow rates, the heat transfer coefficient improves with the

increase of tube diameter, whereas for smaller flow rates, the heat transfer coefficient

is large and an optimum flow rate for a particular tube size could be estimated on the

Page 22


basis of flow rate and total mass flux relation. For a given tube diameter, there was an

optimum solution flow rate that maximized the vapor absorption in the film.

Miller and Perez-Blanco (1993) studied the performance of advanced (pin fin tube,

grooved tube) surfaces. Their result showed that the pin fin tube with 6.4 mm pitch and

grooved tubes might enhance absorption to levels comparable to chemical

enhancement in horizontal smooth tube absorbers.

To better understand the mechanisms driving the heat and mass transfer processes in a

falling film, Miller and Keyhani (2001) conducted an experimental investigation. They

showed that the concentration gradient in the direction of flow is approximately

constant. Thermo graphic phosphors were used successfully to determine the

temperature profile along the length of vertical absorber tube and the measure of

temperature enabled the calculation of the bulk concentration. Several correlations for

the coupled heat and mass transfer processes were validated against the experimental

results.

In this Chapter, the published literature on the various aspects of evaporator

performance that are relevant to the present investigation were reviewed. From the

study it is evident that although a lot of work and investigations had been performed

on the vertical tube configuration and on configuration of horizontal tube having less

than five tubes, very few studies had been done by using horizontal heat exchanger for

a higher number of tubes in the configuration. The performance of the evaporator is

limited by the poor evaporation rate at the vapor liquid interface. The difficulty of

maintaining a uniform film over the evaporator surface has contributed to the poor

Page 23


performance of the evaporator along with other factors. To improve the evaporation

process several techniques including the use of enhanced modified surface, the use of

active agent were developed and used. An objective of the present study is to study the

performance of a new evaporator configuration and to develop new models by

analyzing the heat and mass transfer process.

Page 24

Chapter-3 The Experiments

THE S

Experiments were carried out to

processes occurring in a falling fi

and for the different thermodynam

experiments an experimental rig w

the experimental setup and the ex

3.1 Description of the Expe

The schematic diagram and a p

Figures 3.1 and 3.2, respectively

main sub-systems. The main one

the evaporator heat exchanger, ai

the measuring devices. The other

heating medium and the air flow s

solution bath and the distributor.

were used as the components of

system consists of the air circulat

systems, there are temperature &

process safety devices. The detai

individually in the following secti

CHAPTER 3

EXPERIMENT

provide a better understanding of the evaporation

lm of water for different flow conditions of the fluids

ic situations, involved in the system. To perform the

as designed, fabricated and installed. The details of

periments are discussed in the following section.

rimental Set-up

hotograph of the experimental set-up are shown in

. The total experimental system is composed of four

is the evaporation system, which mainly consists of

r guiding plates and solution holding cage along with

sub-systems are the solution distribution system, the

ystem. The solution distribution system includes the

The hot water tank and hot water circulating pump

the heating medium and finally the air circulating

ing fan and the air chamber. In addition to these sub

flow-rate measuring devices, set-up supporting, and

ls of all components involved in the set-up are given

on.

Page 25


9

Figure 3.1

T= Thermocouple G= Valve R= Humidity sensor

Solution flow path

Airflow Path

Hot Water flow path

Solution distribution

Solution Pump S

Solution flow meter

Solution Inlet

Hot water Inlet

Hot water Outlet

Solution Outlet

G2

Evaporation Chamber

Heat Exchanger

T10

T8

T1

T14 R2

Air Outlet

Distributor

T9

3.1.1 Heat Exchanger, dis

The most important comp

of 24 horizontal copper tub

T

Hot Water tank

Schematic Diagram of Experimental Set-up

Heater

G1

How water flow meter

olution bath

T13 R1

Air Inlet

Fan Hot wire

tributor and Evaporation Chamber

onent of the set-up, the evaporator heat exchanger, consists

es mounted in a vertical plane with a gap of 6 mm between

Page 26


consecutive tubes as shown in Figure 3.3. The nominal diameters of the copper tubes

were 19 mm and the effective lengths of the tubes were 160 mm. The copper tubes

were connected with each other in such manner that the hot water traveled through it in

a serpentine flow path.

Solution Bath Hot water pump

Air circulating fan

Evaporator / heat exchanger

Hot water tank

Restrictor

Figure 3.2 Details of the Experimental Set-up

The structure was fabricated in the form of a cross flow heat exchanger, where the hot

water flowing through the tubes enters at the bottom and leaves at the top; whereas the

solution flows over the tubes entering at the tip of the tube and leaves at the bottom.

As a result, the arrangement of the fluid was in counter-flow mode. The detailed

dimension of this continuous counter flow exchanger was given in Appendix F. Eight

Page 27


thermocouples were inserted inside the horizontal tubes at the right sides of the rig at

different levels of the heat exchanger for measuring the temperatures of hot water at

different location, as shown in Figure 3.3.

Thermocouple

Falling Film

Figure 3.3 photograph of heat exchanger

The exchanger was placed inside a rectangular chamber whose length and width were

45 cm and 18.5 cm, respectively. The chamber was made of perspex material and

mounted on a plate made of polycarbonate having length and width of 400mm and 250

mm, respectively. The thickness of the surrounding Perspex plate was 6mm; whereas

that of the base plate was 10mm. This thickness of the base plate of the chamber was

chosen higher to support the weight of the exchanger and to keep it horizontally

aligned vertically upright. One hole of 15 mm in diameter was created at the middle of

Page 28


the base plate to connect the pipe to continue the circulation of the solution with the

solution bath. Besides that, two rectangular holes having width of 20 mm and length of

22 cm were created at two sides of the base plate each at a distance 50 mm apart from

the centre for allowing the flow of air into the chamber. The height of the case was 98

cm.

Figure 3.4 Insulated evaporation chamber

Two plates made of Perspex installed and placed vertically inside the chamber each at

a distance 110 mm from the center of the plate, having width and height equal to the

width and height of the chamber, respectively. The purpose of using these two vertical

plates was to allow the air to exchange heat only within the effective area of the

exchanger. The chamber was essential in maintaining the desired air flow over the

Page 29


exchanger by preventing the interference of air outside the chamber with the air inside

the chamber. For this reason, the upper side of the chamber was open to the

atmosphere for smooth flow of air. A case made of Perspex material was constructed

and placed on the top of the base plate of the evaporator chamber to ensure that all the

solution that was flowing over the evaporator had been collected and allowed to flow

vertically back to the solution bath through the center hole of the base plate. The

detailed dimension of the case is given in Appendix-F

A distributor mounted on the top of the tubes was used to distribute the solution over

the evaporator tube surfaces. The water was delivered to the distributor from a water

bath. The main body of the distributor is a 40-mm diameter tube sealed at both ends

with an effective length of 160 mm, placed horizontally over the topmost evaporator

tube by maintaining a gap of 20 mm. Seven holes of equal diameter each of 5 mm

were created at a distance 20 mm apart from each other at the bottom surface of this

main body of the distributor to distribute the solution uniformly over the evaporator

tube. The solution (water) first falls on the topmost tube and then drips on to the next

tube of the evaporator heat exchanger and continues until it reaches the lowest tube.

Some strings made of cotton were used over the distributor and the heat exchanger

tube to maintain a uniform distribution of the solution and to prevent the spilling of the

water from the heat exchanger. To get an even distribution, it needs to shift the string

position to and fro. This process was usually done manually before starting the actual

experiment. For that reason an option was kept to disconnect one side wall of the

evaporation chamber.

Page 30


3.1.2 Solution Bath

A solution bath having physical dimensions 46 cm×38 cm×54 cm was used in the set-

up to maintain the circulation of distributed water and to feed it at a fixed temperature.

Arrangement of the water bath was shown in Figure 3.1. As the temperature of the

distributed water becomes higher on receiving the heat energy from the hot water, it

needs to be re-set to the desired value after each circulation. The solution bath reduces

the temperature of the distributed water to maintain the desired temperature at the

inlet. One heating and cooling circuit was installed inside the bath for heating and

cooling purpose. The rectangular shape heater coil has 5 layers that can supply water

up-to 250° C of temperature. The volume of the solution holding place inside the bath

was 4 liters having dimensions of 15 cm×15 cm×30 cm and the flow rate was 20

lit/min. The detailed Figure is shown in Figure. 3.5.

Controller

Heater Coils

Figure 3.5 Photograph of the solution bath

Page 31


3.1.3 Hot Water Tank

A water tank filled with a heater of capacity 15 kW was used to supply the hot water

through the heat exchanger. The capacity of the tank was 45 liters having an inside

dimensions 70 cm×35 cm× 33cm and the tank can deliver water at about 100 °C. The

cover plate of the tank is replaced by the armeflux insulator of thickness 20 mm, so

that, it will be easy to install the hot water supplying pipe and to reduce the heat losses

into the surroundings, as shown in Figure 3.6. The sides of the tanks were also

insulated by the same insulation materials. There was a temperature controller to set

the temperature within the desired range. One cutoff switch was used to set the

temperature to a maximum desired value for safety purposes.

On/off

Temp. fixer

Safety cut-out

Figure 3.6 Photograph of hot water tank

3.1.4 Flow Circuits

A 0.37 kW centrifugal pump (Model PKM 60) was used to circulate the hot water

from the hot water tank to the heat exchanger entering at the bottom and leaving at the

Page 32


top, as shown in Figures 3.1 and 3.6. The volume flow capacity of the pump was 1.1 to

2.4 m3/h corresponding to the total head of 40 to 5 m, respectively, which was

controlled by a valve and by a by-pass line with another valve, as shown in Figure 3.7.

Outlet

Inlet

Figure 3.7 Photograph of Centrifugal pump

3.1.5 Air Circulating Fan

A centrifugal fan, which can supply air up to a temperature of 60 °C, was used to

supply atmospheric air to the evaporation chamber. The circulation of air continues

through the air chamber and the boxes connecting the evaporation and air chamber, as

shown in Figures 3.2 and 3.8. A circular pipe of 10 cm in diameter and 160 cm in

length made of perspex materials was connected at the inlet of the fan. The outlet of

the fan was connected to the diverging section of the air chamber. The fan can provide

ten different speeds with the help of a speed regulator, as shown in Figure 3.8;

whereas, the experiment was conducted only at the lowest three speeds. The details of

the calculation of the fan speed and the values were described in Appendix-A

Page 33


Outlet Inlet

Speed Regulator

Figure 3.8 Photograph of air circulation fan

3.1.6 Air Chamber

An air chamber was fabricated and installed in between the fan and the evaporation

chamber to supply the atmospheric air to the evaporation chamber. The chamber has

two sections namely the diverging section having a length of 50 cm and the

rectangular section having a length of 90 cm. The main purpose of the diverging

section was to convert the velocity head of the air into the pressure head. Two, 2mm

thick flow straightness restrictors having numerous holes of 5 mm in diameter onto it

were used inside the rectangular section of the chamber maintaining a distance of 15

cm to make the flow straight and homogeneous. The humidity sensor and the

thermocouple to measure the inlet properties of air were installed at a distance 50 cm

from the end point of the diverging section and just after the restrictors. Two boxes

made of perspex having a length equal to the width of the rectangular section of the

chamber were installed in between the top plate of the rectangular section and the

bottom plate of the base plate of the evaporation chamber by maintaining a distance of

Page 34


20 cm in between them. These boxes serve as the flow passage from the air chamber to

the evaporation chamber. The detailed dimensions of the chamber are given in

Appendix-F.

3.1.7 Insulation and Support Structure

As shown in Figure 3.4, to minimize the heat losses to the ambient, armeflux

insulation materials having 10 mm thickness were used as insulator at the outside

surfaces of the surrounding plates of the evaporation chamber. The empty places

among the outside surfaces of chambers connecting boxes, the lower surface of the

base plate of the evaporation chamber and the upper plate of the air chamber were

carefully packed with rock wool.

The whole experimental setup was placed inside a structure, which was formed in

three layers. The angle bars made of steel were used to make the structure having

dimensions of 52 cm×52 cm ×175 cm. As shown in Figure 3.2, in the upper layer the

evaporation chamber as well as the evaporation heat exchanger was placed. The

middle layer held half of the total air chamber, and the lower layer was empty. To

support the rest of the air chamber including the diverging section along with the fan

connected to it, an auxiliary supporting structure was used which was also made of the

same materials. The additional purpose of this supporting structure was to keep the fan

strictly horizontal to the air chamber for ensuring a uniform flow of air through the

chamber. Finally, another small supporting structure was used to keep the pipe

connected at the inlet of the fan horizontal for a smooth flow of air for measuring the

mass flow rate of air.

Page 35


3.1.8 Measuring Equipment

To evaluate the performance of the evaporation process, it was necessary to measure

the flow rate and temperature of the hot water and distributed water at different

locations of the flow circuits. In addition, the humidity of the air at the inlet and outlet

of the evaporation chamber was measured. The instruments used for these

measurements are described below.

Variable Area Flow Meter

To measure the volume flow rate of the hot water and the distributed water, two

variable area flow meters, each with a capacity of 0.5 to 4 lit/min, were used. Each

meter was connected parallel to a by-pass path that has a valve to control the flow of

the fluid through the meter. These meters that have an accuracy of ±1.5%, were

calibrated manually by using standard measuring volumes. The details of the

calibration are given in Appendix-A.

Figure 3.9 Photograph of variable area flow meter

Page 36


Humidity sensors

In order to determine the properties of the air at the inlet and the outlet sections of the

evaporation chamber one more property other than the temperature was essential to

know. So the second property selected was relative humidity. By using these two

properties the moisture content and the enthalpy of the air can be determined from the

psychometric chart. Two humidity sensors (Model EE20X-6XXX) were used to

measure the humidity of the air at the inlet and outlet of the evaporation chamber.

These sensors were also able to measure the temperature of the air.

Humidity sensor

Figure 3.10 Photograph of humidity sensor.

The working ranges of the sensor were from 0 to 100% for relative humidity and from

-20°C to +80°C for the temperature. The output was given in mA. To convert the

result from mA to voltage two resistors of 250 Ω were used separately with an input

Page 37


power source of 20 V. The conversion equations from voltage to percentage of

humidity are shown in Appendix A.

Temperature measuring devices

Fifteen type-K (Chromel-Alumel) thermocouples were used to measure the

temperature of the hot water and the distributed water at different locations of the

experimental set-up, as shown in Figures 3.1 and 4.2. All thermocouples were

calibrated using a standard liquid-in-glass thermometer with an accuracy of ±0.05°C.

The calibration graphs for the thermocouples are tabulated in Appendix A.

3.1.9 Data Acquisition System

A data acquisition system consisting of a data logger (FLUKE HYDRA) associated

with a computer was used in the experimental set-up. The data logger can

accommodate a maximum of 20 input channels. A software program associated with

the above data logger was used to transfer the data into the computer for further

processing. All thermocouples and the humidity sensors were connected to the data

logger and the data sampling speed was controlled manually.

Figure 3.11 Photograph of Fluke Hydra data logger

Page 38


3.2 Experimental Procedure and Experimental data

The water, which represents the solution, creates a falling film over the surface of the

evaporator, when flowing over it. An even distribution of the solution was maintained

by the distributor located at the top of the heat exchanger. The constant temperature

hot water circulated by the pump through the heat exchanger, exchanges heat with the

solution and increases the temperature of the falling film. As a result, water was

evaporated from the film. Air at a moderate flow rate, forced by the fan, flows over the

outer surface of the falling film in the reverse direction of solution flow. The

evaporated water as well as energy from the film was absorbed by this air, leading to

an increase in moisture content and the enthalpy at the exit.

3.2.1 Actual Experimental Investigation of Evaporation Performance

The setup of the experiment was shown earlier in the Figure 3.2. All experiments were

conducted at atmospheric pressure. At the beginning of each test, the heater of the hot

water tank would switch on to increase the temperature of the water inside the tank to

a desired value. The temperature controller and cutoff switch were used to get the

desired temperature and the safety, respectively. Usually, it took nearly 30 to 40

minutes to heat up the water depending upon the desired temperature. The circulation

of the solution required nearly 20 minutes to get the homogeneous distribution of the

solution over the heat exchanger pipe. By opening one side cover of the evaporation

chamber and by shifting the position of the string at the distributor and at the pipes the

homogeneous distribution of the distributed water over the heat exchanger was usually

achieved. After completion of this manual work the side cover of the chamber was

closed again.

Page 39


After connecting the hot water circulating pipe with the tank, the water circulation

pump was turned on. To continue the air flow over the falling film of the water the air

circulating fan was also turned on at the same time. As a result, the hot water flows

through the heat exchanger pipe, the distributed water flows over the pipe as falling

film and air flow over the falling film. The system was allowed to run for about 30

minutes to reach steady state operating conditions. When the conditions were steady,

the temperature of the hot water at different locations of the exchanger, the

temperature of the distributed water at the inlet and outlet of the heat exchanger, the

temperature and the humidity of the air at the inlet and outlet of the evaporation

chamber were recorded. The mass flow rate of the hot water, distributed water and the

air were also recorded at this time. The procedure was repeated for a range of

operating conditions.

3.2.2 Experimental Heat and Mass Transfer Data

To understand the behavior of the evaporation processes extensive experimental

studies were performed. In total, 77 sets of experimental data were acquired and

analyzed as shown in Table B.3, Appendix-B.

Page 40

Chapter-4 Mathematical Models

MATHE S

In the present study, an attempt

mass transfer processes in counte

start with a detailed model. This

mass transfer occurring in an eva

calculated directly from the mode

evaporator. Although the variatio

instant in the control volume, the

neglecting the variation of mass f

as the simplified model was deve

and mass transfer coefficients ac

this chapter, the detailed model w

4.1 Physical Arrangement o

The horizontal tube evaporator he

among evaporators. The solution,

the evaporator surface at the top a

flows in a direction that was coun

4.1 and 4.2. The vapor evaporates

shape and surface structure were

with a falling film on one side and

CHAPTER 4

MATICAL MODEL

has been made to develop the modeling of heat and

r-flow evaporators. The aim of this approach was to

model was made on the basis of the actual heat and

porator. The heat and mass transfer coefficients were

l that can be used to evaluate the performance of the

n of flow rates of the fluids was very small at any

y were taken into account in the detailed model. By

low rates of all working fluids another model named

loped to validate and to compare the values of heat

hieved by the detailed model. In the next section of

as developed followed by the simplified model.

f the evaporator heat exchanger

at exchanger was one of the common configurations

which in the present case was water, was sprayed on

nd flows under gravity as a falling film. The hot fluid

ter to the solution flow direction, as shown in Figures

from the exposed surface of the film. If the detailed

ignored, the evaporator can be idealized by a surface

the hot fluid on the other side.

Page 41


Air flow inlet

Distributed water Inlet

Distributed water Outlet

Hot water Inlet

Hot water Outlet

Figure 4.1 Flow circuits of all fluids included in the system (3D)

T2 T1

T3 T4

T5

T6

T7

T8

Distributed water outlet

Hot water outlet

Distributed water inlet

Air flow inlet

Air flow Outlet

Water Distribution

Hot water inlet

T9 T10

Figure 4.2 Flow circuits of all fluids included in the system (2D)

Page 42


Necessity of two heat transfer coefficients

Figure 4.3 shows the approximate temperature profile of a falling film flowing over a

vertical plate. The temperature of the plate was higher than that of the film exposed to

the surface. As a result, the flow within the film can be considered as fluid flowing in

between two plates of dissimilar temperatures. Thus the temperature of the film varies

from wall to a certain thickness of the film in a parabolic way. After that, until the

surface of the film, the flow pattern becomes an opposite parabolic shape (Mills,

1995). These two different profiles may be because of the bulk condition of the

system.

Liquid film Vapor

Tw

T

TSat

Air

Figure 4.3 Temperature profile of distributed water within the film

The total heat flux was divided into two parts within the falling film. One part of the

total heat was taken away by the solution in the axial direction and the rest part flows

from the falling film to the interface. For this reason and, due to the variation of the

Page 43


temperature profile in these two regimes, the amount of heat transfer in these two

regions will be different, producing two transfer coefficients.

4.2 Detailed Model

An approach of the falling film flowing over the horizontal tubular evaporator is

presented in Figure 4.4. A sequential presentation within one tube is presented in

Figure 4.5 followed by Figure 4.6, where half circular portion of the pipe is

considered, along with the presence of air flow over the film. And by considering the

circumferential portions of the tube as a flat plate another presentation is shown in

Figure 4.7 with an analysis of different flow conditions. A schematic diagram of the

counter flow evaporator is shown in Figure 4.8, which is considered a detailed version

of Figure 4.7, where a thin film of distributed water flows over a plate in downward

direction. The hot water flows in the opposite direction to form a counter-flow heat

and mass exchanger. At inlet, the hot water enters at a higher temperature and after

exchanging heat with the distributed water it becomes lower at the outlet. By taking

this heat energy, the water evaporated from the distributed water film and was carried

out by the air.

4.2.1 Assumptions

The following assumptions were made in obtaining the governing equations of mass,

momentum and energy conversion.

1. Heat transfer by conduction and mass transfer by evaporation in the direction of

distributed water flow were negligible.

