A

Project Report on

Tri Duct Heat Exchanger

Submitted in partial fulfillment of

The requirement for the award from

DEPARTMENT OF CHEMICAL ENGINEERING

Submitted by

HARISH K

Under the guidance of

Smt. J. Gouthami, (H.O.D)

Sri. S. Vijay Kumar (Sr.Lecturer)

DEPARTMENT OF CHEMICAL

ENGINEERING

DEPARTMENT OF CHEMICAL ENGI-

NEERING Approved by

Andhra University, Hyderabad

CERTIFICATE

This is to certify that the project entitled, Tri Duct Heat Ex-

changer is the bonafied work of Mr. K HARISH bearing PIN No: 09096 -

CH - 006 from Department of chemical engineering 7th semester (2012),

submitted in the partial fulfillment of his course period.

J.Gouthami S. Vijay Kumar

(Head of the Department) (Guide)

Contents

List of Figures

List of Tables

List of symbols

INTRODUCTION

Heat Transfer

Project Background

Functions of Heat exchanger

Flow arrangements of Heat Exchanger

Types of Heat Exchanger

TRI DUCT HEAT EXCHANGER

Introduction

Construction

Flow arrangements

TDHE Fig.

THEORY PART

Overall resistance

Dimensionless values

Forced & Natural Convection

Film Co-efficient

PROBLEMATIC PART

Introduction

Assumptions

Calculation

Results

List of Figures

Figure No. Title

1.1. Co-Current (or) Parallel flow

1.2. Counter flow

1.3. Cross flow

2.1. Double pipe heat exchanger

3.1. Heat transfer through boundary layer

List of Tables

Table No. Title

2.2. Table of Diameters of duct according to TEMA

4.2. Table of Properties of fluids

List of Symbols

Ai --------Area of the inner duct

Am --------Area of the middle duct

Ao --------Area of the Outer duct

CP --------Specific heat

D1 --------Outer diameter of inner duct

D2 --------Inner diameter of middle duct

D3 --------Inner diameter of Outer duct

Di --------Inner diameter of inner duct

Dm --------Inner diameter of middle duct

Do --------Inner diameter of Outer duct

Doi --------Outer diameter of inner duct

Dom --------Outer diameter of middle duct

DoO --------Outer diameter of Outer duct

Dii --------Inner diameter of inner duct

Dim --------Inner diameter of middle duct

DiO --------Inner diameter of Outer duct

Dwi --------Log mean diameter of inner duct

Dwm --------Log mean diameter of middle duct

DwO --------Log mean diameter of Outer duct

Gi --------Mass velocity through inner duct

Gm --------Mass velocity through middle duct

GO --------Mass velocity through Outer duct

hi --------Heat transfer coefficient of inner duct

hm --------Heat transfer coefficient of middle duct

hO --------Heat transfer coefficient of Outer duct

k --------Thermal conductivity

mi --------Mass flow rate of inner duct

mm --------Mass flow rate of middle duct

mO --------Mass flow rate of Outer duct

NRe --------Reynolds’s number

NPr --------Prandtl’s number

NNu --------Nusselt’s number

u --------Velocity

Uoi --------Over all heat transfer coefficient of inner duct

Uom --------Over all heat transfer coefficient of middle duct

UoO --------Over all heat transfer coefficient of Outer duct

x --------Thickness of the duct

ρ --------Density of fluids

µ --------Viscosity of fluids

INTRODUCTION

1.1 HEAT TRANSFER

It is well established fact that if two bodies of different temperatures

are brought into thermal contact, heat flows from a body at high tempera-

ture to that at lower temperature [second law of thermodynamics]. The net

flow of heat is always in the direction of temperature decrease. Thus, heat is

defined as a form of energy which is in transit between a hot source and

cold receiver. The transfer of heat solely depends on the temperature of the

two parts of the system. In other words, temperature can be termed as a lev-

el of thermal energy i.e., high temperature of the body is the indication of

high level of heat energy content of the body.

