experimental investigation of heat transfer in laser ...€¦ · experimental investigation of heat...

Experimental Investigation of Heat Transfer in Laser Sintered and Wire Mesh Heat Exchangers

by

Reza Rezaey

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy

Department of Mechanical and Industrial Engineering University of Toronto

© Copyright by Reza Rezaey 2017

ii

Experimental Investigation of Heat Transfer in Laser Sintered and

Wire-Mesh Heat Exchangers

Reza Rezaey

Doctor of Philosophy

Department of Mechanical and Industrial Engineering

University of Toronto

2017

Abstract

In this thesis, an experimental investigation of fluid flow and heat transfer through open cell porous

wire mesh and laser-sintered heat exchangers is presented. The thesis consists of two main sections

that describe how to create a compact heat exchanger that uses open-cell porous structures.

In the first part of the thesis a new method of building compact heat exchangers using direct metal

laser sintering (DMLS), a technology which enables heat exchangers with a predetermined, fully

controlled internal geometry to be built was investigated. Laser-sintering was used to fabricate

stainless steel heat exchanger channels filled with struts arranged to form either cubic, round-strut

tetradecahedral or thin-strut tetradecahedral cells. The objective was to demonstrate that the effect

of adding internal struts is not simply to increase surface area, but that cell geometry has a

significant effect on both heat transfer and fluid flow. This section also describes the importance

of the connection between the porous structures, which is used to improve the performance of the

heat exchanger, to the main body of the heat exchanger. It was possible to design internal

geometries that maximize heat transfer while minimizing weight and frictional losses.

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In the second part of the thesis, a simple method of increasing the heat transfer surface area has

been developed by using a twin wire-arc thermal spray system to generate a dense, high strength

coating that bonds porous structures, like wire mesh and perforated sheets, to the plain tube heat

exchanger’s outside surfaces. The porous structure and the main body of the heat exchanger must

be well bonded together to minimize thermal resistance. The extended surfaces of the wire mesh

and perforated sheet enhanced the heat transfer performance of the tube heat exchangers. Finding the

right balance between pore density and number of screens of the porous structures is crucial for

maximizing the heat transfer performance of the heat exchangers.

iv

Acknowledgments

I would like to thank my wonderful supervisor, Professor Sanjeev Chandra, for his time and non-

stop support during the course of this research. It was an honour for me to work under his

supervision and guidance during the last four years. I also want to thank Professor Javad

Mostaghimi, Doctor Larry Pershin and Professor Thomas Coyle at the Center for Advanced

Coating Technologies (CACT), at the University of Toronto, for providing valuable guidance in

every aspect of this research. Also, my special thanks go to my lab mates and friends at CACT,

Mehrdad Taheri, Saeid Salavati, Bharath Krishnan, Christiane Mubikayi, and all other lab mates.

I want to thank my colleague Mr. Felix Loosmann and his supervisor Professor Cameron Tropea

at Technische Universirat Dramstadt for the fabrication of laser-sintered prototypes.

Last but not least, I would like to thank my father, Masieh, for his careful guidance, my mother,

Nasrin, for her invaluable support and my brother, Mojtaba, for always being so supportive and

encouraging.

Finally, I would like to appreciate the endless patience and constant support of my beloved wife

Newsha. Your encouragements in the toughest times, positive attitude and beautiful smile gave

me the strength to finish my studies.

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Table of Contents

Acknowledgments ........................................................................................................................ iv

Table of Contents ...........................................................................................................................v

List of Tables .............................................................................................................................. viii

List of Figures ............................................................................................................................... ix

List of Appendices ..................................................................................................................... xvii

Chapter 1 Introduction..................................................................................................................1

1.1 Introduction ........................................................................................................................1

1.2 Literature Review ..............................................................................................................2

1.3 Objectives............................................................................................................................6

1.4 Organization of Thesis .......................................................................................................7

DMLS Heat Exchangers ........................................................................................9

2.1 Introduction ........................................................................................................................9

2.2 Geometric Characteristics ...............................................................................................11

2.3 Fabrication of DMLS Heat Exchangers ........................................................................14

2.3.1 Fabrication of Heat Exchanger Channels..........................................................15

2.3.2 Material Properties ..............................................................................................19

Conduction Heat Transfer in DMLS Heat Exchangers ...................................23

3.1 Test Samples, Experimental Apparatus and Results ...................................................23

3.2 Heat Transfer Characteristics ........................................................................................38

3.2.1 Theory ...................................................................................................................38

3.2.2 Analytical Models.................................................................................................39

3.2.3 Analysis and Discussion .......................................................................................43

3.3 Conclusion ........................................................................................................................46

vi

Convection Heat Transfer in DMLS Heat Exchangers ....................................47

4.1 Experimental Apparatus .................................................................................................47

4.2 Hydraulic Characteristics ...............................................................................................49

4.3 Heat Transfer Characteristics ........................................................................................54

4.4 Conclusion ........................................................................................................................70

Wire-Arc Thermal Sprayed Heat Exchangers ..................................................71

5.1 Introduction ......................................................................................................................71

5.2 Geometric Characteristic ................................................................................................74

5.3 Fabrication of Wire-Arc Thermal Sprayed Heat Exchangers ....................................75

Preliminary Investigation of Flow over Perforated Sheet and Wire Mesh

Fins ................................................................................................................................80

6.1 Introduction ......................................................................................................................80