2. The system was in a steady-state.

3. There was no chemical reaction

Page 44


4. The working fluids were non Newtonian fluid.

5. The interface was in thermodynamic equilibrium and air-water vapor mixture was

considered ideal gas mixture when computing the mass fraction of the water.

6. The wall temperature of any horizontal tube along the perimeter of the tube can be

assumed to be constant. Therefore, solution flows over a surface were at constant

temperature.

Falling Film

Water distribution over pipe

Figure 4.4 Distribution of Falling film over the horizontal tube

Page 45


Copper Pipe

Distributed water

Falling Film

AirAir

Hot water

θ

Figure 4.5 Geometrical configuration of the flowing film

Evaporated water particles

Copper tube

Air

Figure 4.6 Air water interactions within the film

Page 46


Laminar Film Flow

Wavy Film Flow

Figure 4.7 Temperature profile across an evaporating turbulent falling film

Figure 4.8 Geometrical configuration of the control volume

Air Hot water Falling film

.vmd

ifT dA

.am

aa dHH +

wdw+

cm.

cc dTT + ww mdm

..+

ww dTT +

.am

aH w

wm.

wT

cm.

cT

vH

wohU

hi hc

Turbulent Film Flow

Air flowing Over the film Water Falling

Film

Copper Plate

Page 47


4.2.2 Governing Equations

Heat balance for the hot water

As discussed in Section 4.2, considering the circular section of the tube as a flat plate

and using a small control volume of unit width, as shown in Figure 4.8, the energy

equation for the hot water can be written as:

[ ] ( )(dATTUTCmdTTCm wcccccccc −+=+..

) (4.2.1)

And hence, the equation for the hot water distribution with area can be written as:

( wc

cc

c TTCm

UdAdT

−⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛= )∴ . (4.2.2)

Where, U was the overall heat transfer coefficient from hot water to distributed water.

Heat and mass balance for the falling film

The water flowing over the evaporator takes heat from the hot water flowing inside the

evaporator pipe and thus water evaporated from the surface. Thus the energy equation

for distributed water at the control volume can be expressed as:

( )( ) ( )( )

( ) ( )( )dATThmdH

dTTCmdmdATTUTCm

aifavv

wwwwwwcwww

−+⎟⎟⎠

⎞⎜⎜⎝

⎛+

+⎟⎟⎠

⎞⎜⎜⎝

⎛+=−+

.

...

(4.2.3)

Neglecting the term ( ), the equation (4.2.3), was expressed as: www dTmdc.

( ) dATThmdHmdCTdTCmdATTU aifavvwwwwwwwc )(...

−+⎟⎟⎠

⎞⎜⎜⎝

⎛++=−

(4.2.4)

On re-arranging equation (4.2.4) the following equation was achieved,

Page 48


( )⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−−−−=+⎟

⎠

⎞⎜⎝

⎛∴dAmd

HTThTTUdAmd

CTdA

dTCm v

vaifawcw

www

ww

...

)( (4.2.5)

Where, was the heat transfer coefficient from interface to air, and was the

enthalpy of vapor.

ah vH

Mass balance for water in film

As the distributed water takes heat from the hot water, some water evaporated. So, the

total reduction of distributed water mass flow rate will be equal to the total evaporated

water. By balancing the mass of water vapor, transferring with the control volume, we

can write,

)(....wwvw mdmmdm ++= (4.2.6)

Thus,

..wv mdmd −= (4.2.7)

Energy balance for the air

The evaporated water from the distributed water film was carried out by the air

flowing over the film, which increases the moisture content of the air at the outlet.

Total energy of air at the outlet will be equal to the sum of total energy of air at inlet

and the energy supplied by the distributed water.

Hence, the energy equation for the air can be expressed as:

( ) aaaifavvaaa HmTTdAhHmddHHm...

)( =−+++ (4.2.8)

( ) 0.

.=−+

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+⎟

⎠

⎞⎜⎝

⎛∴ aifav

va

a TThdAmdH

dAdH

m (4.2.9)

Page 49


where, was the mass flow rate of dry air and .am aH was the enthalpy of the air.

Mass balance for air

As, the evaporating water particles were added with the air, the moisture content of the

air will be higher at the outlet than that at the inlet, i.e. the moisture content of the air

at outlet is the summation of the moisture content at the inlet and the evaporated

moisture which can be expressed as:

wmmddwwm ava...

)( =++ (4.2.10)

Hence,

dwmmd av..

−=∴ (4.2.11)

Now from equation (4.2.7) and (4.2.11) the following equation relates the moisture

content of air with the mass flow rate of solution.

dwmmd aw..

=∴ (4.2.12)

Substituting the values and in the equation (4.2.5), the following equation

was obtained:

wmd.

vmd.

( ) ⎟⎠⎞

⎜⎝⎛+−−−=⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛

dAdwmHTThTTU

dAdwmCT

dAdT

Cm avaifawcawww

ww...

)(

(4.2.13)

( ) ( ) )(..

aifawcavwww

ww TThTTUdAdwmHCT

dAdT

Cm −−−=⎟⎠⎞

⎜⎝⎛−+⎟

⎠⎞

⎜⎝⎛∴

(4.2.14)

And again the equation (4.2.9) can be re-arranged as:

Page 50


( ) 0..

=−+⎟⎠⎞

⎜⎝⎛− aifaav

aa TTh

dAdwmH

dAdH

m (4.2.15)

Rate equations

The rate of change of evaporation can be expressed as follow:

( )dAwwKmd ifav −=.

(4.2.16)

where, is the evaporation mass transfer coefficient and waK if and w are the moisture

of the air water interface and air, respectively.

The energy transferred at the evaporation processes can be expressed as:

[ ] vfifwwo mdHdATThdq.

+−= (4.2.17)

where, is the total heat transferred within the control volume at the interface

during the evaporation process, and is the enthalpy of water.

dq

fH

By using the value of from equation (4.2.16), the equation (4.2.17) can be

expressed as:

vmd.

( ) ( )dAwwKHdATThdq ifafifwwo −+−= (4.2.18)

Also the total energy can be expressed as:

( ) ( )aifavifa TTdAhdAHwwKdq −+−= (4.2.19)

By equating equation (4.2.18) and equation (4.2.19) the following equation was

obtained:

( ) ( ) ( )[ ]dATTh

dAwwKHTTdAhdAwwKH

ifwwo

ifafaifaifav

−+

−=−+−

(4.2.20)

Page 51


( ) ( ) ( )aifafgifaifwwo TThHwwKTTh −+−=−∴ (4.2.21)

Where , fgfg HHH −=

From equations (4.2.7) and (4.2.16) the expression for the mass flow rate of distributed

water can be re-arranged as:

( wwKdAmd

ifaw −−=

.

) (4.2.22)

Again by using the equation (4.2.11) and (4.2.16), the following equation was

obtained:

( )dAwifwaKdw.am −=− (4.2.23)

To express the variation of moisture content of air with area, equation (4.2.23) can be

re-written as:

( wwm

KdAdw

if

a

a −−= . ) (4.2.24)

By using the value of dAdw from equation (4.2.24), the equation (4.2.15) can be

modified as:

( ) ( aifaifava

a TThwwKHdA

dHm −−−−=

. ) (4.2.25)

And hence,

( ) ( aif

a

aif

a

ava TTm

hww

m

KHdA

dH−−−−= .. ) (4.2.26)

Now, by using equation (4.2.22) & (4.2.16), the equation (4.2.5) can be written as,

( ) ( ) ( )wwKHTThTTUwwKCTdA

dTCm ifavaifawcifaww

www −−−−−+−= )(

.

Page 52


(4.2.27)

And hence,

( ) ( ) ( )[ ])(.1. aifawcifavww

ww

w TThTTUwwKHCTCmdA

dT−−−+−−

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=⎟

⎠

⎞⎜⎝

⎛

(4.2.28)

4.2.3 Solution Procedure

To solve the governing equations for finding heat and mass transfer coefficients a

FORTRAN computer program was developed. The differential equations were solved

by using the 4th order Runge-Kutta scheme with appropriate boundary conditions. In

Figure 4.9, the flow diagram of the program was described with the sequence of the

various steps of the calculation. Initially, all physical and thermal properties of the

fluids involved in the system were introduced, along with the physical properties of the

evaporator. The whole area of the evaporator was divided into 240 vertical control

elements. By considering the out-let of the evaporator as the reference point and

starting point of calculation (where area of the absorber was considered as zero), the

process of calculation proceeded on, from the first control element to the next grid and

so on up-to the last grid. The values of heat transfer coefficients including the over_all

heat transfer coefficient from the hot water to distributed water, the heat transfer

coefficient from tube wall to the bulk point and the heat transfer coefficient from the

bulk point to the interface were initially guessed with minimum values. Therefore, the

properties of the fluids and the heat transfer coefficients of the system at the first

control element were known. The interface temperature and the interface moisture

content for the first calculation were set equal to the values of the inlet distribution

water temperature and the inlet moisture content of the air, respectively. The coupled

nonlinear equations (4.2.2), (4.2.22), (4.2.24), (4.2.26), and (4.2.28) were then solved

Page 53


by using a 4th order Runge-Kutta method for the first control grid to determine the

temperature, mass flow rate of the hot water and distributed water and enthalpy and

moisture content of the air at the second control element. The interface moisture

content of and the temperature at the second and other control volumes were calculated

by the trial and error method with the help of the algebraic equations (4.2.21).

The calculation continues up to the last control volume and the values of different flow

rates and temperatures of the fluids, moisture content and the enthalpy of the air were

compared with the experimental values at the last control element, which is the inlet of

the evaporator. The difference between the calculated values and the experimental

values were aggregated by using the least square formula. After that, by increasing the

values of heat transfer coefficients the calculation was repeated for the same set of data

and here again the summation of the difference between the experimental and the

calculated values were calculated. The lower value of these two differences was stored

to compare for the next step. The calculation continues repeatedly by increasing the

values of heat transfer coefficients to certain maximum values. The combination sets

of the heat and mass transfer coefficients which give the minimum difference between

the calculated and the experimental values at the inlet of the evaporator, were

considered as the optimum conditions for the process.

Page 54


START

Setting of all fluid properties and parameters

Figure 4.9 Flow Chart for Calculation of solution properties and coolant temperature using detailed model

YesCalculate ε2, from the experimental and calculated values of

properties at the inlet of the evaporator by least squwere method

ha=ha max

U=U max

Calculate Tw, Tc, ω, Ha, m at iw.

th element using 4th order R.K. method

Guess the values of all heat and mass transfer coefficients. The maximum values of these coefficients. Set the values of the sum error, ε1

i=Last control element

Noi=i+1

ε2≤ε1ε1=ε1 No Yes

Calculate moisture and enthalpy of air from the sub-routine.

Hwo=Hwo max

Yes

Yes

No

No

No

Hwo=Hwo+0.001

ha=ha+0.001

U=U+0.001

Uopt=U, haopt=ha

Hwoopt=Hwo, ε1=ε2

Data Output

STOP

Page 55


4.3 Simplified Model for constant mass flow rate of distributed water

A simplified model has been developed where the heat and mass transfer in the falling

film were represented by the rate equations assuming constant flow rate of hot water,

distributed water and air, and using average heat and mass transfer coefficients. To

compare the heat and mass transfer processes with the detailed model, the simplified

model needs much less computational effort than the detailed model. The analysis was

developed for a counter-flow situation described as follows.

4.3.1 Assumptions

The following assumptions were made in the derivation of the governing equations of

mass, momentum and energy.

1. Heat transfer by conduction and mass transfer by evaporation in the direction of

distributed water flow were negligible.

2. The system was in a steady-state.

3. There was no chemical reaction.

4. The working fluids were non Newtonian fluid.

5. The interface was in thermodynamic equilibrium and air-water vapor mixture was in

ideal gas mixture when computing the mass fraction of the water.

6. The mass flow rate of hot water, distributed water and air were considered constant

for the whole system i.e. the variation of mass flow rates were neglected.

7. The wall temperature of any horizontal tube along the perimeter of the tube can be

assumed to be constant. Therefore, solution flows over a surface was at constant

temperature.

Page 56


4.3.2 Governing Equations

In Figure 4.1, the hot water and the distributed water flow arrangement of the counter

flow heat exchanger was shown. Considering a small control element to analyze the

heat and mass transfer processes, the energy balance equations for the hot water to the

distributed water at steady state can be written as

)(..

ccccccci dTTCmTCmdq +=+ (4.3.1)

where, is the total heat supplied by the hot water to the distributed water at the

control volume.

idq

ccci dTCmdq.

=∴ (4.3.2)

Again, the total heat transferred within the control volume from the hot water to the air

flowing over the film can be written as:

aaaaao HmdHHmdq..

)( =++ (4.3.3)

where, is the total heat supplied by the distributed water to the air within the

control volume.

odq

aao dHmdq.

−=∴ (4.3.4)

The total heat supplied by the hot water within the control volume was taken by the

distributed water and air. Mathematically it can be expressed as:

)(..

wwwwoiwww dTTCmdqdqTcm ++=+ (4.3.5)

wwwoi dTCmdqdq.

+= (4.3.6)

By substitution the values of and from the equations (4.3.2) and (4.3.4)

respectively, the equation (4.3.6) can be rearranged as:

idq odq

Page 57


wwwaaccc dTCmdHmdTCm...

+−= (4.3.7)

Considering the constant mass flow rate of distributed water, hot water and the air, the

equation (4.3.7) can be expressed for the whole system as:

1...

aTCmHmTCm wwwaaccc =−+∴ (4.3.8)

where, is a constant. 1a

The energy equation for the distributed water can be written as:

( iwooo TThAdq −= )δ (4.3.9)

Where, is the convective heat transfer coefficient from the distributed water to the

interface of the water and air and δA

oh

o is the area of the control volume at outer side of

the heat exchanger.

Again, the value of can be expressed in terms of heat transfer coefficient from the

interface to the air as this value of is experienced by that area also.

odq

odq

( aipm

coo HH

Ch

Adq −⎟⎟⎠

⎞⎜⎜⎝

⎛= δ ) (4.3.10)

where, and were the enthalpy of the air at air-water interface and the enthalpy

of air flowing over the film, respectively.

iH aH

Similarly, the overall energy equation for the hot water and the distributed water can

be written as:

( )wcii TTUAdq −= δ (4.3.11)

Where, δAi is the area of the control volume at inner side of the heat exchanger and U

is the overall heat transfer coefficient from the hot water to distributed water.

Page 58


Assuming, small variation of the area of the heat exchanger/evaporator at the inner and

outer side and considering the values were equal to the area of the control volume i.e

δAo=δAi=dA (4.3.12)

By equating the value of from the equation (4.3.2) and (4.3.12), the following

relation can be developed.

idq

( wcccc TTAUdTCm −= δ.

) (4.3.13)

Hence,

( wc

cc

c TTcm

UdAdT

−⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛= . ) (4.3.14)

Similarly, by equating the value of from equations (4.3.4) and (4.3.10), the

following relation can be developed.

odq

( aipm

caa HH

ch

dAdHm −⎟⎟⎠

⎞⎜⎜⎝

⎛=−

.) (4.3.15)

Hence, the variation of the enthalpy of air with area can be expressed as,

( ai

pma

ca HHCm

hdA

dH−

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−= . ) (4.3.16)

From equations (4.3.9) and (4.3.10), by equating the value of the following

relation was obtained:

odq

( ) ( aiopm

ciw HH

hCh

TT −⎟⎟⎠

⎞⎜⎜⎝

⎛=− ) (4.3.17)

Page 59


Let ⎟⎟⎠

⎞⎜⎜⎝

⎛=

c

opm

hhC

λ (4.3.18)

Then, the equation (4.3.19) becomes:

( ) ( )iwai TTHH −=− λ (4.3.19)

From equation (4.3.7)

dAdT

CmdA

dHm

dAdT

Cm www

aa

ccc

...+−= (4.3.20)

On substituting the values dAdTc and

dAdH a from the equations of (4.3.14), (4.3.16)

respectively, the equation (4.3.20) can be modified as:

( ) ( ai

pma

cawc

cc

ccw

ww HHCm

hmTT

Cm

UCmdA

dTCm −

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−

+−= .

.

.

..) (4.3.21)

Hence,

( ) ( aipm

cwc

www HH

Ch

TTUdA

dTCm −⎟

⎟⎠

⎞⎜⎜⎝

⎛−−=

.) (4.3.22)

By substituting the relation from the equation (4.3.19), the above equation can be re-

written as:

( ) ( iwpm

cwc

www TT

Ch

TTUdA

dTCm −⎟

⎟⎠

⎞⎜⎜⎝

⎛−−=

λ.) (4.3.23)

( ) ( iw

wwc

opm

pm

cwc

ww

w TTCmh

hCCh

TTCm

UdA

dT−

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛×−−= ..

1 ) (4.3.24)

Finally,

( ) ( iw

ww

owc

ww

w TTCm

hTT

Cm

UdA

dT−

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−−

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛= .. ) (4.3.25)

Page 60


From equation (4.3.8), the expression for the enthalpy of air in terms of different

temperature and flow rates of the fluids can be written as follow:

c

a

ccw

a

ww

a

a Tm

CmT

m

Cm

m

aH .

.

.

.

.1 −+= (4.3.26)

And by using equation (4.3.26) the equation (4.3.20) can be expressed as follows

(⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−+

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+= iwc

a

ccw

a

ww

a

i TTTm

CmT

m

Cm

m

aH λ.

.

.

.

.1 ) (4.3.27)

The mass transfer coefficient from the interface to the air can be expressed with

respect to the heat transfer coefficient from the interface to the air, defined below as

described in appendix D (D7):

ch

⎟⎟⎠

⎞⎜⎜⎝

⎛=

pm

cc C

hk (4.3.28)

where is the specific heat capacity of the moisture. pmC

4.3.3 Solution Procedure

The solution procedure for the simplified model was nearly the same as that of the

detailed model. In this case, the differential equations decrease from five to two, which

were for the variation of the hot water and distributed water temperature only. To solve

these governing equations for finding all heat and mass transfer coefficients another

FORTRAN computer program was developed, where the differential equations were

again solved by using the same 4th order Runge-Kutta method with appropriate

boundary conditions. In Figure 4.10, the flow diagram of the program was described

with the sequence of the various steps of the calculation. As before, initially all

physical and thermal properties of the fluids involved in the system were introduced,

Page 61


along with the physical properties of the evaporator. The whole area of the evaporator

was divided into 24 grids. Each grid was again sub-divided into 10 sub-grids for

precise calculation, but the output was taken after 10 sub-grids i.e. after one main grid.

Here also, the outlet point of the evaporator was considered as the reference point of

calculation and the area at this point was considered nil and the process of calculation

continues as like as that of the detailed model. The values of heat transfer coefficients

including the over-all heat transfer coefficient from the hot water to distributed water,

the heat transfer coefficients from tube wall to the bulk point and from the bulk point

to the interface were initially guessed with minimum values. Therefore, the properties

of the fluids and the heat transfer coefficients of the system at the first control element

were known. The interface temperature was taken equal to the temperature of

distributed water at this point. The coupled nonlinear equations (4.3.14) and (4.3.25)

were then solved by using a 4th order Runge-Kutta method for the first control grid to

determine the temperatures at the second control volume. The interface temperature

and enthalpy at the second control volume was then determined by the trial and error

method with the help of the algebraic equations (4.3.29). And then the enthalpy of air

was calculated from the equation (4.3.28). The calculation continues up to the last

control volume and the values of different temperatures of the fluids, the enthalpy of

the air at the last control grid were compared with the experimental values. The

difference between the calculated values and the experimental values for different

variables were added by using the same least square formula. Again the calculation

repeats by increasing the values of heat transfer coefficients for the same set of data

and here again the summation of the difference was calculated.

Page 62


START

Setting of all fluid properties and parameters

Figure 4.10 Flow Chart for Calculation of solution properties and coolant temperature using Simplified model

YesCalculate ε2, from the experimental and calculated values of

properties at the inlet of the evaporator by least square method

hc=hc max

U=U max

Calculate Tw, Tc,Hv, Ha, Tif, Hif at ith element using 4th order R.K. method.

Guess the values of all heat and mass transfer coefficients. And set the maximum values of these coefficients. Set the values of the sum error, ε1

i=Last control element

Noi=i+1

ε2≤ε1ε1=ε1 No Yes

Calculate moisture and enthalpy of air from the sub-routine.

ho=ho max

Yes

Yes

No

No

No

ho=ho+0.001

hc=hc+0.001

U=U+0.001

Uopt=U, hcopt=hc

hoopt=ho, ε1=ε2

Data Output

STOP

Page 63


The lower value of these two differences was stored for comparison in the next step.

The calculation continues repeatedly by increasing the values of heat transfer

coefficients up-to the maximum set values of heat transfer coefficients. All other

supporting equations were given in Appendix-D.