Whenever the temperature difference (driving force for heat transfer) exists

between two parts of the system, the heat may flow by one or more of the

three basis mechanisms, namely, conduction, convection, and radiation.

Conduction It is the transfer of heat from one part of the body to the another part

of the body or from one body to another which is in physical contact to it,

without appreciable displacement of particles of the body. In metallic solids

, thermal conduction results from the motion of unbound electrons. It is re-

stricted to flow of heat in solids.

Convection It is the transfer of heat from one point to another point within a fluid

(gas or liquid) by mixing of hot and cold portions of the fluid. It is attribut-

ed to the macroscopic motion of the fluid. Convection is restricted to flow

of heat in fluids and closely associated with the fluid mechanics.

Radiation Radiation refers to the transfer of heat energy from one body to an-

other, not in contact with it, by electromagnetic waves through space.

Boundary layers

Since for every fluid flowing with low flow rates there will be a re-

sistance offered to the transfer of heat due to the formation of a static layer

of that fluid around the walls. This layer is called boundary layer. Being a

static layer it offers resistance to the flow of heat through the wall. And this

resistance can be overcome by increasing the flow rate of the passing fluid.

This results to the decrease of the thickness of the boundary layer.

If the resistance to heat transfer is considered as lying within the film cover-

ing the surface, the rate of heat transfer Q is given as

Q = kA ΔT/x

The effective thickness x is not generally known and therefore the

equation is usually re-written in the form :

Q = hA ΔT

This is the basic equation for the rate of heat transfer by convection

under steady state conditions.

Where ‘h’ is called as film heat transfer co-efficient or surface co-efficient

or simply film co-efficient.

Numerically, heat transfer co-efficient (h) is the quantity of heat

transferred in unit time through unit area at a temperature difference of one

degree between the surface and surrounding.

PROJECT BACKROUND :

The heat exchanger is a device which transferred the heat from hot medium

to cold medium without mixed both of medium since both mediums are

separated with a solid wall generally. There are many types of heat ex-

changer that used based on the application. For example, double pipe heat

exchanger is used in chemical process like condensing the vapor to the liq-

uid. When to construct this type of heat exchanger, the size of material that

want to uses must be considered since it affected the overall heat transfer

coefficient. For this type of heat exchanger, the outlet temperature for both

hot and cold fluids that produced is estimated by using the best design of

this type of heat exchanger.

HEAT EXCHANGER :

Heat exchanger is a device, such as an automobile radiator, used to transfer

heat from a fluid on one side of a barrier to a fluid on the other side without

bringing the fluid into direct contact (Fogies, 1999). Usually, this barrier is

made from metal which has good thermal conductivity in order to transfer

heat effectively from one fluid to another fluid. Besides that, heat exchanger

can be defined as any of several devices that transfer heat from a hot to a

cold fluid. In engineering practical, generally, the hot fluid is needed to cool

by the cold fluid. For example, the hot vapor is needed to be cool by water

in condenser practical. Moreover, heat exchanger is defined as a device

used to exchange heat from one medium to another often through metal

walls, usually to extract heat from a medium flowing between two surfaces.

In automotive practice, radiator is used as heat exchanger to cool hot water

from engine by air surrounding same like intercooler which used as heat

exchanger to cool hot air for engine intake manifold by 4 air surrounding.

Usually, this device is made from aluminum since it is lightweight and good

thermal conductivity.

1.3 FUNCTIONS OF HEAT EXCHANGER :

Heat exchanger is a special equipment type because when heat exchanger is

directly fired by a combustion process, it becomes furnace, boiler, heater,

tube-still heater and engine. Vice versa, when heat exchanger make a

change in phase in one of flowing fluid such as condensation of steam to

water, it becomes a chiller, evaporator, sublimated, distillation-column re-

boiler, still, condenser or cooler-condenser. Heat exchanger may be de-

signed for chemical reactions or energy-generation processes which become

an integral part of reaction system such as a nuclear reactor, catalytic reac-

tor or polymer (Fogiel, 1999). Normally, heat exchanger is used only for the

transfer and useful elimination or recovery of heat without changed in

phase. The fluids on either side of the barrier usually liquids but they can be

gasses such as steam, air and hydrocarbon vapor or can be liquid metals

such as sodium or mercury. In some application, heat exchanger fluids may

use fused salts.