Page 64

Chapter-5 The Experimental Result and Discussion

EXPERIMENTAL N

A detailed analysis and discussi

variables that affect the values o

affects the performance of the

discussed in this Chapter. The

simulate and to analyze the expe

parts. The comparison of the resu

been discussed after the main resu

5.1 Experimental Results an

The experimental results and dis

with the procedure for the calcul

obtained by models. Subsequentl

mass transfer correlations were d

transfer coefficients for both mo

data were compared with the

experimental data were also co

models cited in the literature. Th

wall to the bulk solution and the b

5.1.1 Calculation procedure

The procedure of extraction of h

Chapter-4 under the title of ‘solut

CHAPTER 5

RESULTS AND DISCUSSIO

on of the characteristic behavior of different field

f heat and mass transfer coefficients which in turn

evaporation processes, have been performed and

two models presented in Chapter-4 were used to

rimental data. The Chapter is divided into two main

lts between models and with experimental data has

lts and the discussion part.

d Discussion

cussion mentioned in the following section started

ation and then followed the discussion of the results

y, the effects of different variables on the heat and

iscussed. The output results of non-dimensional heat

dels were compared. Besides that, the experimental

simulated data. Finally, the numerical and the

mpared with the available data obtained from the

e development of correlations for two regimes, tube

ulk solution to the interface, were also performed.

eat and mass transfer coefficients were described in

ion procedure’ of the models. This part of calculation

Page 65


procedure includes the details of the correlations and supporting equations that were

used for the calculation of dimensionless heat and mass transfer correlations. The

calculation procedure described separately for three regimes namely for hot water to

tube wall, tube wall to the interface of air and water, and interface to air.

For hot water to tube wall region, as the hot water flowing through the horizontal

copper tube in serpentine path, the flow was considered as the fluid flowing inside a

tube. Several correlations available for measuring the heat transfer coefficient for such

conditions for both laminar and turbulent flow. A most cited and used correlation

presented by Suryanarayana (1995), as shown in equation (5.1.1), was used for

calculating the heat transfer coefficient:

2400RePrRe023.0

2400Re36.4Nu

8.0

c

≥=

<==

cn

cc

cc

hc

for

forkDh

(5.1.1)

where, the value of n=0.3 for heating. is the hydraulic diameter of the flow path

which is equal to the inside diameter of the tube, is the thermal conductivity of hot

water and is the heat transfer coefficient from the hot water to the tube wall.

hD

ck

ch

For equation 5.1.1, the value of the Prandtl number for the hot water ( ) can be

found from Holman and White (1992) and the value of Reynolds number can be

calculated from its original equation which is

cPr

µπµ

ρ

i

ci

DmvD

.4

Re == (5.1.2)

where, is the mass flow rate of hot water in kg/sec, and is the inner diameter of

exchanger tube.

.cm iD

Page 66


In the detailed model, the interface temperature and the interface moisture content

needed to be calculated; whereas, in the simplified model interface enthalpy needed to

be measured in lieu of moisture content along with interface temperature. For both

case, the process was performed by setting the minimum and maximum values of the

interface temperature and then by calculating the moisture content or the enthalpy,

depending on the model, for these two corresponding temperatures. The equations

used were taken from the psychometric chart and listed in Appendix-D. In this

calculation the saturation pressure of the water was obtained from a 4th degree

polynomial set as a function of the temperature. Once, the required values were

calculated for the maximum and minimum interface temperatures, the values were fed

to the equation (4.2.21) for the detailed model and to equation (4.3.27) for the

simplified model. A follow up trial error bisection method was used until the exact

interface temperature and other properties were found.

As for the modeling, the flow was considered as flow over flat plates, the area of the

evaporator was measured as the summation of the surface area of twenty four

horizontal tubes and forty six (twenty three time of two, for both sides) time of the area

rectangular gap in between two consecutive tubes. The equation and the values are

given in Appendix-D.

As the overall heat transfer coefficient from hot water to the distributed water, U can

be calculated directly from the program by the iteration method, described earlier in

Chapter 4 and the heat transfer coefficient from hot water to tube wall, from

equation (5.1.1), the heat transfer coefficient from tube wall to bulk solution, can be

calculated from the equation of overall heat transfer coefficients which is as follows:

ch

ih

Page 67


w

w

ic khhUδ

++=111 (5.1.3)

where, wδ is the thickness of the copper tube wall and is the thermal conductivity

of the copper.

wk

Once the value of is found, the value of dimensionless heat transfer correlation

from tube wall to the bulk solution can be calculated from its original

equation

ih

⎟⎠

⎞⎜⎝

⎛=

khDhNu . In this case, the characteristic length , as used by Chen and

Seban (1971), was used from equation (5.1.4) to compare the values with other

researchers.

hD

31

2

⎥⎥⎦

⎤

⎢⎢⎣

⎡=

gDh

ν (5.1.4)

The equation of film thickness can be expressed by the equation expressed by

Choudhury et al. (1993) as,

Film thickness, 31

sin3

⎥⎦

⎤⎢⎣

⎡ Γ=

θρνδ

g (5.1.5)

where, g is the gravitational acceleration and ν is the kinematic viscosity of the water

that is equal to the ratio of the absolute viscosity, (µ) to the density (ρ) and θ is the

angle of inclination in radian, as shown in Figure 4.3.

For the vertical tube evaporator 31

3⎥⎦

⎤⎢⎣

⎡ Γ=

gρνδ (5.1.6)

Page 68


The value of heat transfer coefficient from bulk solution to the interface can be

used to calculate the Nusselt number for that region (Nu

woh

o). The value of the

characteristic length was also used, as given in equation (5.1.4)

Finally, from the interface to air regime, for calculating the mass transfer coefficient an

assumption was made, where the value of mass transfer coefficient is considered equal

to the heat transfer coefficient from the interface to air divided by the specific heat of

air moisture.

5.1.2 Results

The results consist of the overall heat transfer coefficient from hot water to the

distributed water, the heat transfer coefficient from bulk solution to the interface, the

heat transfer coefficient from the interface to air, and the mass transfer coefficient. The

output results for the detailed model and the simplified model were tabulated in

Appendix-B.

It was found from the results of the models that, among all heat and mass transfer

coefficients, the value of the overall heat transfer coefficient from hot water to

distributed water, U responded exactly for both models. There was a very small

difference between the results extracted by the two models for heat transfer coefficient

from interface to air. As the mass transfer coefficient was calculated from the heat

transfer coefficient of interface to air, the values of that vary negligibly between the

models as it varies for heat transfer coefficients. The differences of the error for any

two values of this heat transfer coefficient do not vary by a significant amount. Thus

several attempts were made to improve and to find the exact values of this heat transfer

Page 69


coefficient. Initially, the estimation of the total error was done based on the summation

of the individual errors of different field variables. Later the approach was changed to

the separation of total error for the energy of different fluids rather than individual

variables. But it was found that the first way of calculation was much better than the

later one. Although the individual value of this heat transfer coefficient did not match

but the regression average values agreed very well with the results of Chun and

Seban’s (1971) correlation as shown in Figure 5.19.

To confirm the validity of the equations of the model, an integration method was used

to recover the basic heat and mass transfer equations from the differential equations for

both model and the process was done successfully, as described in Appendix-C.

5.1.3 Effects of different variables on heat and mass transfer coefficients

In this section, a detailed graphical presentation has been made to provide a better

understanding of different variables on the heat and mass transfer coefficients. The

comparisons were carried out only for the detailed model, as they are also similar for

the simplified model. The experimental inlet temperature of air was considered the

same as the temperature of the ambient air of a temperature controlled experimental

room that did not vary more than one degree throughout the entire experimental

period. Thus, no provision can be made to observe the effect of the inlet temperature of

the air as well as the inlet moisture content. As the variation of heat and mass transfer

coefficients was affected by the variation of any important variables described earlier,

the result should be presented in non-dimensional form as in Figures 5.13 & 5.14.

Page 70


Variation of overall heat transfer coefficient from hot water to solution, U

Falling film evaporation heat transfer coefficients increase with both heat flux and

saturation temperature, as reported by Zeng et al. (1995). Chen. et al. (1997) showed

that, with the decrease of the temperature difference between the hot fluid and the

distributed fluid, the overall heat transfer coefficient increased.

0.50

0.70

0.90

1.10

30 32 34 36 38 40

Inlet Temperature of distributed water, 0C

Ove

rall

heat

tran

sfer

coe

ffici

ent f

rom

ho

t wat

er to

dis

trib

uted

wat

er U

, kW

/m2 K

At Ms= 0.029508 kg/sAt Ms= 0.037877 kg/s

Figure 5.1 Variation of overall heat transfer coefficient from hot water to distributed water, U with inlet temperature of solution at different mass flow rate of solution

A higher inlet solution temperature leads to a higher average value of the saturation

temperature and, with the increase of the saturation temperature of distributed water,

the difference between the temperature of hot water and the distributed water will

decrease. Thus, if it is needed, for maintaining the value of heat flux nearly constant,

the overall heat transfer coefficient from hot water to the distributed water must be

increased. And this fact is revealed in Figures 5.1, 5.2 and 5.4, where the positive

variation of overall heat transfer coefficient from hot water to distributed water, U can

be observed with the increasing of inlet temperature of the distributed water. Within

Page 71


the working range of the inlet temperature of distributed water from 32 ° C to 38° C,

the value of U varied from 0.7kW/m2k to 1.15kW/m2k.

0.50

0.70

0.90

1.10

30 32 34 36 38 40


Ove

rall

heat

tran

sfer

coe

ffici

ent f

rom

ho

t wat

er to

dis

trib

uted

wat

er U

, kW

/m2 K

At Mc 0.037726 kg/s

At Mc 0.040635 kg/s

Figure 5.2 Variation of overall heat transfer coefficient with distributed water inlet temperature at different mass flow rate of hot water

From Figures 5.1 and 5.2, the positive variation of U with the inlet temperature of the

distributed water could be observed directly for different mass flow rate of distributed

water and different mass flow rate of hot water, respectively. The other experimental

conditions were kept constant. Whereas, from Figure 5.3, the positive variation of U,

with the variation of inlet temperature of distributed water would be observed from the

upward shifting tendency.

Page 72


0.50

0.70

0.90

1.10

1.30

0.01 0.02 0.03 0.04 0.05 0.06

Mass flow rate of distributed water, kg/se

Ove

rall

heat

tran

sfer

coe

ffici

ent f

rom

ho

t wat

er to

dis

trib

uted

wat

er U

, kW

/m2 K

At Tsin=34.40 CAt Tsin=37.50 C

Fig 5.3 Variation of overall heat transfer coefficient with the drate at different inlet temperature of distributed

An increase of the hot water temperature leads to increases of

other variables were maintained constant. The increase of th

higher overall heat transfer coefficient, as exposed in Figure 5.4

et al. (1995).

c

istributed water flow water

the heat flux, when all

e heat flux leads to a

also reported by Zeng

Page 73


0.50

0.70

0.90

1.10

36 38 40 42 44 46

Inlet temperature of Hot water,oC

Ove

rall

heat

tran

sfer

coe

ffici

ent f

rom

hot

w

ater

to d

istr

ibut

ed w

ater

U, k

W/m

2 KAt Ms=0.029508 kg/s

At Ms=0.037877 kg/s

Figure 5.4 Variation of overall heat transfer coefficient with the inlet temperature of hot water at different mass flow rate of distributed water

From the study of Chyu and Bergles (1987), Conti (1978), and Owens (1978) it was

found that the heat transfer performance of a non-boiling turbulent film is independent

of film flow rate, whereas, Zeng et al. (1995) reported that, at higher temperature of

distributed solution, the heat transfer coefficient increases with both spray or film flow

rate and nozzle height. Finally, Chen et al. (1997) showed that, with the increase of the

spray Reynolds number, that is, with the increase of the solution mass flow rate, the

heat transfer coefficient increases. According to their results, at Re<500, heat transfer

coefficient increased linearly as the Reynolds number increased. At 500<Re<1600, the

heat transfer coefficient remained fairly constant or decreased slightly and at Re>1600,

the heat transfer coefficient increased slightly, as Reynolds number increased. In this

experiment, the range of the Reynolds number varied from 1 to 1100 and within this

Page 74


range the behavior of the heat transfer coefficients was found to agree with the

literatures.

0.50

0.70

0.90

1.10

1.30

0 0.02 0.04 0.06Mass flow rate of distributed water, kg/se

Ove

rall

heat

tran

sfer

coe

ffic

ient

from

ho

t wat

er to

dis

trib

uted

wat

er U

, kW

/m2 K

At Mc=0.037726 kg/sAt Mc=0.029417 kg/s

Figure 5.5 Variation of overall heat transfer coefficient with distributed water at different mass flow rate of hot

Within the mass flow rate of distributed water from 0.02 kg

correspond to the Reynolds number from 400 to 1025, an increa

transfer coefficient was found with flow rate, i.e. the heat tran

tube wall to the bulk solution increases. The evaporation heat t

their study was predicted for the electrically heated tube to the s

among three heat transfer coefficients the equivalent heat trans

named and discussed earlier as heat transfer coefficient from the

solution lay inside the value of U by a positive relation as depicte

Thus, with the increase of the value of U, the value of heat tran

tube wall to the bulk solution will also increase for a steady state

c

mass flow rate of water

/s to 0.05 kg/s that

se in the overall heat

sfer coefficient from

ransfer coefficient of

olution. In this study,

fer coefficient that is

tube wall to the bulk

d in equation (5.1.3).

sfer coefficient from

condition.

Page 75


0.50

0.70

0.90

1.10

1.30

1.50

1.70

0.025 0.035 0.045 0.055 0.065 0.075

Mass flow rate of Hot water, kg/sec

Ove

rall

heat

tran

sfer

coe

ffici

ent f

rom

ho

t wat

er to

dis

trib

uted

wat

er U

, kW

/m2 K

At Tsin 34.50 C

At Tsin 37.65 C

Figure 5.6 Variation of overall heat transfer coefficient with the hot water flow rate at different inlet temperature of distributed water

As discussed earlier, with the increase of the value of the hot water Reynolds Number,

the value of the Nusselt Number will increase, which leads to an increase of the value

of the heat transfer coefficient. From Figure 5.6, with the increase of the mass flow

rate of hot water, an increase in overall heat transfer coefficient at different inlet

temperature of the distributed water has been achieved.

Page 76


0.70

0.80

0.90

1.00

1.10

0.025 0.03 0.035 0.04 0.045 0.05

Mass flow rate of air, kg/sec

Ove

rall

heat

tran

sfer

coe

ffici

ent f

rom

hot

w

ater

to d

istr

ibut

ed w

ater

U, k

W/m

2 K


Fig 5.7 Variation of overall heat transfer coefficient from hot water to distributed water with the mass flow rate of air

Eckert et al. (1972) demonstrated that the gas-liquid interface is semi-permeable. It

was shown that the solubility of air in the liquid film is negligibly small, so that the air

does not move radially at the interface. By considering this fact, the effect of flow rate

of air over the liquid film was observed and presented in the following section. The

heat transfer along the air-liquid interface is dominated by the latent heat transfer in

conjunction with the liquid film evaporation reported by Feddaoui et al (2003). They

also Figure out that with the increase of the Reynolds number of air i.e. the air flow

rate, the value of the overall heat transfer coefficient increases. This fact has been

revealed in our experimental condition, as demonstrated in Figure 5.7. The

experiments were conducted at three different air flow rates, 0.033 kg/sec, 0.0407

kg/sec and 0.0431 kg/sec that correspond to the air Reynolds numbers 23000, 28000

Page 77


and 30500, respectively; and, within these conditions, an increase of overall heat

transfer coefficients has been observed with the Reynolds number.

Variation of mass transfer coefficient

The mass transfer coefficient from the interface to air was calculated from the program

for different experimental conditions. It was observed that the mass transfer coefficient

varied within a very small range. For the vertical length of the evaporator, the mass

transfer coefficient from the interface to the air can also be calculated directly by using

the basic equations and the correlations, as described in Appendix D. It was again

found that these coefficients maintained the values within the same range.

Angeletti and Moresi (1983) suggested that there are two mechanisms of vapor

evaporation from a falling film. One is direct evaporation at the liquid-vapor interface;

the other is bubble formation at the heated tube wall. They also pointed out that the

mechanism of direct liquid-vapor interface evaporation prevails when the total

temperature difference is less than 10 °C. Chun and Seban (1971) found that a

superheat of 3.7 °C was required for the bubble formation at the heating tube wall at

atmospheric pressure. As our experimental condition is very much lower than the

saturation temperature of the water at atmospheric pressure, so only the direct

evaporation has been considered here. And the convection of heat by the flowing

liquid film became the main mechanism for heat removal from the heated tube.

Page 78


0.00

0.01

0.02

0.03

37 39 41 43 45

Hot water Temperature, oC

Mas

s tr

ansf

er c

oeffi

cien

t Ka,

kg/

m2 s

At Ms=0.029508 kg/s

At Ms=0.037877 kg/s

Figure 5.8 Variation of mass transfer coefficient Ka, with hot water inlet temperature at different mass flow rates of distributed water

From Figure 5.8, it was clearly observed that the values of the mass transfer coefficient

varied from 0.015 to 0.025 kg/m2sec. These values were not too sensitive to the hot

water temperature, as shown in Figure 5.8. The variation of mass transfer coefficient

from interface to air with the variation of the inlet temperature of the distributed water

is presented in Figure 5.9. As shown in Figure 5.9, the values were found slightly

decreasing with the increases of inlet temperature of distributed water from 31 to 38

°C. Besides, the comparison was also made with the variation of the mass flow rate of

distributed water and hot water as shown in Figures 5.10 and 5.11, respectively.

Page 79


0.01

0.02

0.02

0.03

0.03

30 32 34 36 38 40


Mas

s tr

ansf

er c

oeffi

cien

t Ka,

kg/m

2 sAt Mc 0.037726 kg/s

At Mc 0.029508 kg/s

Fig 5.9 Variation of mass transfer coefficient Ka with the inlet temperature of distributed water at different hot water flow rate

0.00

0.01

0.02

0.03

0 0.01 0.02 0.03 0.04 0.05 0.06

Mass flow rate of distributed water, kg/se

Mas

s tr

ansf

er c

oeffi

cien

t Ka,

kg/

m2 s


Figure 5.10 Variation of mass transfer coefficient, Ka with the distrate at different inlet temperature of distributed wa

c

ributed water flow ter

Page 80


Feddaoui et al. (2003) numerically presented a reduction of mass flow rate of the

liquid cause greater film evaporation. Due to a lower mass flow rate of the distributed

water, the interfacial temperature became higher; therefore, the corresponding mass

fraction is also larger for the system with lower mass flow rate. This is observed in

Figure 5.10 where the negative correlation of mass transfer coefficients with the

distributed water mass flow rate has been demonstrated for different inlet temperature

of the distributed water.

0.00

0.01

0.02

0.03

0.04

0.05

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Mass flow rate of Hot water, kg/sec

Mas

s tra

nsfe

r coe

ffici

ent K

a, k

g/m

2 s

At Tsin 34.50 CAt Tsin 37.65 CAt Tsin 32.20 C

Figure 5.11 Variation of mass transfer coefficient Ka, with the variation of hot water flow rate at different inlet temperature of distributed water

Again, from the correlation of Suryanarayana (1995), it is seen that, with the increase

of Reynolds number, non-dimensional heat transfer coefficient increases. In other

words with the increase of the hot water flow rate the heat flux increases. From the

numerical study of Feddaoui et al. (2003), it is seen that, the evaporation rate increases

with the increase of the heat flux. In this experiment, a small amount of mass transfer

Page 81


coefficient increment was observed for the mass flow of hot water from 0.02 kg/sec to

0.06 kg/sec which has been shown in Figure 5.11.

The same principle can be applied for the temperature of the hot water and the

temperature of the distributed water. The fact is that the amount of evaporation

increases with the increase of the heat flux. Also, with the increase of the hot water

temperature keeping the temperature of the distributed water unchanged or with the

decrease of the distributed water temperature keeping the hot water temperature fixed,

the amount of heat flux will increase. As a result, the evaporation of water from the

falling film surface will increase. From Figure 5.12, a graphical presentation of this

fact has been demonstrated.

0.00

0.01

0.02

0.03

0.04

0.05

0.03 0.035 0.04 0.045 0.05

Mass flow rate of air, kg/sec

Mas

s tra

nsfe

r coe

ffici

ent K

a, kg

/m2 s

At Tcin=45.00 CAt Tcin=43.00 C

Figure 5.12 Variation of mass transfer coefficient, Ka with the mass flow rate of air

Page 82


5.2 Comparison of the results

Although the simulation results for the models were shown in Appendix-B in tabular

form, it would be appropriate to compare the values in a graphical manner for better

understanding. For this a typical comparison between the models was made in Chapter

6 in the form of numerical results and discussion. In addition to that, the variations of

the Nusselt number from tube wall to the bulk solution and from the bulk solution to

the interface with the solution flow Reynolds number is shown in the Figures 5.13, and

5.14, respectively.

0

0.1

0.2

0.3

0.4

0.5

0 200 400 600 800 1000

Reynolds Number, Re

Nus

selt

Num

ber,

Nu i

DetailedSimplified

Figure 5.13 Variation of Nusselt Number from the tube wall to the bulk solution with the solution Reynolds number

From Figure 5.13, it is seen that, in the wavy laminar region, the value of non

dimensional heat transfer coefficient from tube wall to the solution, Nui varies from

0.08 to 0.45 for different experimental conditions. On the other hand, Figure 5.14

shows the variation of Nuo with the solution Reynolds number for both models. The

Page 83


deviation from the detailed model and the simplified model for both heat transfer

coefficients was found very small.

0

0.1

0.2

0.3

0.4

0.5

0 200 400 600 800 1000

Reynolds Number, Re

Nus

selt

Num

ber,

Nu o

Detailed Simplified

Figure 5.14 Variation of Nusselt Number from the bulk solution to the interface with the solution Reynolds number

The average trends of the relationship between the Nusselt and Reynolds numbers has

been demonstrated in Figures 5.15 and 5.16 for the tube wall to the solution and the

solution to the interface, respectively. By plotting non-dimensional heat transfer

coefficients from tube wall to the solution for all mass flow rates of solution, it was

seen that the values are negatively correlated with each other for both cases. For each

mass flow rate of solution, the variation of heat transfer coefficient was also observed

within a very small range. The regression average was taken for the case.

Page 84


0

0.1

0.2

0.3

0.4

0.5

0 200 400 600 800 1000

Reynolds Number, Re

Nus

selt

Num

ber,

Nu i

DetailedAverage

Figure 5.15 Average Variation profile of Nusselt Number from the tube wall to the bulk solution with the solution Reynolds number by detailed model

0

0.1

0.2

0.3

0.4

0.5

0 200 400 600 800 1000

Reynolds Number, Re

Nus

selt

Num

ber,

Nu o

Detailed Average

Figure 5.16 Average Variation profile of Nusselt Number from the bulk solution to the tube wall with the solution Reynolds number by detailed model

Page 85


5.3 Comparison of experimental data with the simulated data

Only the provision for measuring the temperature of hot water at different points of the

flow path along the vertical distance was made during the designing of the evaporator.

The values of all other parameters were measured at the inlet and the outlet sections of

the evaporator. So, successful comparison between the experimental data and the

simulated data can be made only for the hot water temperatures in Figure 5.17.

30

35

40

45

50

0 0.05 0.1 0.15 0.2 0.25

Area, m2

Tem

pera

ture

, C

Experimental Detailed modelSimplified model ExperimentalDetailed model Simplified model

Figure 5.17 Comparison of experimental and simulated hot water temperature for two different hot water inlet temperatures

The variation of these temperatures has been plotted for both the detailed model and

the simplified model. Only a very small deviation of these three values occurred at any

at the entire evaporator surface. Although, the detailed values of all other variables at

different location of the evaporator could not be compared within the whole area their

inlet and outlet experimental values were compared with those of the simulated results

and tabulated in Tables 5.1, 5.2 and 5.3.

Page 86


Table 5.1 Comparison of the distributed water temperatures

Inlet solution Temperature, °C Outlet solution Temperature, °C Exp. Set

No. Exp. Detailed Simplified Exp. Detailed Simplified

1 34.44 34.45 34.45 38.89 38.85 38.92

2 31.57 31.57 31.57 34.75 34.56 34.75

3 34.68 34.68 34.68 39.61 39.62 39.61

4 32.41 32.41 32.41 39.08 39.22 39.05

5 37.71 37.71 37.71 40.16 40.31 40.14

Table 5.2 Comparison of the moisture contents of air.

Inlet moisture content

(kg/kg of dry air)×10-2

Outlet moisture content

(kg/kg of dry air)×10-2

Exp. Set

No.

Exp. Detailed Simplified Exp. Detailed Simplified

1 1.06 1.05 1.07 1.45 1.45 1.45

2 1.09 1.09 1.11 1.48 1.48 1.48

3 1.05 1.04 1.06 1.44 1.44 1.44

4 1.05 1.05 1.07 1.41 1.41 1.41

5 1.04 1.04 1.06 1.47 1.47 1.47

Table 5.3 Comparison of the enthalpies of air

Inlet enthalpy of air

(kJ/kg of dry air)×103

Outlet enthalpy of air

(kJ/kg of dry air)×103

Exp. Set

No.

Exp. Detailed Simplified Exp. Detailed Simplified

1 50.94 51.01 50.44 62.91 62.91 62.91

2 51.65 51.73 51.21 63.32 63.32 63.32

3 50.57 50.65 49.94 62.66 62.66 62.66

4 50.99 51.36 50.72 62.10 62.10 62.10

5 50.48 50.49 49.77 63.52 63.52 63.52

Page 87


5.4 Development of correlations for two regimes

For laminar falling film fully developed and with constant heat rate along the wall,

analytical solutions are easily obtained by introducing the film thickness derived by

Nusselt. In the case where all of the heat transferred from the heating surface are

absorbed in the liquid film,

31

3.12

* Re27.2−

=⎟⎟⎠

⎞⎜⎜⎝

⎛

==k

gh

NuH

υ

(5.1.7)

And in another case, all heat was removed from the film surface.

31

3.12

* Re76.1−

=⎟⎟⎠

⎞⎜⎜⎝

⎛

==k

gh

NuH

υ

(5.1.8)

In the fully developed region, convective heat transfer leads to evaporation at the

vapor/liquid interface. Chun and Seban (1971) developed the following correlations

for heat transfer for evaporating liquid films on smooth tubes based on a heated length

of only 0.3 m. They presented correlations for heat transfer coefficients in the wavy

laminar and the turbulent regimes as functions of the Reynolds and Prandtl numbers

less than 5.

Laminar:

22.031

2

3606.0

−

⎟⎟⎠

⎞⎜⎜⎝

⎛ Γ⎟⎟⎠

⎞⎜⎜⎝

⎛=

µνgkhc for Re<Rec (5.1.9)

Turbulent:

65.04.031

2

3 40038.0 ⎟⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛ Γ⎟⎟⎠

⎞⎜⎜⎝

⎛=

αν

µνgkhc for Re>Rec (5.1.10)

where, k is the thermal conductivity and ν is the kinematic viscosity.

Page 88


The critical transition Reynolds number (Rec) was given by the following equation.

3106.1

215.0Pr5900Re

Kac == (5.1.11)

Both correlations gave the local heat transfer coefficient as a function of film Reynolds

number, 4Γ/µ. In the laminar region, equation (5.1.9) indicates the influence of waves

and ripples which have the effect of increasing heat transfer by reducing the effective

film thickness. Equations (5.1.9) and (5.1.10) should apply equally well for either

constant heat flux or constant wall temperature boundary conditions. Dukler (1972)

presented that the surface of waves on a falling film appear at liquid film Reynolds

number greater than 16.

By observing the higher values for the Nusselt number provided by the correlation of

Chun and Seban (1971), rather than predicted by Nusselt’s solution in the laminar

region and by observing the variation of the Seban’s (1971) correlation in laminar

region for a higher Prandtl number, Alhusseini et al. (1997) presented that even in the

laminar region, Nu is effected by an additional dimensionless number besides

Reynolds number, Re. They showed that the surface wave governed by surface,

viscous and body forces, enhances heat transfer beyond that predicted by Nusselt

theory for smooth laminar films. By dimensional analysis they showed that the Nusselt

number should be dependent upon both Reynolds number and the Kapitza number

(Ka) where, 3

4

ρσµ gKa = . They got the data with fair agreement with Chun and Seban

(1971) correlation for water with a maximum deviation of 30% for laminar and

turbulent regions. In this experiment they used the tube of 2.9 m which is greater than

that used by Chun and Seban of 0.3m. So they demanded that their experiment was in

Page 89


fully developed thermal conditions. Based on the new and extended experimental data

for laminar falling films, the following dimensionless correlation was proposed by

them for the evaporative heat transfer Nusselt number in the wavy laminar region,

0563.0158.0

3.12

* Re65.2 Kak

gh

Nuh =⎟⎟⎠

⎞⎜⎜⎝

⎛

==

υ

(5.1.12)

The effect of the vertical spacing between two consecutive horizontal tubes in the

evaporator was studied and demonstrated experimentally by Liu (1975). By

considering the effect of the diameter of horizontal tube (D) and the vertical distance

between two consecutive tubes (H), Owens (1978) developed new correlations for

horizontal tube falling film heat transfer coefficients for both laminar and turbulent

flow. The mathematical formulations of his correlations are shown bellow:

Laminar: 31

1.0

3.12

42.2−

⎟⎟⎠

⎞⎜⎜⎝

⎛ Γ⎟⎠⎞

⎜⎝⎛=

⎟⎟⎠

⎞⎜⎜⎝

⎛

=µ

υ

DH

k

gh

Nu (5.1.13)

Turbulent: ( ) 5.01.0

3.12

Pr185.0 ⎟⎠⎞

⎜⎝⎛=

⎟⎟⎠

⎞⎜⎜⎝

⎛

=DH

kg

hNu

υ

(5.1.14)

To find out the transition Reynolds number, one mathematical formulation was also

provided as shown in equation (5.1.15).

5.1Pr1680Re −=Trsns (5.1.15)

In addition, Mitrovic (1986) showed that the water-feed system geometry does not

affect the heat transfer coefficient on a horizontal tube.

By considering all factors, two correlations were developed for the heat transfer

coefficient for both the tube wall to the bulk solution and bulk solution to the interface.

Page 90


No correlation is needed for the value of mass transfer coefficient from the interface to

air as it didn’t vary too much, as described in section 5.1.3. The mass transfer

coefficient can be calculated directly from the basic equation of heat and mass transfer

at that regime. The process of calculation of this coefficient from the basic equation

and the comparison of the values predicted by this method and by the program has

been done and shown in Appendix-F. As the mass transfer coefficient is calculated

directly from the heat transfer coefficient from interface to air, the same opinion can be

applied for heat transfer coefficient from the interface to air.

Correlation for the tube wall to the bulk solution

From the above discussion, it can be said that the heat transfer coefficient depends on

the following variables

( DHkghh ,,,,,,, σµρΓ= ) (5.1.16)

For the calculation of heat transfer, an average value of temperature was chosen due to

the small variation of the temperature and the values of different thermal properties

like kinematic viscosity, thermal conductivity and other properties were considered

constant. The effects of Prandtl number and Kapitza number have been neglected with

the solution flow rate for the experimental conditions. By dimensional analysis, for the

development of the correlation, following primary equation can be proposed for the

wavy laminar flow.

For the region tube wall to the bulk solution

11Re1

31

2

cb

i

i DHa

k

gh

Nu ⎟⎠⎞

⎜⎝⎛=

⎟⎟⎠

⎞⎜⎜⎝

⎛

=

υ

(5.1.17)

Page 91


For the region of the bulk solution to the interface

22Re2

31

2

cb

o

o DHa

k

gh

Nu ⎟⎠⎞

⎜⎝⎛=

⎟⎟⎠

⎞⎜⎜⎝

⎛

=

υ

(5.1.18)

where, are constant. H is the distance between two consecutive

tube surfaces, which was 6mm and D is the nominal diameter of each tube was 19 mm.

From the analysis of the data the following values of the constants were found as

follows:

211121 ,,,,, ccbbaa

1.01.01097.01432.0

3976.0487.0

21

21

21

==−=−=

==

ccbbaa

(5.1.19)

5.5 Comparison of the simulated data with different models from literature

The comparisons of the experimental data with the computations using models of four

other researchers have been made. The source and the experimental conditions for

these researchers are listed in details in Table 5.4. Even though a brief description of

their work was highlighted in the literature review sections of the Chapter 2, the

graphical comparison has been demonstrated in Figures 5.18 and 5.19.

Page 92


Table 5.4 Experimental studies on falling film evaporation of water

Author Year Heating Method

Heating Length, (m)

Test Fluid

Reynolds Number Range

Prandtl’s Number Range

Flow Regimes

Chun & Seban

1971 Electrical 0.29 Water 320-21,000

1.77-5.7 Laminar& Turbulent

Fujita & Ueda

1978 Electrical 0.6-1.0 Water 700-9,100

1.8-2.0 Turbulent

Shmerler & Mudawwar

1988 Electrical 0.78 Water 5,000-37,500

1.73-46.6 Turbulent

Alhusseini et al.

1995 Electrical 2.9 Water 34-15,600

1.73-46.6 Laminar& Turbulent

Present study

2004 Hot water

1.57 Water 234-1154 4.0-6.0 Wavy Laminar

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

200 400 600 800 1000 1200

Chen & SebanNusselt solnmodified NusseltOwensPresent study

µΓ

=4Re

Figure 5.18 Graphical comparison of the Nusselt number from tube wall to the bulk solution with the studies of different researchers

From Figures 5.18 and 5.19 it is seen that the value of non dimensional heat transfer

coefficients is decreasing with the non dimensional solution Reynolds number. Unlike

Page 93


other researchers as two heat transfer coefficients were considered within the solution

itself, the values for both coefficients are compared with others. The variations of both

tube wall to the solution and the solution to the interface heat transfer coefficients are

found to be nearly same as shown in Figures 5.18 and 5.19.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

200 400 600 800 1000 1200

Chen & SebanNusselt solnmodified NusseltOwensPresent study

µΓ

=4Re

Figure 5.19 Graphical comparison of the bulk solution to the interface Nusselt number with the studies of different researchers.

Page 94

Chapter-6 Numerical Analysis and Discussion

NUMERICAL A N

A numerical investigation had bee

effects of different field variable

This analysis and discussion in

temperatures of all fluids, the mas

the moisture content of air and a

absorber along the vertical length

find the exact variation and the

achieve the detail values of differ

the evaporator heat exchanger wa

absorber arrangements were used

a tube. The vertical length of the e

area by multiplying by the width.

both models were described in Ch

6.1 Variation of the variables o

simplified model

To describe the variation of diffe

contents, the topmost evaporator

point.

The characteristic variation of th

values of overall heat transfer coe

CHAPTER 6

NALYSIS AND DISCUSSIO

n performed to provide a better understanding of the

s involved in the process of heat and mass transfer.

clude the influence of the variation of different

s flow rate of the distributed water, the enthalpy and

ir-vapor mixture at different location of the tubular

. Both detailed and simplified models were used to

values obtained by both models were compared. To

ent parameters along the length, the vertical height of

s divided into 24 segments. As 24 horizontal tubular

in the experimental setup, each segment represented

xchanger was replaced and expressed in terms of the

The details calculation and simulation processes for

apter 5.

f all fluids with area by both detailed model and

rent temperatures, flow rates, enthalpy and moisture

heat exchanger pipe was considered as a reference

e temperatures is shown in Figure 6.1 for a set of

fficient from hot water to distributed water, U.

Page 95


15.00

20.00

25.00

30.00

35.00

40.00

45.00

50.00

0.00 0.05 0.10 0.15 0.20 0.25

Area, m2

Tem

pera

ture

, 0C

Tc TwTa Tif

Figure 6.1 Variation of different fluid temperature with area. [U=0.71 kW/m2K, ha=0.019 kW/m2K, hwo=3.14 kW/m2K, and Ka=0.0189 kg/m2sec].

Along with Figure 6.1, Figures 6.2, 6.3, 6.4 show the typical variation of the

temperatures including hot water, distributed water, air and air-vapor mixture. From

the variation of the hot water and the distributed water temperature (Figure 6.1), the

characteristics of the counter flow processes is clearly demonstrated and established.

The hot water temperature increases along the distance from the top to the bottom of

the evaporator, as shown in Figures 6.1 and 6.2.

Page 96


15.00

20.00

25.00

30.00

35.00

40.00

45.00

50.00

0.00 0.05 0.10 0.15 0.20 0.25

Area, m2

Tem

pera

ture

, 0C

At Tc,in=44.20C,U=0.7,ha=0.016,Ka=0.0145At Tc,in=39.60C,U=0.77,ha=0.017,Ka=0.016At Tc,in=41.02 C,U=0.89,ha=0.024,Ka=0.022

Figure 6.2 Variation of hot water temperature with area by simplified model.

The temperature of hot water, which enters at the bottom and leaves at the top

decreases as it flows through the evaporator pipe. Whereas distributed water flows in

opposite direction, entering the evaporator at the top and leaves at the bottom; the

temperature of this water is increased with the direction of its flow, as shown in

Figures 6.1 & 6.3.

According to the Figure 6.1, the differences between the hot water temperature and the

distributed water temperature at any horizontal tube are nearly the same throughout the

path. It means that the heat transfer process was nearly homogeneous over the entire

area of the evaporator.

From Figure 6.1 it is clearly observed that the interface temperature was dominated by

the temperature of the distributed water. This may be because of the lower values of

Page 97


heat transfer coefficients from interface to air and the interface region was very near to

the distributed water. And from the deflection it can be said that the heat transfer in the

interface region over the entire area was also uniform with the temperature of

distributed water.

15.00

20.00

25.00

30.00

35.00

40.00

45.00

50.00

0.00 0.05 0.10 0.15 0.20 0.25

Area, m2

Tem

pera

ture

, 0C

At Tw,in=31.55C,U=0.70,ha=0.016,Ka=0.0145At Tw,in=34.37C,U=0.83,ha=0.024,Ka=0.021At Tw,in=37.67C,U=0.88,ha=0.023,Ka=0.019

Figure 6.3 Variation of distributed water temperature with area by simplified model at different inlet temperature of distributed water

Page 98


16.00

18.00

20.00

22.00

24.00

26.00

28.00

30.00

0.00 0.05 0.10 0.15 0.20 0.25

Area, m2

Tem

pera

ture

, 0C

Ta,in=24.09 deg. CTa,in=23.82 deg. C Ta,in=24.85 deg. C

Figure 6.4 Variation of air temperature with area by detailed model for different inlet temperature of air

From Figures 6.1 and 6.4, the typical variation of the air temperature can be observed.

At the time, when it enters into the evaporator chamber through the bottom side, the

temperature of the air was nearly equal to the temperature of the atmosphere. As it

experiences more heat from the interface while flowing over the film, the temperature

of this air increases and, at exit from of the chamber, its temperature became always

higher than that at the inlet. The difference between the exit temperature and the inlet

temperature of the air varies approximately between 3 and 5 °C for the whole process

as most of the heat was used for evaporation processes.

Page 99


0.00

0.01

0.01

0.02

0.02

0.03

0.03

0.04

0.04

0.05

0.05

0.00 0.05 0.10 0.15 0.20 0.25

Area, m2

Moi

stur

e co

nten

t, kg

/kg

of d

ry a

ir

wwif

Figure 6.5 Variation of moisture content of air and air-vapor mixture with area

The typical variation of the moisture content of the air and interface mixture is shown

in Figure 6.5 as well as in Figure 6.6. As the evaporated water vapor is taken by the

air, the moisture content of the air increased with the flow of air from the bottom of the

evaporator to the top.

On the contrary, at the air-vapor interface, the moisture content of the mixture at the

bottom side of the evaporator is very much higher than that of the mixture at the top

portion. This may be because the interface temperature is dominated by the

temperature of the distributed water and as the moisture content is a function of the

temperature, the value of the moisture content of the mixture will increase as the

distributed water temperature increases along the top to the bottom of the evaporator.

Page 100


0.010

0.012

0.014

0.016

0.00 0.05 0.10 0.15 0.20 0.25

Area, m2

Moi

stur

e co

nten

t, kg

/kg

of d

ry a

ir

w,in=0.010749 kg/kg of dry airw,in=0.010841 kg/kg of dry airw,in=0.011046 kg/kg of dry air

Figure 6.6 Variation of moisture content of air with area for different inlet moisture content [detailed model].

At the first control element, the moisture of the interface was assumed equal to the

moisture of air and it experiences its exact value for the first time at the second control

segment. Thus, the first portion of the profile for the interface moisture variation was a

sudden change from the presuming value to the actual value in the next control

element as depicted in Figures 6.5 and 6.9.

Figure 6.7 reveals the fact that, with the increasing of the area of the evaporator, the

mass flow rate of distributed water decreases. As the distributed water flowing from

the top to bottom of the evaporator over the horizontal tube it takes heat from the hot

water, attaining the saturation temperature and the water evaporated from the outer

surface of the distributed water mixes with the air flowing over it. Thus, the thickness

of the film, in other words the mass flow rate of the distributed water decreases as the

Page 101


flow approaches the last tube. The variation of this mass flow rate was not too sharp

due to the lower value of evaporation mass transfer coefficient.

0.0291

0.0292

0.0293

0.0294

0.0295

0.0296

0.00 0.05 0.10 0.15 0.20 0.25

Area, m2

Solu

tion

Mas

s flo

w ra

te, k

g/se

c

(A) (B)(C) (D)

Figure 6.7 Variation of mass flow rate of distributed water with area, at different experimental conditions for inlet mass flow rate 0.029508 kg/sec [(A): Tw,in=31.58 o C,

(B): Tw,in=34.68 o C, (C): Tw,in=34.46 o C, (D): Tw,in=37.58 o C,]

The enthalpy of the air is a function of the temperature as well as the moisture content

of the air. From Figure 6.8, the variation of the enthalpy of the air is seen, where it

decreases with area very sharply. This may be because of the higher temperature and

moisture content of the air at the outlet of the evaporator than that at the inlet.