1.4 FLOW ARRANGEMENTS OF HEAT EXCHANGER :

There are three basic flow arrangements,

1. Parallel flow/Co-current flow

2. Counter current flow and

3. Cross flow.

Consider a double pipe heat exchanger wherein hot fluid is flowing through

inside pipe and cold fluid is flowing through annular space for explanation

of parallel and counter current flow.

When both the fluids flow in same direction from one end of the heat ex-

changer to the other end, then the flow is called co-current (or) parallel

flow.

Such flow is shown in Fig. 1.1.

When the fluids are flowing through the heat exchanger in opposite direc-

tions with respect to each other (i.e. one fluid enters at one end of heat ex-

changer and other fluid enters at opposite end of the heat exchanger), then

the flow is termed as counter current flow.

It is shown on Fig. 1.2.

When the fluids are directed at the right angles to each other through heat

exchanger, then the flow arrangement is called cross flow.

It is show in Fig. 1.3.

1.5 CLASSIFICATION OF HEAT EXCHANGERS :

There are mainly three types of Heat exchangers which are most used in

industries.

1. Double pipe Heat Exchanger

2. Shell and tube Heat Exchanger and

3. Plate-type Heat Exchanger.

2 TRI - DUCT HEAT EXCHANGER

2.1 INTRODUCTION :

It is one type of heat exchanger which is a combination of double pipe heat

exchanger and shell and tube heat exchanger. It is mainly associated to in-

crease the surface contact to the hot fluid to the cold fluid more than that of

double pipe heat exchanger and occupying the almost same space as the

double pipe heat exchanger does.

Finally it can be employed in those industries where :-

1) the heat transfer rate should be more than that of double

pipe heat exchanger and

2) the occupying space of the instrument should be less than that of shell

and tube heat exchanger.

Hence, the main purpose of the Tri - Duct Heat Exchanger is to removing

(or) transferring the heat in the center of the hot fluid flowing in the duct.

Demonstration of the above statement :- Let us consider a hot fluid flowing in the tube of an double pipe heat

exchanger and a cold fluid which is passing counter currently between the

annular space of the double pipe heat exchanger,

as shown in the Fig. 2.1.

If we observe it according to the rate of heat transfer, there will be

two main resistance offered to the heat transfer.

1) Resistance offered by the tube wall (metal wall)

2) Resistance offered by the boundary layer.

Hence, the first resistance which is due to the tube wall can be re-

duced by decreasing the thickness(x) of the metal wall.

And the second one is caused by the friction offered by the inside

wall of the tube which causes to static arrangement of water molecules and

forms a layer which causes resistance. Well this problem can be overcome

by increasing the flow rate of the fluid which produces the turbulence and

eddies in the fluid. These eddies will create some disturbance in the static

layer and make the molecules in that layer to flow with them.

But here the main thing we have to consider is that “As the liquid flows, the

flow rate increases from the boundary layer to the center point of the liq-

uid”.

This notifies us that the fluid which is flowing in contact with the boundary

layer will have much more heat transfer rate than the fluid flowing in the

center of the pipe.

To overcome this problem within a given space Tri - Duct Heat Exchanger

is introduced.