Page 102


40.00

50.00

60.00

70.00

0.00 0.05 0.10 0.15 0.20 0.25

Area, m2

Enth

alpy

of a

ir, k

J/kg

At Ta,in=23.82 deg. CAt Ta,in=24.07 deg. CAt Ta,in=24.09 deg. CAt Ta,in=23.89 deg. C

Figure 6.8 Variation of enthalpy of air with area

50

70

90

110

130

150

170

0.00 0.05 0.10 0.15 0.20 0.25

Area, m2

Enth

alpy

, kJ/

kg

(a) (b) (c)

Figure 6.9 Variation of enthalpy of interface with area [(a): Tw, in=31.58 o C,

(b): Tw, in=32.11 o C, (c): Tw, in=34.64 o C,]

Page 103


Figure 6.9 shows the variation of the enthalpy of interface for three different sets of

experimental conditions. As described earlier in Figure 6.5, the interface enthalpy

increases as it travels through the evaporator and reaches the bottom tube, and the

magnitudes depend on the temperature and the moisture content of the interface.

6.2 Numerical comparison of detailed model and Simplified model

The detailed model was able to exhibit the variation of the temperature of hot water,

distributed water, air and air-vapor mixture along with the variation of moisture

content of air and air-vapor mixture. In addition, the variation of the enthalpy for the

air can be successfully plotted from the detailed model. On the other hand, the

simplified models was able to show the variations of all important variables as

mentioned earlier except, the variation of air temperature and moisture content of the

air vapor mixture. Besides that, this model was able to show not only the variation of

the enthalpy of air but also that of air vapor mixture. As a result, the numerical

comparison of both detailed model and simplified model was done on the basis of the

above noted information.

In Figure 6.10, the deviation between the temperatures measured by detailed model

and the simplified model can be observed for hot water, distributed water and air-

vapor mixture for a set of experimental condition. It is clearly seen from the profiles

that the temperatures for any fluid measured by both models at any corresponding

positions are nearly same along the vertical length of the heat exchanger. It means that

the value of the heat transfer coefficients at this regime for both models will be equal.

In Chapter 5, the heat transfer coefficients values were established and compared for

different experimental condition for both models.

Page 104


25.00

30.00

35.00

40.00

45.00

0.00 0.05 0.10 0.15 0.20 0.25

Area, m2

Tem

pera

ture

, 0C

Tc (detailed model)Tw (detailed model)Tif (detailed model)Tc (simplified model)Tw (simplified model)Tif (simplified model)

Figure 6.10 Variation of the temperatures with area at U=0.70 kW/m2K, ha=0.016 kW/m2K, Ka=0.0145 kg/m2K

40.00

45.00

50.00

55.00

60.00

65.00

70.00

0.00 0.05 0.10 0.15 0.20 0.25

Area, m2

Enth

alpy

of a

ir, k

J/kg

Ha (Detailed model)Ha (Simplified model)Ha (Detailed model)Ha (Simplified model)

Figure 6.11 Variation of the enthalpy of air with area, by detailed and simplified model

Page 105


A different scenario is seen in Figure 6.11, where the variation of the enthalpy of the

air for two different sets of experimental conditions is plotted by using both detailed

model and simplified model. From this Figure, it can be clearly observed that the

variation of the enthalpy by simplified model shows slightly higher values than that

measured by detailed model over the entire area. It means that, the values of heat

transfer coefficients for the interface to air for simplified model were predicted smaller

than that of detailed model. This may be attributed to the variation of process

equations used by the models for the calculation of enthalpy of air. In detailed model,

the calculation was carried out directly by using the equations established in the

psychometric chart; on the contrary, in simplified model, a trial and error approach

was used to calculate the interface temperature and enthalpy, and then the enthalpy of

the air was calculated from the differential equation by using this value of the interface

enthalpy. Due to the higher prediction of the value of heat transfer coefficient from

interface to air by the simplified model, the mass transfer coefficient will also be

higher in this model rather than that of detailed model. The mass transfer coefficients

for both models were calculated from the heat transfer coefficient by dividing it by the

specific heat of moisture which was used as 1.005kJ/kg K. The variation of the heat

and mass transfer coefficients for both models was not appreciable.

Page 106

Chapter-7 Analysis of absorbers using linearized model

ANALYSIS OF ABSOR

In practice, beside the falling fil

mass transfer process, the absorpt

evaporation, is considered and us

features regarding the environme

are becoming viable alternatives

applications. Unlike the evapora

absorbed by the solution in a cont

one of the most essential compo

mainly occurs. Thus, the improve

considerations for improving the p

have been developed and extensiv

better understanding of the absorp

water vapor in the falling film of

heat and mass transfer coefficient

Moreover, design studies are ne

practical absorbers.

The concept of considering two h

in the evaporation process in C

simplified model was used earlier

Chapter, by using the experiment

bromide as the solution and, by u

CHAPTER 7

BERS USING LINEARIZED MODEL

m evaporation process, another important heat and

ion, which is more or less the reverse process of the

ed to a great extent. Due to some of its attractive

nt and power used, absorption refrigeration systems

to vapor compression systems in air conditioning

tion process, in this process, the water vapor is

rolled lower pressure atmosphere. So, the absorber is

nents in this system, where the absorption process

ment of the absorber is one of the most important

erformance of the system. Many theoretical models

e experimental works have been performed to gain a

tion process. However, the process of absorption of

the working fluid and the estimation of the actual

s from experimental data need further investigation.

eded for the improvement of the performance of

eat transfer coefficients within the solution, as used

hapter 4, for deriving the detailed model and the

for absorption process by Islam et al. (2002). In this

al data of a vertical tube absorber that used lithium

sing the liniearized model developed by Islam et al.

Page 107


(2002), the estimation of the heat and mass transfer coefficients were performed to

have an idea about the heat transfer coefficients in the processes either absorption or

the evaporation.

7.1 Linearized Model

The coupled heat and mass transfer model presented by Islam et al. (2002), which

embodied the theoretical approach of the Patnaik et al.(1993), Tsai and Perez-Blanco

(1998) and Grossman (1983), was used in the present analysis.

Figure 7.1 Physical models for counter flow absorber

In Figure.7.1 the counter flow absorber is represented schematically. All heat and mass

transfer coefficient (vapor-liquid interface to solution, solution to tube wall and overall

Coolant .com

Tco

Solution film

m .sVapor

Ts is

δmv .

ho hi hco

Ko δA

iv

m +δm .s

.s

A

Ts+δTs is+δis

.com

Tco+δTco

Page 108


from solution to coolant) were studied by Grossmann (1983) for a laminar falling film

using an analytical model. Applying the conservation laws of mass and energy to the

elemental control volume shown in Figure 7.1, the following governing equations were

obtained.

For the coolant

The lithium bromide solution flow over the pipe from the top to the bottom of the

absorber; whereas the coolant flows inside the tube of the absorber. As described in

Chapter 4, by considering the tube wall as a flat plate, i.e. coolant flows in one side of

the plate and solution flows in the other side of the plate in counter flow direction as

demonstrated in Figure 7.1 the energy equation for the coolant can be written as,

( cosco

coco TTUdA

dTcm −−=

.) (7.1.1)

where, U is overall heat transfer coefficient from the bulk solution to the coolant.

The energy conservation equation for the solution was obtained by following the

derivation of Tsai and Perez-Blanco (1998). The energy balance for the elemental

control volume, shown in Figure 7.1, gives:

( ) ( ) ATTUiimmimim cosssssvvss δδδδ −+++=+ )(....

(7.1.2)

Mass balance

Total mass of vapor absorbed by the solution will be equal to the total mass of the

solution increased which can be expressed as,

)(....ssvs mmmm δδ +=+ (7.1.3)

Page 109


The change in enthalpy of the solution can be expressed Islam et al. (2002) in the form

of

.''sxssos XcTcci ++= (7.1.4)

It was assumed that the heat and mass transfer coefficients were suitably scaled to

have a common heat transfer area dA. Using (7.1.3), the mass balance for the film can

be expressed in the form:

( sifos XXK

dAmd

−=

.

) (7.1.5)

In order to linearize (7.1.5), the following condition for the LiBr flow rate was

invoked.

( ) .1..

constXmm ssl =−= (7.1.6)

Over the relatively small temperature range experienced by the solution, the

equilibrium relation between the interface temperature and mass fraction of water at

constant pressure was expressed in the linear form, Patnaik (1993).

ifif bTaX −= (7.1.7)

By defining two new variables for the temperature difference and the mass fraction

difference, the governing equations could be reduced to two coupled linear differential

equations. These new variables were defined as

cos TT −=θ (7.1.8)

ss XbTa −−=ψ (7.1.9)

The temperature difference, θ between the bulk solution and the coolant is

proportional to the heat flux. And ψ is the difference between the bulk solution mass

fraction and the equilibrium mass fraction corresponding to local solution temperature,

Ts, which is proportional to the mass flux.

Page 110


The reduced equations are

ψθθ13 gg

dAd

+−= (7.1.10)

and βψθψ12 gbg

dAd

−= (7.1.11)

where, the coefficients are given by

),/1)](/([ '.

1 vsxssvsef ficcmiKg −= (7.1.12)

,11

o

v

oef hbi

KK+= (7.1.13)

,.2

ss cm

Ug = (7.1.14)

,..3

cocss cm

U

cm

Ug −= (7.1.15)

and

⎟⎟⎠

⎞⎜⎜⎝

⎛−

⎟⎟⎠

⎞⎜⎜⎝

⎛−+

=

vs

x

vs

x

vs

s

fic

fibc

fIc

b

'

'

1

β (7.1.16)

The overall heat transfer coefficient from the solution to the coolant can be expressed

as:

w

w

ico khhUδ

++=111 (7.1.17)

And the solution of equations (7.1.10) and (7.1.11) are obtained as:

( ) AA eaeaA 2121

ααθ += (7.1.18)

and, (7.1.19) ( ) AA ebebA 2121

ααψ +=

where, the roots of the characteristic equations are:

( ) ( ) ( )[ ]21

2312

131321 45.05.0, bggggggg −−+±+−= βββαα (7.1.20)

Page 111


The coefficients are given by:

( )[ ] ( 21101101 / )ααψβαθ −++= gga (7.1.21)

( )[ ] ( )12101202 / ααψβαθ −++= gga (7.1.22)

( )[ ] ( 21203101 / )ααθαψ −++= bggb (7.1.23)

( )[ ] ( )12203202 / ααθαψ −++= bggb (7.1.24)

where, θ0 and ψ0 are the values at A=0.

The above solutions are used to ‘extract’ the heat and mass transfer coefficients from

the experimental data reported recently in literature Miller (1998) for a vertical tube

absorber. The values of the variables, θ and ψ, at the inlet and outlet of the test

absorber can be calculated directly from the measured temperatures of the solution and

the cooling water and the water mass fractions of the solution. All other parameters

such as cs, cx’ , a, b and ivs were obtained from data sources which can be found from

Islam (2002 b). This leaves U and Kef as the only unknowns in equation (7.1.18) and

(7.1.19) which can be determined by solving these simultaneously using the Newton–

Raphson method, Stoecker (1989) or Iterative method. It should be noted that, because

ho and Ko were embedded in Kef in the equation (7.1.13), their individual values can be

obtained only by invoking a condition such as the heat and mass transfer analogy in

the form.

n

s

sScD

KKh

⎟⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=

Pr

0

0 (7.1.25)

where Pr and Sc are the Prandtl number and Schmidt numbers, respectively.

Page 112


7.3 Simulation

Miller (1998) presented detailed experimental data for a vertical tube absorber. For the

heat and mass transfer tests, a single stainless steel absorber tube of 0.01905 meter

outer diameter and 1.524 meter length, was used. The lithium bromide brine was used

at a mass fraction of 0.62.

Prior to entering the solution into the absorber the strong solution was tempered by a

tube in tube heat exchanger. A coolant flowing countercurrent to the falling film and

supports the coupled heat and mass transfer process, as the falling film of strong

solution absorbs the water vapor in the LiBr salt. The weak solution was gravity fed

from the absorber to the sump tank. The weak solution was pumped from the sump

and was injected into the boiler. The water was desorbed from brine by using a heater

of 2.5 kW capacities in the boiler. As a result, the brine becomes stronger in LiBr salt,

and the strong solution was used as the falling film in the absorber. To trim the flow of

the vapor, coming from the boiler to the absorber and to tune the vapor pressure within

the absorber, a linear gate valve was used.

In total, 26 sets of data from Miller (1998), at three different pressures were selected

for the analysis. To simulate these data a computer program was written in

FORTRAN. To extract the heat and mass transfer coefficients and other important

variables an iterative method was used in the program. The program code was able to

predict and to show the variation of different temperatures, concentrations, heat flux,

mass of water vapor absorbed etc. with the design parameters of the absorber, such as,

solution flow rate and area of the absorber. The variation of different heat and mass

transfer coefficients with the solution flow rate can also be found by using the code.

Finally, the variation of Films Nusselt number and the films Sherwood number with

Page 113


the film Reynolds number can be observed and correlated. The code was also able to

check the sensitivity of the heat and mass transfer coefficient to the enthalpy of

absorption and with the index, n in the relation (7.1.25) of heat and mass transfer

analogy.

7.4 Results and discussion

The result includes data from 26 sets of experimental runs for which the range of

conditions and parameters for the model are summarized in Table 7.1.

Table 7.1 Range of experimental conditions and variables

Variables Range

.sm in(kg s-1)

1.5×10-2-2.57×10-2

Ts in(°C) 52.7-58.1

Xs in 0.3764

.com (kg s-1)

6.25×10-2-6.59×10-2

Tco in (°C) 34.84-35.24

Ivs (kJkg-1) 2444.688-2449.346

cs (kJkg-1K-1) 1.866904-1.872599

c′x (kJkg-1) 556.751-574.1659

a 0.642-0.664

b(°C-1) 0.00485-0.00491

f 1.608726-1.613879

U(kWm-2 K-1) 0.78-0.99

Kef(kgm-2s-1) 0.052-0.092

Page 114


The heat transfer coefficient, U varies from 0.78-0.99 kWm-2K-1 and the mass transfer

coefficient Kef varies from 0.052-0.092 kgm-2s-1. From literature Islam et al. (2002), it

is seen that the value of heat transfer coefficient varies from 0.2 to 2.0 kWm-2K-1 and

the mass transfer coefficient varies from 0.01 to 0.09 kgm-2s-1 for different models

provided by the researcher for nearly the same range of experimental conditions.

The value of heat transfer coefficient for coolant, hc was obtained from Dittus-Boelter

correlation for flow in a tube and using that value of hc, the value of solution to tube

wall heat transfer coefficient, hi was calculated from equation (7.17).

0

5

10

15

20

25

0 0.03 0.06 0.09Area, m2

Tem

pera

ture

diff

eren

ce, °

C

(a)(b)(c)

Figure 7.2 Variation of Temperature difference,θ with absorber area (a) Tsin=53.6 °C and Tcoin=35.17 °C (b) Tsin=55.0 °C and Tcoin=35.07 °C (c) Tsin=57.9 °C and

Tcoin=34.94 °C.

The variation of different temperatures with area is shown in Figures 7.2 and 7.3. As

expected, according to the Figure 7.2, due to the linear relationship between

Page 115


temperature difference, θ and solution temperature, for a constant coolant inlet

temperature, lower solution inlet temperatures lead to a reduction of the value of

temperature difference, θ.

The cooling water temperature distribution was calculated by integrating equation

(7.1.1) after substituting for (Ts-Tco) from equation (7.1.17).

20

30

40

50

60

0 0.03 0.06 0.09Area, m2

Tem

pera

ture

, °C

coolantsolutioninterface

Figure 7.3 Variation of solution, coolant and interface temperature with area, at Tco,in= 35 °C and Ts,in= 53.6 °C.

From Figure 7.4, it is seen that, for a constant coolant inlet temperature, with the

increase of the solution inlet temperature the value of mass fraction difference is

increased.

Page 116


0.000

0.010

0.020

0.030

0.040

0.050

0 0.03 0.06 0.09Area, m2

Mas

s fra

ctio

n di

ffer

ence

(a)(b)(c)

Figure 7.4 Variation of mass fraction difference,ψ with area. (a) Tsin=53.6 °C and Tcoin=35.17 °C (b) Tsin=55.0 °C and Tcoin=35.07 °C (c) Tsin=55.5 °C and Tcoin=35.12

°C.

50

54

58

62

66

0 0.03 0.06 0.09

Area, m2

Con

cent

ratio

n, (%

)

(A)(B)

Figure 7.5 Variation of concentration with area, at Tco,in= 35 °C and Ts,in= 53.6 °C. (A) for experimental solution concentration, (B) solution concentration at solution to vapor

interface.

Page 117


Another comparison between the concentration of the solution at the solution and at

the interface is made in Figure (7.5). It is seen that the concentration at the interface

decreases more sharply than that of at the solution.

0.00

1.00

2.00

3.00

4.00

0.01 0.015 0.02 0.025 0.03

Solution flow rate, Kg/sec

Hea

t tra

nsfe

r coe

ffic

ient

,kW

/m2 .K

Hi Ho U

Figure 7.6 Variation of overall heat transfer coefficients with solution mass flow rate at Ts,in=53.6 ° C and Tco,in= 35 ° C. (U) overall , (Hi) solution to tube wall. (Ho)

interface to bulk solution.

Figures 7.6 and 7.7 show the variation of heat transfer and mass transfer coefficient,

respectively, with solution flow rate. From these Figures, it is clear that, with the

increase of solution flow rate, the heat transfer coefficient decreases; whereas the mass

transfer coefficient is found highest for a moderate solution flow rate of 0.02 kg/sec for

a constant solution and coolant inlet temperature. The value of mass transfer

coefficient is found to be nearly 0.06 kg/m2s, which is a little higher than that

described by Tsai and Perez Blanco (1998).

Page 118


0.00

0.03

0.06

0.09

0.12

0.15

0.01 0.015 0.02 0.025 0.03Solution flow rate, Kg/sec

Mas

s tra

nsfe

r coe

ffic

ient

, Kg/

m2 sec Kef

Ko

Mas

s tra

nsfe

r coe

ffic

ient

, kg/

m2 .s

Figure 7.7 Variation of mass transfer coefficient with solution mass flow rate at Ts,in=53.6 ° C and Tco,in= 35 °C. (Kef) overall and (Ko) interface to bulk solution.

The variation of Nusselt Number, Nu (for both solution to tube wall and interface to

bulk solution) with the film Reynolds Number, Re with their correlating equation can

be observed from Figure 7.8. From Figure (7.9), the variation of film Sherwood

Number, Sh with the film Reynolds Number, Re is observed with their correlating

equation. For Figure 7.8 the Nu number for interface to bulk solution shows with

scatter. Similar nature of scatter is also observed in Figure 7.9. This may be attributed

to experimental uncertainty as well as nature of correlations used.

Page 119


Nui = -0.2595Ln(Re) + 1.9568

Nuo = -0.0721Ln(Re) + 1.2556

0.00

0.40

0.80

1.20

1.60

150 200 250 300 350 400

Reynolds Number, Re

Nus

selt

Num

ber,

Nu

(a)(b)

Figure 7.8 Variation of film Nusselt Number ( Nu ) with the film Reynolds Number, Re. (a) solution to tube wall (b) interface to bulk solution.

Sho = -0.3148Ln(Re) + 5.5202

Shef = -0.2371Ln(Re) + 4.1123

0.00

2.00

4.00

6.00

8.00

150 200 250 300 350 400

Reynolds Number, Re

Sher

woo

d N

umbe

r,Sh

(a)(b)

Figure 7.9 Variation of film Sherwood Number, Sh with the film Reynolds Number, Re. (a) effective (b) interface to bulk solution

Page 120


In the equation of heat and mass transfer analogy, the value of the index, n was

assigned 0.33. By varying the value of n for 0.33, 0.4, 0.5 and 0.6, the effect was

observed, which is shown in Table 7.2. It was seen that, with the increase of n, the heat

transfer coefficient from interface to bulk solution decrease; whereas the mass transfer

coefficient increases up to a maximum value of 0.2 kgm-2s-1.

Table 7.2 Effect of index, n

n ho (kWm-2K-1) ko (kgm-2s-1)

0.33 2.55-5.02 0.070-0.138

0.4 2.06-4.06 0.076-0.150

0.5 1.55-3.07 0.09-0.177

0.6 1.30-2.44 0.111-0.219

The sensitivities of transfer coefficients to the variation of enthalpy of absorption were

also checked. The range of all variables and transfer coefficients, as shown in Table

7.2, are for the range of enthalpy of absorption of 2444.6 to 2449.3 kJkg-1; and it is

seen from Table 7.3, that, if the temperature of the solution is considered as the

interface temperature, the range of enthalpy of absorption does not exceed the actual

range.