2.2 CONTRUCTION OF TRI-DUCT HEAT EXCHANGER

Tri - Duct Heat Exchange is almost similar to double pipe heat ex-

changer. It consists of concentric pipes, connecting tees, return heads, and

return bends. The packing glands will support the inner, middle and outer

pipes. The tees are provided with nozzles or screwed connections for per-

mitting the entry and exit of the annular fluid which crosses from one leg to

the other through the return head. The return bend connects two legs of in-

ner pipes to each other. This exchanger can be very easily assembled in any

pipe fitting shop as it consists of standard parts and it provides inexpensive

heat transfer surface. In this exchanger, one of the fluids flow through the

middle duct and other fluid flows through the inner and outer pipes either in

co-current or in counter current fashion.

The tri-duct heat exchanger is very attractive where the total heat transfer

surface required is small, 9.29 m2

to 14 m2

or less. This is simple in con-

struction, cheap and easy to clean.

The major difference according to the double pipe heat exchanger is that it

consists of another pipe embedded within the inner tube, making the inner

tube as middle one.

And here, hot fluid flows within the middle pipe counter currently to the

cold fluid which flows in the inner tube and annular space (or) outer tube.

This type of construction makes the hot fluid to transfer higher rates of heat

to the cold fluid.

Outer diameter, inches Inner diameter, inches

2 1 1/4

2 1/2 1 1/4

3 2

4 3

2.2 Table of Diameters of ducts according to TEMA :-

2.3 FLOW ARRANGEMENTS :-

In this heat exchanger according to the three types of flows the coun-

ter current flow will be good to achieve higher heat transfer rates.

3 THEORY PART

3.1. OVERALL RESISTANCE :-

Q = hA ΔT

This is the basic equation for the rate of heat transfer by convection

under steady state conditions.

Where ‘h’ is called as film heat transfer co-efficient or surface co-efficient

or simply film co-efficient.

Numerically, heat transfer co-efficient (h) is the quantity of heat transferred

in unit time through unit area at a temperature difference of one degree be-

tween the surface and surrounding.

As shown in the Fig.3.1.

The temperature change from T1 to T2 is taking place in a hot fluid

film of thickness x1. The rate of heat transfer through this film by conduc-

tion is given by :

Q = k1 A1 (T1 -T2) / x1

The effective film thickness x1 depends upon the nature of flow and

nature of surface, and is generally not known. Therefore the equation is

usually rewritten as :

Q = hi Ai (T1 -T2)

where hi is known as inside heat transfer co-efficient or surface co-

efficient or simply film co-efficient.

As seen from the above equation, the film co-efficient is the measure

of rate of heat transfer for unit temperature difference and unit surface of

heat transfer and it indicates the rate or speed of transfer of heat by a fluid

having variety of physical properties under varying degrees of agitation. In

SI system, it has units of W/(m2 .K).

The overall resistance to heat flow from hot fluid to cold fluid is

made up of three resistances in series. they are :

1. Resistance offered by film of hot fluid

2. Resistance offered by the metal wall and

3. Resistance offered by film of cold fluid.

Rate of heat transfer through the metal wall is given by equation :

Q = kAw (T2 -T3) / xw

here, Aw - log mean area of pipe

xw - thickness of wall pipe

k - thermal conductivity of material of pipe.

The rate of heat transfer through cold fluid film is given by

Q = hoAo (T3 -T4)

here, ho is the outside film co-efficient (or) individual heat transfer co-

efficient.

therefore the equation can be written as (T1 -T2) = Q / hiAi

Similarly the equation for the metal wall can be written as

(T2 -T3) = Q / (kAw/xw)

and

(T3 -T4) = Q / hoAo

Adding the above all equations, we get :

(T1 -T2) + (T2 -T3) + (T3 -T4) = Q [1/ hiAi + 1/ (kAw/xw) + 1/ hoAo]

Therefore, (T1 -T4) = Q [1/ hiAi + 1/ (kAw/xw) + 1/ hoAo]

here, T1 and T4 are the average temperatures of hot and cold fluids respec-

tively.

Therefore equation similar to above equation in terms of overall heat

transfer co-efficient can be written as :

Q = Ui Ai (T1 -T4) (or) Q = UoAo (T1 -T4)

here, Ui or Uo are the overall heat transfer co-efficient based on inside and

outside area respectively.