Page 121


Table 7.3 Effect of ivs

Temperature (°C) ivs (kJkg-1)

Experiment temperature 2444.688-2449.346

Interface temperature 2448.306-2449.360

The coupled heat and mass transfer model was used to analyze the experimental data

obtained from a vertical tube absorber. The heat transfer coefficient was nearly 0.8

kWm-2K-1 and the mass transfer coefficient was nearly 0.06 kgm-2s-1. The variation of

different field variables such as temperature difference (θ), mass fraction difference

(Ψ), solution and coolant temperature and solution concentration were investigated and

correlation for Nusselt Number, Sherwood Number have been established as follow:

Nuo=-0.0721 Ln (Re)+1.2556

Nui=-0.02595 Ln (Re)+1.9568

Sho=-0.3148 Ln(Re)+5.5202

Shef=-0.2371 Ln(Re)+4.1123

The effects of enthalpy of absorption and heat and mass transfer analogy index were

also analyzed.

Page 122

Conclusions

C

A falling film evaporation system

fabricated, and tested. A series

operating conditions. Mathemati

within the solution itself have bee

evaluate the effect of different

finally, compared with simulation

the same concept in the linearize

transfer coefficients were calcu

experimental and analytical study

1. In the experimental set-up

The working fluid, called

28 o C to 38 o C, and the he

to 55 o C. The inlet temper

2. Two heat transfer coeffic

from tube wall to the bul

interface. In the model, th

the falling film, U and th

well as the mass transfer c

CHAPTER 8

ONCLUSIONS

using the horizontal tube evaporator was designed,

of experiment have been conducted under different

cal models by using two heat transfer coefficients

n formulated. Experimental results were analyzed to

parameters on the performance of evaporator and,

results and a good agreement was found. By using

d model, the falling film absorption heat and mass

lated for a vertical tube absorber. The detailed

led to the following conclusions.

, a 24 row horizontal tubular evaporator was used.

a falling film, had a water temperature ranging from

ating fluid was also water of temperature from 40 o C

ature of the air was the ambient temperature.

ients were considered within the falling film, one

k solution and another from the bulk solution to the

e overall heat transfer coefficient from hot water to

e heat transfer coefficient from interface to air ha as

oefficient, Ka were calculated.

Page 123

Conclusions

3. The experiments were conducted within the wavy laminar flow regimes, The

calculated heat transfer coefficients ranged from 0.7 to 1.1kW/m2K for overall

heat transfer coefficient, U, 0.9 to 5.5kW/m2K for bulk solution to interface.

The heat transfer coefficient from interface to air varied from 15 W/m2K to 25

W/m2K and the mass transfer coefficient from 0.014 to 0.024 kg/m2s.

4. The heat transfer coefficient from hot water to bulk solution increased with the

increases of inlet temperature of falling film and hot water, mass flow rate of

falling film, hot water, and air. In contrast, while the mass transfer coefficient

increases with the increases of mass flow rate of hot water and air, and with the

temperature of hot water; it decreases with the increase of inlet temperature and

flow rate of falling film.

5. The heat transfer coefficients from tube wall to the bulk fluid and bulk fluid to

the interface were correlated with the solution flow rates and with the physical

properties of the evaporator. Comparison for these correlations was made with

the correlations available in literature.

6. Numerically, the variations of the mass flow rate of falling film and the

temperatures of hot water, falling film, air, and interface were made along the

vertical distance of the evaporator. The temperatures of hot water and the mass

flow rate of falling film decreased along their individual flow direction. The

temperatures of falling film and air increased with their flow direction.

Page 124

Conclusions

7. The analysis of the vertical tube absorber by using the linearized model was

performed. The values for overall heat transfer coefficients were found to vary

from 0.7 to 1.0 kW/m2k. The mass absorption rate varied between 0.052 and

0.092 kg/m2s. Two correlations, one for heat transfer coefficients and the other

for mass transfer coefficient were developed.

Page 125

Recommendations

The evaporatio

present study b

comparing the

the following re

• As men

accurate

Initiativ

• The eva

nominal

understa

made by

• For cu

tempera

study ca

RECOMMENDATIONS FOR FURTHER

n process in a falling film evaporator has been investigated in the

y conducting the experiments, formulating the analytical model and

experiment results with the simulation results. At the end of the study

commendation could be drawn.

tioned in Chapter 5, several attempts had been taken to get the more

values of the heat transfer coefficient from falling film to interface.

es should be taken to find out this coefficient more exactly.

porator tube that was used in this case was made of copper pipe having

diameter 19 mm and length of 16 cm. To have the better

nding of the physical effect in this new model further study can be

changing the dimensions.

rrent experiments, the solution used was water of saturation

tures. In actual practical case it may be the other solution. So further

n be made by using the practically used solution.

Page 126

References

REFERENCES

Alhusseini, A.A., Tuzla, K. and Chen, J.C. Falling film evaporation of single

component liquids, Int. J. Heat Mass Transfer, 41(12), pp. 1623-1632, 1998.

Anfeletti, S. and Moresi, M. Modeling of multiple-effect falling film evaporators, J

Food Technology, 18, pp. 539-563. 1983.

Arshavski, I., Nekhamkin, Y., Olek, S. and Elias, E. Conjugate heat transfer during

falling film evaporation, International Communication in Heat and Mass transfer,

22(2), pp. 271-284, 1995.

Asblad, A. and Berntsson, T. Surface evaporation of turbulent falling films, Int. J. Heat

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Assad, M.E.H. and Lampinen, M. J. Mathematical modeling of falling liquid film

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Benezeguir, B., Setterwall, F. and uddholm, H., Use of a wave model to evaluate

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ASME HTD, 108, 23-32. 1989.

Choudhury, S.K., Hisajima D., Ohuchi T., Nishiguchi A., fukushima T. and Sakaguchi

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Chyu, M.C. and Bergles, A.E. Falling film evaporation on a horizontal tube,

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Chyu, M.C. and Bergles, A.E. Enhancement of Horizontal Tube Spray Film

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Chyu, M.C. and Bergles, A.E An analytical and experimental study on falling film

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Chyu, M.C. and Bergles, A.E Horizontal tube falling –film evaporation with structured

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Fujita, T. and Ueda, T. Heat transfer to falling liquid films and film breakdown-II:

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Grossman G., Simultaneous heat and mass transfer in film absorption under laminar

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References

Zeng, X., Chyu, M.C. and Ayub, Z.H. Performance of Nozzle-Sprayed Ammonia

Evaporator with Square-Pitch Plain-Tube Bundle, ASHRAE Transactions, 103(2),

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Zeng, X., Chyu, M.C. and Ayub, Z.H. Ammonia Spray Evaporation Heat Transfer

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104(1), paper no. 4109, 1998.

.

Page 137

Appendix-A

Appendix A

CALIBRATION OF GRAPH

Page 138

Appendix-A

APPENDIX A- CALIBRATION OF INSTRUMENTION

A.1 Calibration of Thermocouples

A liquid-in-glass thermometer having an accuracy of ±0.05°C was used to calibrate

thermocouples which were connected to the respective channels of a data logger. By

emerging all thermocouples in a constant temperature water bath they were calibrated

for heating and cooling. The equation of the calibration curves of the thermocouple are

given in Table A.1.

Table A.1. Equations of calibration curves of the thermocouples

Thermocouples Type Equation of calibration curve(y=m.x+c)

T1 K y=0.9928*x+0.0895

T2 K y=0.9929*x+0.0338

T3 K y=0.992*x+0.0006

T4 K y=0.9923*x-0.0036

T5 K y=0.9897*x+0.1016

T6 K y=0.997*x-0.1383

T7 K y=0.9952*x-0.1111

T8 K y=0.9944*x-0.2047

T9 K y=0.9940*x-0.0659

T10 K y=0.9952*x-0.0684

T13 K y=0.995*x+0.2260

T14 K y=0.9973*x+0.1644

Where, y=Actual temperature, °C; x= Measured temperature, °C

Page 139

Appendix-A

y = 0.9928x + 0.0895

0

10

20

30

40

50

60

70

80

0 20 40 60 80

Measured Temperature, C

Act

ual T

empe

ratu

re, C

Figure A1. Calibration graph for channel 1

y = 0.9929x + 0.0338

0

10

20

30

40

50

60

70

80

0 20 40 60 80


Act

ual T

empe

ratu

re, C


Page 140

Appendix-A

y = 0.992x + 0.0006

0

10

20

30

40

50

60

70

80

0 20 40 60 80


Act

ual T

empe

ratu

re, C


y = 0.9923x - 0.0036

0

10

20

30

40

50

60

70

80

0 20 40 60 80


Act

ual T

empe

ratu

re, C


Page 141

Appendix-A

y = 0.9897x + 0.1016

0

10

20

30

40

50

60

70

80

0 20 40 60 80


Act

ual T

empe

ratu

re, C


y = 0.997x - 0.1383

0

10

20

30

40

50

60

70

80

0 20 40 60 80


Act

ual T

empe

ratu

re, C


Page 142

Appendix-A

y = 0.9952x - 0.1111

0

10

20

30

40

50

60

70

80

0 20 40 60 80


Act

ual T

empe

ratu

re, C


y = 0.9944x - 0.2047

0

10

20

30

40

50

60

70

80

0 20 40 60 80


Act

ual T

empe

ratu

re, C


Page 143

Appendix-A

y = 0.994x - 0.0659

0

10

20

30

40

50

60

70

80

0 20 40 60 80


Act

ual T

empe

ratu

re, C


y = 0.9952x - 0.0684

0

10

20

30

40

50

60

70

80

0 20 40 60 80


Act

ual T

empe

ratu

re, C


Page 144

Appendix-A

y = 0.995x + 0.226

0

10

20

30

40

50

60

70

80

0 20 40 60 80


Act

ual T

empe

ratu

re, C


y = 0.9973x + 0.1644

0

10

20

30

40

50

60

70

80

0 20 40 60 80


Act

ual T

empe

ratu

re, C


Page 145

Appendix-A

A.2 Calibration of Humidity Sensors

The humidity sensors that were used for measuring the relative humidity of air at the

inlet and outlet of the evaporation chamber were calibrated by using the ranges of the

volts with the measuring range of relative humidity of air.

The calibration graphs for two humidity sensors with corresponding equations are

given below in figure A15.

y = 25x - 25

0

20

40

60

80

100

1 2 3 4 5

Voltage, mV

Rel

ativ

e H

umid

ity, %

Figure A15. Calibration graph for humidity sensors

y=25*x-25

where, y is the relative humidity in percentage and

x is the voltage in volts

Page 146

Appendix-A

A.3 Calibration of Variable Area Flow Meters

The variable area flow meters used for measuring the hot water and the distributed

water flow rates were calibrated by measuring the actual volume flow of water for a

specified time over the operating range of volume flow rates.

Table A.2. Equations of calibration curves of flow meters

Measuring Fluid Flow meter Type Equations of calibration curve

(y=m.x+c)

Hot water Rota meter y=0.9971*x-0.2292

Distributed water Rota meter Y=1.0042*x-0.2379

The calibration graphs for two flow meters with corresponding equations are given

below

y = 0.9971x - 0.2292

0.0

1.5

3.0

4.5

0 1.5 3 4.5

Indicated Flow Rate, Litr/min

Act

ual F

low

Rat

e, L

itr/m

in

Figure A16. Calibration graph for Hot Water Flow Meter

Page 147

Appendix-A

y = 1.0042x - 0.2379

0.0

1.5

3.0

4.5

0 1.5 3 4

Indicated Flow Rate, Litr/min

Act

ual F

low

Rat

e, L

itr/m

in

.5

Figure A17. Calibration graph for Distributed Water Flow Meter

A.4 Calibration of Air Flow Rates:

A hot wire probe was used to calibrate the flow rates of the air supplying fan at three

different flow rates. To continue the calibration, the hot wire anemometer was inserted

from the upper direction to the bottom direction inside the air flow inlet circular pipe.

The total diameter of the circular tube was divided into nine points maintaining equal

distances from each other. The velocity at each point was measured by the probe. The

velocity near the inside surface of the pipe was taken as zero. By inserting the probe

from the right to left direction inside the pipe the measurement was also taken by

scaling the same distance as before. The average values of four points at any distance

from the center were calculated and were considered the velocity at that

circumferential position. Thus in total 9 average values were calculated at any specific

speed of the fan. The calculation was done for the lowest three speeds among 10

Page 148

Appendix-A

speeds. After calculating when the values were plotted the profiles have been found for

a turbulent flow as shown in figures A17, A18, and A19

-1

0

1

2

3

4

5

6

-50 -40 -30 -20 -10 0 10 20 30 40 50

Distance, mm

Velo

city

, m/s

ec

Figure A18. Calibration graph for lowest speed of fan

-1

0

1

2

3

4

5

6

-50 -40 -30 -20 -10 0 10 20 30 40 50

Distance, mm

Velo

city

, m/s

ec

Figure A19. Calibration graph for 2nd lowest speed of fan

Page 149

Appendix-A

-1

0

1

2

3

4

5

6

7

8

-50 -40 -30 -20 -10 0 10 20 30 40 50

Distance, mm

Velo

city

, m/s

ec

Figure A20. Calibration graph for 3nd lowest speed of fan

The calibration equations for three flow rates are given below: (unit: kg/sec). In the

figures all pink colored graphs represents the profile from the left to the right insertion

of the probe inside the circular tube and the other one for up to down insertion. The

values of the mass flow rates are tabulated below.

Table A.3. Values of the mass flow rates of air at different fan speed

Regulator point Mass flow rate

1 0.033072

2 0.040787

3 0.043142

Page 150

Appendix-B

Appendix B

TABULATED DATA AND RESULTS

Page 151

Appendix-B

APPENDIX B- EXPERIMENTAL HEAT AND MASS TRANSFER DATA

The salient features of the copper evaporator tubes and stainless steel absorber tube are

given in the Table B.1 and Table B.2 respectably along with a description of the

tabulated data for falling film evaporation in Table B.3. All other experimental data for

falling film absorption can be found from miller (1998).

Table B.1. Salient data of copper tube evaporator

Description Value SI Units

Surface Area 0.2512906 m2

Outside diameter of test tube 1.905E-02 m

Inside diameter of test tube 1.700E-02 m

Absorber tube length 1.5705663 m

Width of the tube 0.16 m

Table B.2. Salient data of stainless steel tube absorber

Description Value SI Units

Surface Area 9.120E-02 m2

Outside diameter of test tube 1.905E-02 m

Inside diameter of test tube 1.422E-02 m

Absorber tube length 1.524 m

Page 152

Appendix-B

Table-B.3. Operating conditions of the experiments, falling film evaporation

Out

let

rela

tive

hum

idi

ty. (

%)

66.1

20

66.3

38

65.5

00

65.2

75

64.6

25

64.9

12

70.1

00

69.4

10

69.3

95

69.9

37

66.7

90

68.7

78

69.7

50

65.9

68

64.9

95

Inle

t re

lativ

e hu

mid

ity

. (%

)

58.9

57

59.0

73

57.5

00

57.0

38

58.0

00

57.5

00

61.5

00

61.5

00

60.7

95

61.0

45

59.2

85

60.5

05

60.5

45

58.8

68

57.3

80

Out

let

dry

bulb

T

empe

ratu

re, °

C

25.6

41

25.8

21

25.9

00

26.3

06

25.7

00

25.7

39

25.4

02

25.6

37

25.8

02

25.9

18

25.9

95

25.8

29

25.9

29

25.5

51

26.0

00

Inle

t dry

bu

lb

Tem

pera

ture

, °C

22.9

88

22.9

81

23.3

25

23.9

88

23.2

80

23.4

62

23.0

41

23.2

00

23.0

66

22.9

73

23.4

27

22.9

27

22.8

60

23.7

94

24.1

61

Air

Flow

ra

te,

(kg/

s)

0.03

3072

0.03

3072

0.03

3072

0.03

3072

0.03

3072

0.03

3072

0.03

3072

0.03

3072

0.03

3072

0.03

3072

0.03

3072

0.03

3072

0.03

3072

0.03

3072

0.03

3072

Out

let

tem

per

atur

e,

°C

37.3

46

38.4

79

39.4

54

39.0

12

37.3

70

37.8

05

37.1

98

37.6

38

38.5

50

39.8

77

38.0

15

39.1

66

40.2

32

36.3

61

37.0

25

Inle

t te

mpe

rat

ure,

°C

44.4

27

44.4

43

44.3

04

44.3

56

44.3

44

43.0

00

44.2

59

44.3

27

44.3

28

44.3

52

44.3

93

44.2

82

44.2

94

39.6

64

41.1

70

Hot

wat

er

flow

rat

e (k

g/s)

0.03

7725

83

0.03

7725

83

0.03

7725

83

0.03

7725

83

0.29

4166

70

0.03

7725

83

0.03

7725

83

0.03

7725

83

0.03

7725

83

0.03

7725

83

0.04

6035

00

0.04

6035

00

0.04

6035

00

0.03

7725

83

0.03

7725

83

Out

let

tem

per

atur

e,

°C

39.1

74

39.6

03

39.8

50

39.8

88

38.7

20

38.7

43

38.0

32

38.4

72

38.9

71

39.7

81

39.0

77

39.6

08

40.1

57

35.9

10

36.7

82

Inle

t te

mpe

rat

ure,

°C

32.5

48

34.5

59

37.6

70

34.3

47

34.6

00

34.6

72

31.5

88

32.1

14

34.4

65

37.5

82

32.4

09

34.6

89

37.7

10

34.2

82

34.2

43

Solu

tion

flo

w r

ate

(kg/

s)

0.02

1140

00

0.02

1140

00

0.02

1140

00

0.02

1140

00

0.02

1140

00

0.02

1140

00

0.02

9508

33

0.02

9508

33

0.02

9508

33

0.02

9508

33

0.02

9508

33

0.02

9508

33

0.02

9508

33

0.02

9508

33

0.02

9508

33

R

un

1 2 3 4 5 6 7 8 9 10

11

12

13

14

15

Page 153

Appendix-B

Table-B.3. Experimental data Contn

O

utle

t re

lativ

e hu

mid

it y

. (%

)

64.7

75

64.2

15

64.8

77

66.5

10

66.7

42

67.8

25

67.4

43

67.6

95

65.9

20

65.6

40

65.8

45

66.4

62

64.7

88

65.0

78

63.3

10

Inle

t re

lativ

e hu

mid

ity.

(%)

57.2

43

58.

052

58.8

95

58.3

88

59.8

63

59.7

87

59.2

45

58.8

33

58.5

45

59.3

68

58.8

87

59.0

13

58.1

50

58.3

40

56.7

03

Out

let

dry

bulb

T

empe

rat

ure ,

°C

26.3

53

25.5

53

25.5

34

25.9

55

25.4

29

25.6

38

26.2

23

26.2

44

25.4

97

25.8

09

25.9

71

25.9

56

25.6

00

26.5

04

26.5

03

Inle

t dry

bu

lb

Tem

pera

ture

, °C

24

.307

23.5

04

23.3

60

23.1

99

23.0

26

23.1

94

23.1

96

23.2

39

23.5

52

23.6

57

23.7

15

23.5

33

23.2

00

24.3

75

24.4

99

Air

Flow

ra

te,

(kg/

s)

0.03

3072

0.03

3072

.033

0720

.033

0720

.033

0720

.033

0720

.033

0720

.033

0720

.033

0720

.033

0720

.033

0720

.033

0720

.033

0720

.040

7866

.043

1422

Out

let

tem

per

atur

e,

°C

37.9

29

35.6

41

36.8

43

39.2

00

37.6

49

38.6

01

40.2

63

40.1

75

36.1

91

37.3

21

38.2

00

39.0

47

36.8

08

38.3

58

38.2

08

Inle

t te

mpe

ratu

re,

°C

43.0

90

44.

255

44.4

63

44.3

53

44

.544

44.4

24

44.2

63

44.2

99

44.3

91

44.2

79

44.3

09

44.2

25

44.3

24

44.2

40

44.3

37

Hot

wat

er

flow

rat

e (k

g/s)

.037

7258

3

.021

1075

0

.029

4166

7

.054

3441

7

.021

1075

0

.029

4166

7

.054

3441

7

.062

6533

3

.029

4166

7

.037

7258

3

.046

0350

0

.054

3441

7

.029

4166

7

.037

7258

3

.037

7258

3

Out

let

tem

per

atur

e,

°C

38.1

22

36.6

81

38.0

50

39.8

85

38.2

14

39.0

43

40.4

57

40.4

32

37.1

91

38.3

21

39.0

14

39.6

54

37.9

70

38.6

55

38.3

80

Inle

t te

mpe

rat

ure,

°C

34

.340

34.2

46

34.2

68

34.4

00

37.6

08

37.5

88

37.5

34

37.6

11

32.0

12

32.1

20

32.1

20

32.5

30

34.7

20

34.3

34

34.3

08

Solu

tion

flo

w r

ate

(kg/

s)

0.02

9508

33

0.02

9508

33

0.02

9508

33

0.02

9508

33

0.02

9508

33

0.02

9508

33

0.02

9508

33

0.02

9508

33

0.02

9508

33

0.02

9508

33

0.02

9508

33

0.02

9508

33

0.02

9508

33

0.02

9508

33

0.02

9508

33

R

un

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

Page 154

Appendix-B


Out

let

rela

tive

hum

idi

ty (%

)

64.5

30

65.4

00

68.1

47

67.9

35

67.9

97

68.6

00

66.0

70

67.5

37

68.6

15

67.6

40

70.0

52

71.6

02

71.7

72

70.9

65

62.5

42

Inle

t re

lativ

e hu

mid

ity

(%)

58.3

40

59.8

47

59.8

47

59.8

07

59.8

07

59.8

07

59.5

88

58.8

60

62.7

50

58.4

15

58.6

97

62.8

70

62.9

45

61.6

38

56.3

95

Out

let

dry

bulb

T

emp.