Resistance form of overall coefficient :-

Reciprocal of the overall heat transfer co-efficient can be considered

as the overall resistance and it may be given by equation :

1/Uo = 1/hi (Do/Di) + xw/k (Do/Dw) + 1/ho

The individual terms on R.H.S. of the above equation represents the

individual resistances of the two fluids and a metal wall.

The overall temperature drop is proportional to 1/U. Similarly, indi-

vidual temperature drops in the two fluids and metal wall are proportional

to individual resistance.

3.2 DIMENSIONLESS QUANTITIES :-

Reynolds’s number = Duρ/µ

Nusselt’s number = hL/k

Prandtl’s number = Cpµ/k

3.3 FORCED AND NATURAL CONVECTION :-

For natural convection :-

NNu = f(NPr, NGr)

For forced convection, Reynolds’s number influences the heat trans-

fer characteristics and the Grashof’s number may be omitted. Thus for

forced convection

NNu = f(NRe, NPr)

3.4 HEAT TRANSFER CO-EFFICIENTS :-

In laminar flow

The sider- tate equation for the calculation of heat transfer coefficient

for laminar flow in horizontal ducts is—

NNu = 1.86 [(NRe)(NPr)(D/L)]1/3

[µ/µw]0.14

In turbulent flow

The Dittus-Boelter equation for the calculation of heat transfer coef-

ficient for turbulent flow in horizontal ducts is—

For heating :

NNu = 0.023 (NRe)0.8

(NPr)0.4

For cooling :

NNu = 0.023 (NRe)0.8

(NPr)0.3

In transition flow

For transition region i.e. for 2100 < NRe <10000, the following empirical

equation can be used.

NNu = 0.116 [(NRe)2/3

-125] (NPr)1/3

[1+(D/L)2/3

] [µ/µw]0.14

4 PROBLEMATIC PART

4.1. INTRODUCTION :

Being our equipment is a Tri Duct Heat Exchanger, the hot fluid

should be flowing through the middle pipe and the cold fluid which is used

to absorb the heat from the hot fluid should be flowing through the inner

and outer ducts.

Hence, the ducts should be made up of Stainless Steel and the flow is

counter current.

Other moulding like fines on the tubes can be used to increase the

heat transfer rate. When these are attested there will be a negligible loss inn

flow rate but being negligible they are not taken into account.

4.2. ASSUMPTIONS :

Let,

the hot fluid (middle) be ethylene glycol

the cold fluid (inner, outer) be toluene

the entering temperature of the hot fluid be 85 C

the entering temperature of the cold fluid be 30 C

the outside diameter of the outer pipe be 90mm

the outside diameter of the middle pipe be 75mm

the outside diameter of the inner pipe be 30mm

the wall thickness of all the pipes be 3mm

the flow rates of all the fluids be 5000kg/h

Property Ethylene glycol Toluene

Density

Specific heat

Thermal con-

ductivity

Viscosity

1080 kg/m3

2.680 kJ/(kg.K)

0.248 W/(m.K)

3.4 x 10-3

Pa.s

840 kg/m3

1.80 kJ/(kg.K)

0.146 W/(m.K)

4.4 x 10-4

Pa.s

Table :- 4.2. Properties of fluids

Thermal conductivity of metal pipes is 46.52 W/(m.K), ethylene gly-

col is flowing through the middle and toluene is flowing through the inner

and outer pipes counter current to each other.

4.3. CALCULATION :

For toluene flowing through the inner pipe :

mass flow rate of toluene = mi

= 5000 kg/h

= 1.388 kg/s

Outer diameter of inner pipe = 30 mm

Inner diameter of inner pipe = 30 - 2x3

= 24 mm

= 0.024 m

Area of inner pipe = A i

= (π/4) D2

i

= (π/4) (0.024)2

A I = 0.000452 m2

Mass velocity G = m i/A i

= 1.388/0.000452

= 3070.7 kg/(m2.s)

NR = D iuρ/µ

= D iG/µ

Since,

Viscosity of the toluene µ = 4.4 x 10-4

Pa.s

= 4.4 x 10-4

kg/(m.s)

Specific heat of toluene Cp = 1800 J/(kg.K)

Thermal conductivity of toluene k = 0.146 W/(m.K)

NRe= (0.024 x 3070.7)/ 4.4 x 10-4

= 1,67,492

NPr= Cpµ/k

= 1800 x 4.4 x 10-4

/ 0.146

= 5.42

As NRe > 10,000 we can use the Dittus - Boelter equation [for heating]

NNu= 0.023 (NRe)0.8

(NPr)0.4

= 0.023 (167492) 0.8

(5.42) 0.4

= 683.1

Since NNu = hiDi/ k

hiDi/ k = 683.1

= 683.1 x 0.146 /0.024

hi = 4155 W/(m2.K)

-------------------------------------------------------------------------------------------

For Ethylene glycol flowing through the middle pipe :

mass flow rate of ethylene glycol = mm

= 5000 kg/h

= 1.388 kg/s

Outer diameter of middle pipe = 75 mm

Inner diameter of middle pipe = 75 - 2x3

= 69 mm

= 0.069 m

Equivalent diameter of middle pipe = Dm

= D22

- D12 / D1

= (0.0692 - 0.03

2) /0.03

= 0.128 m

Area of cross section for flow = A m

= (π/4) [D22

- D12]

=(π/4)[(0.0692 - 0.03

2)]

= 0.00303 m2

Mass velocity Gm = m m/Am

= 1.388/0.00303

= 458.08 kg/(m2.K)

NRe = D muρ/µ

= D mGm/µ

Since,

Viscosity of the ethylene glycol µ = 3.4 x 10-3

Pa.s

= 3.4 x 10-3

kg/(m.s)

Specific heat of ethylene glycol Cp = 2680 J/(kg.K)

Thermal conductivity of ethylene glycol k = 0.248 W/(m.K)

NRe = (0.128 x 458.08)/ 3.4 x 10-3

= 17,245

NPr = Cpµ/k

= 2680 x 3.4 x 10-3

/ 0.248

= 36.74

As NRe > 10,000 we can use the Dittus - Boelter equation [for cooling]

NNu = 0.023 (NRe) 0.8

(NPr) 0.3

=0.023 (17245)0.8

(36.74)0.3

= 166.18

Since NNu = hmDm/ k

hmDm/ = 166.18

= 166.18 x 0.248 /0.128

hm = 321.97 W/(m2.K)

-------------------------------------------------------------------------------------------

For toluene flowing through the outer pipe :

mass flow rate of toluene = mo

= 5000 kg/h

= 1.388 kg/s

Outer diameter of outer pipe = 90 mm

Inner diameter of outer pipe = 90 - 2x3

= 84 mm

= 0.084 m

Equivalent diameter of outer pipe = Do

= D32

- D22 / D2

= (0.0842 - 0.069

2) /0.069

= 0.033 m

Area of cross section for flow = A o

= (π/4) [D32

- D22]

= (π/4) [(0.0842 - 0.069

2)]

= 0.0018 m2

Mass velocity Go= m o/Ao

= 1.388/0.0018

= 771.1 kg/(m2.s)

NRe = D ouρ/µ

= D oGo/µ

Since, Viscosity of the toluene µ = 4.4 x 10-4

Pa.s

= 4.4 x 10-4

kg/(m.s)

Specific heat of toluene Cp = 1800 J/(kg.K)

Thermal conductivity of toluene

k = 0.146 W/(m.K)

NRe = (0.033 x 771.1)/ 4.4 x 10-4

= 57,832

NPr = Cpµ/k

= 1800 x 4.4 x 10-4

/ 0.146

= 5.42

As NRe > 10,000 we can use the Dittus - Boelter equation [for heating]