°C

25.6

22

26.3

31

26.2

95

26.8

28

27.0

36

28.1

63

25.1

15

26.1

52

26.3

99

26.9

22

27.2

59

24.9

78

25.5

34

26.0

56

26.4

01

Inle

t dry

bu

lb

Tem

p.

°C

23.9

07

23.3

26

23.1

23

23.0

32

22.9

08

24.2

09

23.5

45

23.5

63

23.2

27

23.7

11

23.6

33

22.9

49

22.9

85

23.0

71

24.4

80

Air

Flow

ra

te,

(kg/

s)

.033

0720

.033

0720

.033

0720

.033

0720

.033

0720

.033

0720

.033

0720

.033

0720

.033

0720

.033

0720

.033

0720

.033

0720

.033

0720

.033

0720

.033

0720

Out

let

tem

pera

tur

e,

°C

35.4

34

35.0

11

35.7

96

37.3

23

38.8

53

40.3

49

33.5

08

40.1

32

36.4

50

37.6

30

39.1

13

33.1

78

34.6

41

36.3

18

36.8

25

Inle

t te

mpe

rat

ure,

°C

39.6

90

43.9

17

43.8

32

43.8

27

43.8

05

43.7

71

44.3

00

44.3

18

43.0

18

43.0

18

43.0

12

39.6

30

39.6

30

39.6

35

41.0

58

Hot

wat

er

flow

rat

e (k

g/s)

.037

7258

30

.029

4166

70

.029

4166

70

.029

4166

70

.029

4166

70

.029

4166

70

.021

1075

00

.062

6533

30

.037

7258

30

.037

7258

30

.037

7258

30

0.03

7725

83

.037

7258

30

.037

7258

30

.037

7258

30

Out

let

tem

per

atur

e,

°C

35.3

55

36.3

83

36.3

18

37.8

05

38.9

23

39.9

64

34.9

22

40.6

16

36.9

94

37.8

01

38.7

48

33.9

69

34.7

48

35.8

66

36.7

68

Inle

t te

mpe

rat

ure,

°C

32.3

13

30.4

09

31.4

90

36.0

37

38.0

89

40.1

06

30.0

88

33.9

56

32.5

43

34.6

42

37.6

86

29.0

26

31.5

79

34.5

30

34.5

20

Solu

tion

flo

w r

ate

(kg/

s)

0.02

9508

33

0.02

9508

33

0.02

9508

33

0.02

9508

33

0.02

9508

33

0.02

9508

33

0.02

9508

33

0.02

9508

33

0.03

7876

67

0.03

7876

67

0.03

7876

67

0.03

7876

67

0.03

7876

67

0.03

7876

67

0.03

7876

67

R

un

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

Page 155

Appendix-B


O

utle

t re

lativ

e hu

mid

ity

(%)

64.7

90

63.2

95

63.3

10

65.0

97

63.4

12

65.3

10

67.0

00

65.5

00

66.1

25

69.1

70

69.1

28

68.4

30

65.5

00

65.9

00

69.8

88

Inle

t re

lativ

e hu

mid

ity

(%)

55.8

53

56.5

65

56.6

75

57.6

40

56.3

25

57.2

70

58.5

00

58.5

33

58.3

75

59.6

50

59.5

83

59.8

70

58.2

75

58.4

50

58.6

35

Out

let

dry

bulb

T

empe

ratu

re, °

C

25.9

77

25.4

35

25.5

38

26.0

17

26.4

30

25.9

14

25.6

87

25.4

00

25.3

20

26.2

63

26.2

39

25.9

25

25.2

30

25.9

60

26.3

56

Inle

t dry

bu

lb

Tem

p.

°C

24.0

13

23.7

61

23.7

39

23.5

74

24.2

38

23.9

92

23.2

22

23.2

00

23.2

00

23.2

57

23.2

75

23.1

69

23.2

20

23.1

70

23.1

63

Air

Flow

rat

e,

(kg/

s)

.033

0720

00

.033

0720

00

.033

0720

00

.033

0720

00

.033

0720

00

.033

0720

00

.033

0720

00

.033

0720

00

.033

0720

00

.033

0720

00

.040

7866

60

.043

1422

60

.040

7866

60

.043

1422

60

.033

0720

00

Out

let

tem

per

atur

e,

°C

37.6

97

34.7

10

35.2

57

39.0

62

38.2

55

37.5

24

38.9

90

36.4

30

36.8

50

37.6

34

37.7

11

37.3

75

36.6

70

36.5

10

36.2

17

Inle

t te

mpe

rat

ure,

°C

44.3

03

39.5

67

41.0

23

44.3

60

41.0

40

44.3

78

44.3

00

44.3

00

43.0

00

45.1

48

45.0

80

44.9

92

43.0

00

43.0

00

45.0

15

Hot

wat

er

flow

rat

e (k

g/s)

.037

7258

.037

7258

.037

7258

.037

7258

.037

7258

.037

7258

.037

7258

.029

4166

.037

7258

.037

7258

.037

7258

.037

7258

.037

7258

.037

7258

.029

4166

Out

let

tem

per

atur

e,

°C

38.2

21

35.0

86

36.0

07

39.4

00

37.6

41

38.0

69

39.3

22

37.2

95

37.5

15

38.6

34

38.5

45

38.2

51

37.3

00

37.0

00

37.3

41

Inle

t te

mpe

rat

ure,

°C

34.3

77

32.5

84

32.6

13

37.7

00

37.4

49

34.4

11

37.7

50

34.6

50

34.7

65

34.3

97

34.6

61

34.4

28

34.5

00

34.4

30

33.3

90

Solu

tion

flo

w r

ate

(kg/

s)

0.03

7876

67

0.03

7876

67

0.03

7876

67

0.03

7876

67

0.03

7876

67

0. 0

4624

500

0. 0

4624

500

0. 0

4624

500

0. 0

4624

500

0. 0

4624

500

0. 0

4624

500

0. 0

4624

500

0. 0

4624

500

0. 0

4624

500

0. 0

4624

500

R

un

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Page 156

Appendix-B


O

utle

t re

lativ

e hu

mid

ity

(%)

67.8

73

68.6

55

68.1

55

68.0

10

67.6

28

68.6

82

68.7

65

67.8

40

68.0

80

69.1

82

69.1

70

69.4

63

69.5

73

68.8

05

Inle

t re

lativ

e hu

mid

ity

(%)

59.9

13

60.2

52

59.7

72

58.9

85

58.4

63

59.0

10

59.0

27

58.4

87

58.2

02

59.4

70

59.3

45

59.1

45

58.7

98

59.1

58

Out

let

dry

bulb

T

emp.

(C

)

25.8

66

25.7

56

24.9

13

25.3

95

25.5

35

26.4

46

26.5

34

26.3

61

26.8

38

26.7

30

26.5

16

26.6

90

26.5

57

26.2

11

Inle

t dry

bu

lb

Tem

p.

( C)

23.2

97

23.2

29

23.5

72

23.5

34

23.3

82

23.4

42

23.5

92

23.6

69

23.7

72

23.6

64

23.6

99

23.4

36

23.3

65

23.4

14

Air

Flow

rat

e,

(kg/

s)

.040

7866

60

.043

1422

60

.033

0720

00

.040

7866

60

.043

1422

60

.033

0720

00

.040

7866

60

.043

1422

60

.033

0720

00

.040

7866

60

.043

1422

60

.033

0720

00

.040

7866

60

.043

1422

60

Out

let

tem

pera

tur

e,

(C)

35.4

86

36.0

99

29.5

09

31.3

12

32.5

15

38.3

59

38.2

17

37.8

14

38.8

00

38.6

91

38.4

56

39.1

66

38.8

68

38.3

59

Inle

t te

mpe

rat

ure,

°C

45.9

37

45.7

64

41.3

78

44.0

56

44.7

98

44.8

39

44.8

21

44.7

09

44.4

33

44.3

86

44.2

76

44.0

56

43.9

02

43.6

84

Hot

wat

er

flow

rat

e (k

g/s)

.029

4166

70

.029

4166

70

.021

1075

00

.021

1075

00

.021

1075

00

.046

0350

00

.046

0350

00

.046

0350

00

.054

3441

70

.054

3441

70

.054

3441

70

.062

6533

30

.062

6533

30

.062

6533

30

Out

let

tem

per

atur

e,

°C

37.1

49

37.2

44

30.7

98

32.8

5

33.8

46

39.1

32

38.9

89

38.5

04

39.4

90

39.3

19

39.0

01

39.7

12

39.3

71

38.8

42

Inle

t te

mpe

rat

ure,

°C

32.9

48

33.3

76

26.6

35

28.3

61

30.1

32

35.2

29

35.1

48

34.7

23

35.5

05

35.4

37

35.1

60

35.7

28

35.4

07

34.9

59

Solu

tion

flo

w r

ate

(kg/

s)

0. 0

4624

500

0. 0

4624

500

0. 0

4624

500

0. 0

4624

500

0. 0

4624

500

0. 0

4624

500

0. 0

4624

500

0. 0

4624

500

0. 0

4624

500

0. 0

4624

500

0. 0

4624

500

0. 0

4624

500

0. 0

4624

500

0. 0

4624

500

R

un

61

62

63

64

65

66

67

68

69

70

71

72

73

74

Page 157

Appendix-B

Table-B.4. The results for the heat and mass transfer coefficients

U (kW/m2.K) Hwo (kW/m2.K) Ha(kW/m2.K)×10-2 Ka(kg/m2.s)×10-2Run

Detailed Simplif. Detailed Simplif. Detailed Simplifi. Detailed Simplif.

1 0.88 0.86 2.01 0.60 1.60 3.10 1.59 3.08

2 0.83 0.82 1.29 3.01 1.40 2.10 1.39 2.09

3 0.95 0.88 1.29 1.83 1.41 2.30 1.395 2.29

4 0.70 0.71 2.76 1.23 1.50 1.60 1.49 1.59

5 0.82 0.76 2.42 0.67 1.40 2.70 1.39 2.69

6 0.86 0.83 2.59 0.60 1.40 2.50 1.39 2.49

7 0.71 0.70 3.13 4.77 1.90 1.60 1.89 1.59

8 0.70 0.69 4.43 4.72 1.80 1.30 1.79 1.29

9 0.71 0.72 3.49 3.32 1.80 1.60 1.79 1.59

10 0.76 0.76 1.54 3.87 1.70 1.70 1.69 1.69

11 0.85 0.85 2.76 0.64 1.70 2.30 1.69 2.29

12 0.81 0.81 4.24 1.55 1.70 1.70 1.69 1.69

13 0.86 0.86 1.59 0.67 1.70 2.20 1.69 2.19

14 0.66 0.66 5.49 1.87 1.40 1.70 1.39 1.69

15 0.67 0.68 2.22 3.32 1.50 1.70 1.49 1.69

16 0.71 0.71 2.45 4.54 1.50 1.60 1.49 1.59

17 0.77 0.69 2.40 4.19 1.40 2.30 1.39 2.29

18 0.85 0.79 5.49 0.65 1.30 2.70 1.29 2.69

19 0.95 0.97 2.28 1.47 1.60 2.20 1.59 2.19

20 1.10 0.82 1.15 2.58 1.40 2.30 1.39 2.29

Page 158

Appendix-B

Table-B.4. the results for the heat and mass transfer coefficients contn

U (kW/m2.K) Hwo (kW/m2.K) Ha(kW/m2.K)×10-2 Ka(kW/m2.K)×10-2Run

Detailed Simplif. Detailed Simplif. Detailed Simplifi. Detailed Simplifi.

21 0.97 0.85 2.76 1.17 1.40 2.40 1.39 2.39

22 1.03 1.03 4.12 0.60 1.50 2.60 1.49 2.59

23 1.10 1.25 2.02 1.78 1.60 2.90 1.59 2.89

24 0.67 0.67 2.34 4.90 1.60 1.90 1.59 1.89

25 0.73 0.74 2.73 1.91 1.50 1.70 1.49 1.69

26 0.79 0.78 5.49 3.98 1.50 1.50 1.49 1.49

27 0.82 0.82 1.80 0.85 1.60 1.50 1.59 1.49

28 0.92 0.83 5.49 0.62 1.40 3.10 1.39 3.08

29 0.72 0.72 3.15 4.74 1.80 1.80 1.79 1.79

30 0.73 0.73 3.07 0.64 1.80 2.70 1.79 2.69

31 0.66 0.67 1.67 2.63 1.50 1.70 1.49 1.69

32 0.67 0.68 5.50 0.65 2.10 2.70 2.09 2.68

33 0.63 0.63 5.50 0.66 2.50 2.90 2.49 2.89

34 0.89 0.84 4.77 2.96 2.20 2.80 2.19 2.79

35 0.83 0.82 3.80 5.00 2.10 2.10 2.09 2.09

36 0.75 0.78 2.59 1.48 2.10 1.80 2.09 1.79

37 0.60 0.58 5.48 0.62 1.60 2.90 1.59 2.89

38 0.89 0.87 2.73 1.19 1.60 1.20 1.59 1.19

39 0.79 0.78 5.49 4.71 2.1 1.80 2.09 1.79

40 0.78 0.77 5.50 0.60 2.2 2.10 2.19 2.09

Page 159

Appendix-B



Detailed Simpl. Detailed Simpl. Detailed Simplifi. Detailed Simplfie.

41 0.80 0.81 5.00 2.06 2.30 2.0 2.29 1.99

42 0.77 0.77 3.81 4.42 2.50 1.70 2.48 1.69

43 0.74 0.74 3.77 5.00 2.50 2.00 2.48 1.99

44 0.70 0.70 2.46 0.61 2.40 2.00 2.38 1.99

45 0.76 0.75 1.64 0.62 1.40 1.80 1.39 1.79

46 0.84 0.83 5.46 0.69 1.50 2.40 1.49 2.39

47 0.89 0.87 1.34 1.48 1.50 2.20 1.49 2.19

48 0.92 0.89 5.50 0.64 1.40 2.40 1.39 2.39

49 1.10 1.00 3.43 4.22 1.30 2.20 1.29 2.19

50 0.82 0.78 5.49 1.94 1.40 1.80 1.39 1.79

51 0.88 0.87 1.62 5.00 1.50 1.70 1.49 1.69

52 1.10 1.04 2.86 0.64 1.40 2.60 1.39 2.59

53 0.93 0.88 1.49 0.65 1.50 2.70 1.49 2.69

54 1.02 0.98 1.58 0.62 1.50 2.50 1.49 2.49

55 0.92 0.92 3.25 1.15 2.10 1.90 2.08 1.89

56 0.91 0.92 3.13 1.50 2.60 2.10 2.58 2.09

57 0.94 0.94 3.17 0.65 2.50 2.80 2.48 2.79

58 0.99 0.97 5.47 1.74 1.70 2.30 1.69 2.29

59 0.99 0.97 3.50 0.60 2.40 3.50 2.39 3.48

60 0.79 0.81 5.49 3.01 2.60 1.70 2.58 1.69

Page 160

Appendix-B



Detailed Simplif. Detailed Simplif. Detailed Simplifi. Detailed Simplifi.

61 0.92 0.91 5.49 2.12 2.40 2.70 2.39 2.69

62 0.83 0.84 3.58 4.52 2.60 2.30 2.58 2.29

63 0.64 0.64 5.50 0.60 2.70 3.30 2.68 3.29

64 0.65 0.66 5.50 5.00 3.39 2.10 3.37 2.09

65 0.68 0.69 5.50 3.41 3.30 2.70 3.28 2.69

66 1.07 1.06 2.32 3.48 2.00 2.20 1.99 2.19

67 1.07 1.07 3.38 0.65 2.50 3.10 2.48 3.09

68 1.09 1.07 3.55 0.62 2.50 3.79 2.48 3.76

69 1.16 1.16 2.69 3.99 2.00 2.20 1.99 2.19

70 1.16 1.16 3.95 1.68 2.50 2.60 2.48 2.59

71 1.15 1.15 3.09 0.63 2.60 3.49 2.58 3.47

72 1.24 1.23 5.42 2.87 2.00 2.20 1.99 2.19

73 1.23 1.23 4.08 0.87 2.60 2.90 2.58 2.89

74 1.27 1.26 2.89 0.61 2.50 3.99 2.48 3.96

Page 161

Appendix-C

Appendix-C

COMPARISON WITH BASIC EQUATION

Page 162

Appendix-C

Appendix-C ACHIEVEMENT OF BASIC EQUATION FROM THE MODELS C.1 Detailed model: The five differential equations of the detailed models are listed here:

( wc

cc

c TTCm

UdAdT

−⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

.) (C.1.1)

( wwKdAmd

ifaw −−=

.

) (C.1.2)

( )wwm

KdAdw

if

a

a −−= . (C.1.3)

( ) ( )aif

a

aif

a

ava TTm

hww

m

KHdA

dH−−−−= .. (C.1.4)

( ) ( ) ( )[ ])(.1. aifawcifavww

ww

w TThTTUwwKHCTCmdA

dT−−−+−−

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=⎟

⎠⎞

⎜⎝⎛

(C.1.5) Now, by substituting the value of ( )[ ]wwK ifa −− from equation (C.1.2) to the equation (C.1.4) we can get,

( )dA

dHdAmd

m

HTT

m

h aw

a

vaif

a

a −=−

.

.. (C.1.6)

( )dA

dH

Cm

mdAmd

Cm

HTT

Cm

h a

ww

aw

ww

vaif

ww

a.

..

.. +−=−− (C.1.7)

Page 163

Appendix-C

Again by substituting the values of ( )[ ]wwK ifa −− , ( )[ ]wc TTU − and

(⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−− aif

ww

a TTCm

h.

) from the equation (C.1.3), (C.1.1) and (C.1.7) respectively to

the equation (C.1.5) we can get,

( )dAmd

Cm

HdA

dH

Cm

mdAdT

Cm

CmdAmd

Cm

HCTdA

dT w

ww

va

ww

ac

ww

ccw

ww

vwww.

..

.

.

..

. −++⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−

=⎟⎠

⎞⎜⎝

⎛

(C.1.8)

( )dA

dH

Cm

mdAdT

Cm

CmdAmd

Cm

H

Cm

HCTdAdT a

ww

ac

ww

ccw

ww

v

ww

vwww.

.

.

..

.. ++⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−

−−=⎟

⎠⎞

⎜⎝⎛

(C.1.9)

⎭⎬⎫

⎩⎨⎧+

⎭⎬⎫

⎩⎨⎧+

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−=⎟

⎠

⎞⎜⎝

⎛dA

dH

Cm

mdAdT

Cm

CmdAmd

Cm

CTdAdT a

ww

ac

ww

ccw

ww

www.

.

.

..

. (C.1.10)

aacccwwwwww dHmdTCmmdCTdTCm....

++−= (C.1.11)

aacccwwwww dHmdTCmmdTdTmC....

+=⎭⎬⎫

⎩⎨⎧

+ (C.1.12)

∫∫∫ +=⎭⎬⎫

⎩⎨⎧

+A

aaA

cccA

wwwww dHmdTCmmdTdTmC0

.

0

.

0

.. (C.1.13)

[ ] [ ]outletinletaa

inletoutletccc

outlet

inletwww HmTCmTmC

...+=⎥

⎦

⎤⎢⎣

⎡ (C.1.14)

ainaaoutacoutcccinccwinwinwwoutwoutw HmHmTCmTCmTmCTmC......

−+−=− (C.1.15)

( ) ( ainaoutawinwinwwoutwoutwcoutcincc HHmTmCTmCTTCm −+−=−....

) (C.1.16)

Page 164

Appendix-C

C.2 Observation for Simplified model:

( wc

cc

c TTcm

UdAdT

−⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

.) (C.2.1)

( ai

pma

ca HHCm

hdA

dH−

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−= . ) (C.2.2)

( ) ( )iwai TTHH −=− λ (C.2.3)

⎟⎟⎠

⎞⎜⎜⎝

⎛=

c

opm

hhC

λ (C.2.4)

( ) ( iw

ww

owc

ww

w TTCm

hTT

Cm

UdA

dT−

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−−

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛= .. ) (C.2.5)

By substituting the values of λ from equation (C.2.4) to the equation (C.2.3) we get

( ) ( )iwc

opmai TT

hhC

HH −⎟⎟⎠

⎞⎜⎜⎝

⎛=−

and, hence putting this value of ( )ai HH − in the right hand side of equation (C.2.2) we can write

( iw

a

oa TTm

hdA

dH−

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−=

.) (C.2.6)

( )dA

dHmTTh a

aiwo.

−=− (C.2.7)

By substituting the values of ( )wc TTU − from equation (C.2.1) and the value of

to the equation (C.2.5), we can express the following equation: ( iwo TTh − )

dAdH

Cm

mdAdT

Cm

cmdA

dT a

ww

ac

ww

ccw

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−

−⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

.

.

.

.