NNu = 0.023 (NRe)0.8

(NPr)0.4

=0.023 (57,832)0.8

(5.42)0.4

= 291.78

Since NNu = hoDo/ k

hoDo/ k = 291.78

= 291.78 x 0.146 /0.033

ho = 1,290.9 W/(m2.K)

-------------------------------------------------------------------------------------------

Over all heat transfer co-efficient :-

Log mean diameter of inner pipe = Dwi

=(0.03-0.024)/[ln (0.03/0.024)]

= 0.0246 m

Over all heat transfer co-efficient based on the outside area of

inner pipe

(UOi )

1/UOi = [(1/hO) + (1/hm) + (1/hi)] [(DOi/Dii) + (x/k)] [DOi/Dwi]

= [(1/1290.9) + (1/321.97) + (1/4155)] + [(0.03/0.024) +

(0.003/46.52)] + [(0.03/0.0246)]

= (4.119 x 10

-3) (1.25) (1.2195)

= 6.278 x 10-3

1/UOi

= 6.278 x 10-3

UOi = 159.28 W/(m2.K)

Log mean diameter of middle pipe = Dwm

=(0.075-0.069)/[ln

(0.075/0.069)]

= 0.0719 m

Over all heat transfer co-efficient based on the outside area

of middle pipe

(UOm)

1/UOm = [(1/hO) + (1/hm) + (1/hi)] [(DOm/Dim) + (x/k)] [DOm/Dwm]

= [(1/1290.9) + (1/321.97) + (1/4155)] + [(0.075/0.069) +

(0.003/46.52)] + [(0.075/0.071)]

= (4.119 x 10

-3) (1.153) (1.056)

= 5.015 x 10-3

1/UOm

= 5.015 x 10-3

UOm = 199.4 W/(m2.K)

Log mean diameter of outer pipe = Dwo

=(0.09-0.084) /[ln (0.09/0.084)

= 0.086 m

Over all heat transfer co-efficient based on the outside area of

outer pipe

(UoO)

1/UoO = [(1/hO) + (1/hm) + (1/hi)] [(DoO/DiO) + (x/k)] [DoO/DwO]

= [(1/1290.9) + (1/321.97) + (1/4155)] + [(0.09/0.084) +

(0.003/46.52)] + [(0.09/0.086)]

= (4.119 x 10

-3) (1.071) (1.046)

= 4.6143 x 10-3

1/UoO

= 4.6143 x 10-3

UoO = 216.7 W/(m2.K).

-------------------------------------------------------------------------------------------

APPENDICES

Transfer of heat from one place to another with or without any medium is

called heat transfer.

Conduction

It is the transfer of heat from one part of the body to the another part of the

body or from one body to another which is in physical contact to it, without

appreciable displacement of particles of the body.

Convection

It is the transfer of heat from one point to another point within a fluid (gas

or liquid) by mixing of hot and cold portions of the fluid. It is attributed to

the macroscopic motion of the fluid.

Radiation

Radiation refers to the transfer of heat energy from one body to another,

not in contact with it, by electromagnetic waves through space.

Boundary layers

Since for every fluid flowing with low flow rates there will be a resistance

offered to the transfer of heat due to the formation of a static layer of that

fluid around the walls. This layer is called boundary layer.

Parallel flow

When both the fluids flow in same direction from one end of the heat ex-

changer to the other end, then the flow is called co-current (or) parallel

flow.

Counter flow

When the fluids are flowing through the heat exchanger in opposite direc-

tions with respect to each other (i.e. one fluid enters at one end of heat ex-

changer and other fluid enters at opposite end of the heat exchanger), then

the flow is termed as counter current flow.

Cross flow

When the fluids are directed at the right angles to each other through heat

exchanger, then the flow arrangement is called cross flow.

Thermal conductivity

It is the quantity of heat passing through a quantity of material at unit thick-

ness with unit heat flow area in unit time when temperature difference of

maintained across the opposite faces of material.