(C.2.8)

Page 165

Appendix-C

aacccwww dHmdTcmdTCm...

+= (C.2.9)

[ ] [ ] [ ]outletinletaa

inletoutletccc

outletinletwww HmTcmTCm

...+= (C.2.10)

[ ] [ ] [ aoutainacoutcinccwinwoutww HHmTTcmTTCm −+−=−...

]

]

(C.2.11)

[ ] [ ] [ aoutainawinwoutwwcoutcincc HHmTTCmTTcm −−−=−...

(C.2.12)

ainaaoutawinwwwoutwwcoutcccincc HmHmTCmTCmTcmTcm......

−+−=− (C.2.13)

Page 166

Appendix-D

Appendix-D

PROPERTY EQUATIONS

Page 167

Appendix-D

APPENDIX D-PROPERTY EQUATIONS OF WATER AND AIR

D1. Saturated pressure and temperature of water

60410064551512.001870003179055.04650000254940.082890000001143.024290000000082.0 234

+×+×+×−×=

sat

satsatsatsat

TTTTP

Where, is the saturation pressure of water at a saturation temperature . satP satT

D2. Enthalpy of vapor and water vapor mixture

6.25027719.1 +×= ifv TH

4.25024108.2 +×−= iffg TH

Where, and are the enthalpy of vapor and water-vapor mixture respectively

at an interface temperature, .

vH fgH

ifT

D3. Moisture content of air with and without Relative Humidity

sat

satif PP

PW

−×

=62198.0

sat

sata PRHP

PRHW

×−××

=62198.0

; P=1.01 kPa

where, is the moisture content of air vapor mixture at the interface and is the

moisture content of air having a saturation pressure and a relative humidity

ifW aW

satP RH .

D4. Enthalpy of air and the temperature of air

( )aaaa TWTH ×+×+= 805.10.2501

( )a

aaa W

WHT

×+×−

=805.10.1

0.2501

Page 168

Appendix-D

Where, is the enthalpy of air at an air temperature of and a moisture content

of .

aH aT

aW

D5. The equation of the area of the evaporator (A)

Area= Total surface area of 24 horizontal tubes+ 2×23 times rectangular area of the

gap in between two horizontal tube.

006.016.023216.0019.014159.324 ×××+×××=A

D6. The mass transfer coefficient from interface to air

31

5.0Re664.0 airairairif

airair ScPL

DK ××××= ρ

Where

000001.0)85712921357142.102020046995202.026840000158398.001010000000351.0( 23

×+×−×+×−= airairairair TTTρ

and Tair= Average temperature of air in °C

air

airair

PLVν×

=Re , and PL= Plate length=1.5 m

airif

airair D

Scν

= , and m000026.0=airifD 2/s

all other symbol carries its original meaning.

D7. Relation of interface heat and mass transfer coefficient

In the interface total heat Q can be expressed in terms of heat transfer coefficient or in

terms of mass transfer coefficient according to the following equations.

TAhQ a ∆=

Page 169

Appendix-D

where, ha is the heat transfer coefficient from interface to air, A is the area and Q is the

total energy.

and

TACkHAkQ pm∆=∆=..

where, is the mass transfer coefficient from interface to air and .k H∆ is the enthalpy

difference, Cpm is the moisture content of vapor

Finally

TCAkHAkTAhQ pma ∆=∆=∆= ...

pma Ckh ..

=

pm

aCh

k =..

Page 170

Appendix-E

Appendix E

ANALYSIS OF UNCERTAINTY

Page 171

Appendix-E

APPENDIX E- UNCERTAINTY ANALYSIS FOR DERIVED PARAMETERS

E.1 Uncertainty Analysis for the Heat and Mass Transfer Coefficients

The heat transfer coefficients and mass transfer coefficient of the evaporation

processes occurring in the heat exchanger are calculated from a set of measurements

using both detailed model and simplified model presented in chapter 3. The

coefficients are functions of a number of input parameters, which can be expressed in

functional dependence form as, follow:

U=U (mc, mw, ma, Tw,in, Tw,out , Tc,in, Tc,out, Ta,in, Ta,out, RHin, RHout) (E.1)

Ha= Ha (mc, mw, ma, Tw,in, Tw,out , Tc,in, Tc,out, Ta,in, Ta,out, RHin, RHout) (E.2)

Hwo= Hwo (mc, mw, ma, Tw,in, Tw,out , Tc,in, Tc,out, Ta,in, Ta,out, RHin, RHout) (E.3)

Ka= Ka (mc, mw, ma, Tw,in, Tw,out , Tc,in, Tc,out, Ta,in, Ta,out, RHin, RHout) (E.4)

Moffat (1988) present a procedures to estimate the uncertainty. The uncertainty in U,

Ha, Hwo, Ka i.e δU, δHa, δHwo, δKa respectively can be expressed as:

5.0

22

2

,,

2

,,

2

,,

2

,,

2

,,

2

,,

2.

.

2.

.

2.

.

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+

⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+

+⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

∂

∂+

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

∂

∂+

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

∂

∂

=

outRHoutRH

UinRH

inRHU

outaToutaT

UinaT

inaTU

outwToutwT

U

inwTinwT

UoutcT

outcTU

incTincT

U

am

ma

Uwm

wm

Ucm

cm

U

U

δδ

δδδ

δδδ

δδδ

δ (E.5)

Page 172

Appendix-E

5.0

22

2

,,

2

,,

2

,,

2

,,

2

,,

2

,,

2.

.

2.

.

2.

.

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+

⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+

+⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

∂

∂+

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

∂

∂+

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

∂

∂

=

outRHoutRHaH

inRHinRHaH

outaToutaTaH

inaTinaTaH

outwToutwTaH

inwTinwTaH

outcToutcTaH

incTincTaH

am

ma

aHwm

wm

aHcm

cm

aH

aH

δδ

δδδ

δδδ

δδδ

δ (E.6)

5.0

22

2

,,

2

,,

2

,,

2

,,

2

,,

2

,,

2.

.

2.

.

2.

.

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+

⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+

+⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

∂

∂+

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

∂

∂+

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

∂

∂

=

outRHoutRHwoH

inRHinRH

woH

outaToutaTwoH

inaTinaT

woHoutwT

outwTwoH

inwTinwT

woHoutcT

outcTwoH

incTincT

woH

am

ma

woHwm

wm

woHcm

cm

woH

woH

δδ

δδδ

δδδ

δδδ

δ (E.7)

and

5.0

22

2

,,

2

,,

2

,,

2

,,

2

,,

2

,,

2.

.

2.

.

2.

.

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+

⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+

+⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

∂

∂+

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

∂

∂+

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

∂

∂

=

outRHoutRHaK

inRHinRH

aK

outaToutaTaK

inaTinaTaK

outwToutwTaK

inwTinwTaK

outcToutcTaK

incTincTaK

am

ma

aKwm

wm

aKcm

cm

aK

aK

δδ

δδδ

δδδ

δδδ

δ (E.8)

In the measurement of the temperature the error involved, δT can be determined as

δT=(δT12+δT2

2)0.5 (E.9)

Page 173

Appendix-E

The fixed error in the measurement of temperature, δT1 is ±0.05 °C and the random

error δT2 can be measured from the standard deviation of the population of measured

data as

5.0

1 12

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

= −

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −−

= ∑M

j N

TjT

Tδ (E.10)

Where the mean of the population of measured data and N is is the population size. −T

The uncertainty in the measurement of hot water flow meter and distributed water flow

meter were taken the half of two successive marks over the meter which gives

δmc=±1.5% and δmw=±1.5% respectively.

The uncertainty in the measurement of relative humidity taken from the manual was

δRH=±1%.

As the expressions of U, Ha, Hwo, Ka involve expressions that are difficult to

differentiate analytically, the gradients are computed numerically by perturbing the

input variables.

Following are the processes used to accomplish the numerical uncertainty analysis

(Moffat, 1988).

1. Calculate the values of U, Ha, Hwo, Ka for the measured data and store the

values as UOPT, HAOPT, HWOOPT, KAOPT.

2. Increase the value of first variable, mc by its uncertainty interval, δmc and

calculate the value of U+, Ha+, Hwo+, Ka+ using the new value of the first

Page 174

Appendix-E

variable, which becomes (mc+δmc), keeping all other variables at their

measured value. Find the difference (U+)-(UOPT), (Ha+)-( HAOPT), (Hwo+)-(

HWOOPT) and (Ka+)-( KAOPT) and store them as C1x+, C2y+, C3z+, C4r+

respectively which represent the contribution to the uncertainty of U, Ha, Hwo,

Ka caused by the increase of first variable by its uncertainty interval +δmc.

3. Decrease the value of the first variable, mc by its uncertainty interval δmc and

repeat step-2 to calculate the value of U-, Ha-, Hwo-, Ka-. Find the difference

(U-)-(UOPT), (Ha-)-(HAOPT), (Hwo-)-(HWOOPT) and (Ka-)-(KAOPT) and

store them as C1x-, C2y-, C3z-, C4r- respectively.

4. Calculate the average of the absolute values of C1x+ and C1x- and store them

as Cx1. Similarly calculate the average of the absolute values C2y+ and C2y- as

Cy2, average of the absolute values C3z+ and C3z- as Cz3, average of the

absolute values C4r+ and C4r- as Cr4.

5. Repeat step 2 to 4 for the other variables mw, ma, Tw,in, Tw,out , Tc,in, Tc,out, Ta,in,

Ta,out, RHin, RHout to get the values of Cx2 to 11, Cy2 to 11, Cz2 to 11, Cr2 to 11.

6. The uncertainty in the value of U, Ha, Hwo, Ka are the root-sum-square of the

Cx1 to 11, Cy2 to 11, Cz2 to 11 and Cr2 to 11 respectively.

Page 175

Appendix-E

Table E.1. Uncertainty in the derived parameters for detailed model

δHw

o/Hw

o

4.16

0

22.7

5

10.2

1

14.5

3

6.21

0

18.4

8

3.30

0

4.41

0

5.05

0

3.81

0

5.44

0

20.3

5

19.9

8

4.21

0

22.7

5

δHw

o

0.00

25

0.01

47

0.00

61

0.01

09

0.00

55

0.01

47

0.00

25

0.00

35

0.00

35

0.00

25

0.00

35

0.01

32

0.01

19

0.00

2

0.01

47

Hw

o

0.06

0

0.06

5

0.06

0

0.07

5

0.09

0

0.08

0

0.07

5

0.08

0

0.07

0

0.06

5

0.06

5

0.06

5

0.06

0

0.06

0

0.06

5

δHa/H

a

6.89

0

25.0

9

9.39

5

15.7

8

6.55

0

11.0

8

4.35

0

7.75

0

5.53

0

5.54

0

8.98

0

25.7

6

12.9

6

7.57

0

26.7

4

δHa

0.00

83

0.02

66

0.01

04

0.01

91

0.00

99

0.01

84

0.00

78

0.01

44

0.00

75

0.00

75

0.01

31

0.03

70

0.01

63

0.01

14

0.04

04

Ha

0.12

1

0.10

6

0.11

1

0.12

1

0.15

1

0.16

6

0.18

1

0.18

6

0.13

6

0.13

6

0.14

6

0.14

6

0.12

6

0.15

1

0.15

1

δKa/K

a

6.89

25.0

8

9.39

5

15.7

8

6.55

6

11.0

8

4.35

0

7.75

4

5.53

9

5.53

9

8.98

3

25.7

6

12.9

6

7.57

3

26.7

4

δKa

0.00

83

0.02

64

0.01

038

0.01

9

0.00

9

0.01

83

0.00

78

0.01

43

0.00

75

0.00

75

0.01

30

0.03

74

0.01

625

0.01

138

0.04

01

Ka

0.12

0

0.10

5

0.11

0

0.12

0

0.15

0

0.16

5

0.18

0

0.18

5

0.13

5

0.13

5

0.14

5

0.14

5

0.12

5

0.15

0

0.15

0

δU/U

4.24

3

3.00

0

1.99

8

3.10

9

1.86

3.84

4.52

5.96

2.41

1.72

3.28

3.80

2.55

2.52

4

3.88

δU

0.04

2

0.03

2

0.01

6

0.02

5

0.01

41

0.04

61

0.05

29

0.06

5

0.02

0

0.01

41

0.02

82

0.03

53

0.02

55

0.02

39

0.04

0

U

1.00

1.08

0.83

0.82

0.76

1.20

1.17

1.09

0.83

0.82

0.86

0.93

1.00

0.95

1.03

Page 176

Appendix-E

Table E.1. Uncertainty in the derived parameters contn

δHw

o/Hw

o

7.21

7

9.31

7

4.16

7

9.21

3

12.4

2

9.37

5

18.4

4

5.41

3

2.77

8

5.43

9

13.5

6

20.7

8

6.37

8

13.1

5

5.55

6

δHw

o

0.00

43

0.00

55

0.00

25

0.00

82

0.01

11

0.00

75

0.01

19

0.00

43

0.00

25

0.00

35

0.01

69

0.02

59

0.00

82

0.01

25

0.00

50

Hw

o

0.06

0

0.06

0

0.06

0

0.09

0

0.09

0

0.08

0

0.06

5

0.08

0

0.09

0

0.06

5

0.12

5

0.12

5

0.13

0

0.09

5

0.09

0

δHa/H

a

9.80

1

12.1

7

8.57

0

12.5

4

11.6

5

8.16

1

12.0

2

4.92

0

3.94

4

9.34

6

6.01

4

11.8

4

5.81

1

13.5

9

7.92

9

δHa

0.01

23

0.01

65

0.01

20

0.01

64

0.01

75

0.01

39

0.01

93

0.00

79

0.00

75

0.00

89

0.00

51

0.01

67

0.00

87

0.02

39

0.01

23

Ha

0.12

6

0.13

6

0.14

1

0.13

1

0.15

1

0.17

1

0.16

1

0.16

1

0.19

1

0.09

6

0.08

6

0.14

1

0.15

1

0.17

6

0.15

6

δKa/K

a

9.80

1

12.1

7

8.57

0

12.5

4

11.6

5

8.16

1

12.0

2

4.92

0

3.94

4

9.34

6

6.01

4

11.8

4

5.81

1

13.5

9

7.92

9

δKa

0.01

229

0.01

647

0.01

202

0.01

636

0.01

750

0.01

389

0.01

926

0.00

788

0.00

750

0.00

893

0.00

515

0.01

662

0.00

873

0.02

381

0.01

231

Ka

0.12

537

0.13

532

0.14

030

0.13

035

0.15

025

0.17

015

0.16

020

0.16

020

0.19

005

0.09

552

0.08

557

0.14

030

0.15

025

0.17

512

0.15

522

δU/U

4.80

7

4.80

5

9.66

0

2.49

1

2.78

4

3.81

2

2.76

4

2.52

2

3.64

0

3.06

1

2.56

4

2.19

2

2.30

5

2.41

8

2.36

2

δU

0.05

431

0.05

958

0.15

166

0.02

291

0.02

450

0.03

240

0.02

598

0.02

345

0.03

640

0.03

123

0.02

000

0.01

732

0.01

936

0.02

345

0.02

693

U

1.13

1.24

1.57

0.92

0.88

0.85

0.94

0.93

1.00

1.02

0.78

0.79

0.84

0.97

1.14

Page 177

Appendix-E


δHw

o/Hw

o

4.55

4.71

3.93

9.85

9.32

3.33

5.88

10.6

10.5

2.63

4.33

5.77

5.00

3.72

22.1

δHw

o

0.00

43

0.00

35

0.00

35

0.00

93

0.00

55

0.00

25

0.00

55

0.01

06

0.00

79

0.00

25

0.00

43

0.00

43

0.00

5

0.00

35

0.01

6

Hw

o

0.09

5

0.07

5

0.09

0

0.09

5

0.06

0

0.07

5

0.09

5

0.10

0

0.07

5

0.09

5

0.10

0

0.07

5

0.10

0

0.09

5

0.07

5

δHa/H

a

6.55

4.67

5.07

9.58

7.63

5.08

5.97

12.4

9.19

5.23

5.71

7.11

4.56

5.06

12.2

δHa

0.01

12

0.00

75

0.00

91

0.01

83

0.00

73

0.00

79

0.01

11

0.02

12

0.01

43

0.01

05

0.01

12

0.01

25

0.00

96

0.00

97

0.00

86

Ha

0.17

1

0.16

1

0.18

1

0.19

1

0.09

6

0.15

6

0.18

6

0.17

1

0.15

6

0.20

1

0.19

6

0.17

6

0.21

1

0.19

1

0.07

1

δKa/K

a

6.55

4.67

5.07

9.58

7.63

5.07

5.97

12.4

9.19

5.23

5.71

7.11

4.56

5.08

12.2

3

δKa

0.01

11

0.00

75

0.00

91

0.01

82

0.00

72

0.00

78

0.01

10

0.02

11

0.01

42

0.01

04

0.01

11

0.01

24

0.00

95

0.00

96

0.00

86

Ka

0.17

0

0.16

0

0.18

0

0.19

0

0.09

5

0.15

5

0.18

5

0.17

0

0.15

5

0.20

0

0.19

5

0.17

5

0.20

9

0.19

0

0.07

0

δU/U

2.61

4

2.71

6

2.65

7

2.58

8

2.90

8

2.43

3

3.43

0

2.34

8

4.38

4

2.78

9

2.67

3

3.25

8

3.30

3

2.94

2

3.81

3

δU

0.02

6

0.03

0

0.03

0

0.02

8

0.03

0

0.03

1

0.04

5

0.03

1

0.06

2

0.03

9

0.03

7

0.04

8

0.04

8

0.04

4

0.02

7

U

1.03

1.12

1.16

1.11

1.06

1.30

1.32

1.33

1.42

1.40

1.40

1.48

1.46

1.52

0.73

Page 178

Appendix-E


δHw

o/Hw

o

3.84

10.1

6

11.1

3

14.3

7

4.16

5.44

4.54

10.2

0

10.2

0

δHw

o

0.00

25

0.00

55

0.00

61

0.00

79

0.00

25

0.00

35

0.00

25

0.00

61

0.00

61

Hw

o

0.06

5

0.05

5

0.05

5

0.05

5

0.06

0

0.06

5

0.05

5

0.06

0

0.06

0

δHa/H

a

8.2

8.5

9.8

12.0

5.7

9.3

8.7

10.8

13.4

δHa

0.00

75

0.00

86

0.01

09

0.01

45

0.00

78

0.00

70

0.00

75

0.01

20

0.01

28

Ha

0.09

1

0.10

1

0.11

1

0.12

1

0.13

6

0.07

6

0.08

6

0.11

1

0.09

6

δKa/K

a

8.27

8.50

9.86

12.0

5.79

9.30

8.76

10.8

4

13.4

3

δKa

0.00

75

0.00

85

0.01

09

0.01

44

0.00

78

0.00

70

0.00

75

0.01

19

0.01

28

Ka

0.09

05

0.10

00

0.11

04

0.12

04

0.13

53

0.07

56

0.08

55

0.11

04

0.09

55

δU/U

2.46

2.81

2.96

2.97

2.52

3.38

2.97

4.93

5.31

δU

0.02

0.02

4

0.02

6

0.02

8

0.02

5

0.03

2

0.03

1

0.06

3

0.08

6

U

0.81

0.87

0.91

0.95

1.01

0.97

1.05

1.29

1.61

Page 179

Appendix -F

Appendix F

DIAGRAMS

Page 180

Appendix -F

APPENDIX F-DETAIL DIAGRAMS OF THE EXPERIMENTAL SETUP

F1. Detail diagram of the absorber, solution case and base plate

B

C

D

F

F G d

c

b

a

A to C=78.

ab=11 cm

Figure F.1. Isometric View of evaporator heat exchanger

5 cm

bc

A

BC=20 cm CD=

=11cm cd= 42 cm

E

13 cm

A= Outlet of hot water

B= Bottom tube

C= Inlet of hot water

D= Outlet of solution

E= Thermocouple

F= Inlet of air

abcd= Solution case

CG=26 cm

Page 181

Appendix -F

F2. Detail diagram of experimental setup

C

A= Distributor B= Evaporator C= Base plate D= Solution bath E= Hot water tank F= Air chamber G= Pump H= Fan I= Flow meter J= Flow meter T= Thermocouple

T9

T10

T8

T7

T1 T2 T3

T6

T5

T4

J

I H

G F

E D

B

A

Figure F.2 Front view of the experimental setup

Page 182

Appendix -F

K F

Q T12 Y X

L

S

R

T13

P2

P1

Z

X= Restrictor

Y= Air chamber

Z= Distributor

T= Thermocouple

P= Humidity sensor

F= Air circulating fan

Q= Diverging Section

R= Evaporation chamber

S= Evaporator

K= Air Inlet

L= Air Outlet

Figure F.3. Left side view of the experimental setup

Page 183

Appendix -F

F3. Detail diagram of the Base plate

Figure F.4. Top view of the base plate

Figure F.5. Front view of the base plate

Page 184

Appendix -F

Figure F.6. Isometric view of the base plate

Page 185

muhammad elias - core · mc mass flow rate of hot water at inlet of the evaporator kg.s-1. mw mass...

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