6.2 Fabrication of Wire-Arc Thermal Sprayed Fins ..........................................................84

6.3 Experimental Apparatus and Methods ..........................................................................88

6.4 Results and Discussion .....................................................................................................91

6.4.1 Plain Tube .............................................................................................................91

6.4.2 Perforated Sheet Fins ..........................................................................................94

6.4.3 Wire Mesh Fins ..................................................................................................103

6.5 Heat Transfer Characterization ...................................................................................108

6.6 Conclusion ......................................................................................................................115

Water-to-Air Wire Mesh Heat Exchangers .....................................................116

7.1 Introduction ....................................................................................................................116

7.2 Fabricated Heat Exchangers .........................................................................................117

7.2.1 Wire Mesh...........................................................................................................117

7.2.2 Fabrication Process ............................................................................................117

7.3 Experimental Apparatus and Methods ........................................................................121

vii

7.4 Pressure Drop Through Wire Mesh Screens...............................................................124

7.5 Results and Discussion ...................................................................................................126


7.6.1 Non-Dimensional Parameters ...........................................................................130

7.6.2 Empirical Fin Model Correlation .....................................................................135

7.6.3 A Model for Prediction of Heat Exchanger Temperature Rise .....................144

7.7 Conclusion ......................................................................................................................151

Air-To-Air Wire Mesh Heat exchangers .........................................................152

8.1 Introduction ....................................................................................................................152

8.2 Heat Exchanger Design .................................................................................................154

8.3 Manufacturing of the Heat Exchanger ........................................................................156

8.4 Experimental Apparatus ...............................................................................................161

8.5 Heat Transfer Calculation ............................................................................................163

8.6 Results and Discussion ...................................................................................................164


8.8 Conclusion ......................................................................................................................168

Summary .............................................................................................................169

9.1 Laser Sintered Heat Exchangers ..................................................................................169

9.2 Wire Mesh Heat Exchangers ........................................................................................169

References ..............................................................................................................................172

Appendices ..............................................................................................................................177

viii

List of Tables

Table 4-1: Structural comparison between the cubic, round-strut tetradecahedral and thin-strut

tetradecahedral heat exchanger channels. ..................................................................................... 52

Table 5-1: Porosity, oxide content, and adhesion strength of the coatings sprayed under different

conditions [6]. ............................................................................................................................... 76

Table 5-2: Wire-arc thermal spray parameters for deposition of stainless steel coating [6]. ....... 78

Table 6-1: Perforated sheet specifications. ................................................................................... 84

Table 6-2: Wire mesh fin specifications. ...................................................................................... 85

Table 6-3: Summary of the porous structures used in the study. .................................................. 86

Table 6-4: Comparison between the variation of NuD and Anon-perf. ........................................... 111

Table 7-1: Parameters of the wire mesh heat exchangers. .......................................................... 119

Table 7-2: Parameters of the wire mesh heat exchangers at a water mass flow rate of 0.015 Kg/s.

..................................................................................................................................................... 147

Table 7-3: Parameters of the wire mesh heat exchangers at a water mass flow rate of 0.0117

Kg/s. ............................................................................................................................................ 148

Table 8-1: Cold air velocities inside the wind tunnel. ................................................................ 163

ix

List of Figures

Figure 2-1: Unit cell geometry (a) cubic, and (b) tetradecahedral. ............................................... 11

Figure 2-2 : Unit cell geometry of the thin-strut tetradecahedral geometry. ................................ 12

Figure 2-3: Unit cell geometry (a) cubic, (b) round-strut tetradecahedral and (c) thin-strut

tetradecahedral. ............................................................................................................................. 12

Figure 2-4: Schematic of DLMS manufacturing procedure [38]. ................................................. 14

Figure 2-5: Channel section (a) cubic, (b) round-strut tetradecahedral, and (c) thin-strut

tetradecahedral. ............................................................................................................................. 16

Figure 2-6: Heat exchanger channels (a) end view of cubic channel (b) end view of round-strut

tetradecahedral channel, and (c) thin-strut tetradecahedral. ......................................................... 17

Figure 2-7: Round-strut tetradecahedral channel with side face removed. .................................. 18

Figure 2-8: Complete assembly of the heat exchanger with four sections welded together. ........ 19

Figure 2-9: SEM images of (a) channel wall surface, and (b) cross section of the channel wall. 20

Figure 2-10: Connection between the strut and the channel wall of the heat exchanger. ............. 21

Figure 2-11: EDS analysis of the coating micro structure at the connection point between the

struts and the wall. ........................................................................................................................ 22

Figure 3-1: Tetradecahedral structure (a) one partially removed wall, and (b) without walls. .... 24

Figure 3-2: Schematic overview over the four different experimental setups. ............................. 25

Figure 3-3: Experimental apparatus to determine the thermal conductivity of laser-sintered

stainless steel (a) a block manufactured with common methods on the left side and a block

sintered using DMLS on the right side, and (b) a schematic of the experimental setup. ............. 26

Figure 3-4: Temperature distribution over sample length for the first set of experiments. .......... 27

x

Figure 3-5: Experimental apparatus, which is used for the third and fourth set of experiments, to

measure the temperature distribution for different heat fluxes with cooling at one side of the

samples and heating on the opposite site, respectively. ................................................................ 29

Figure 3-6: Comparison of experimental results for the outer surface temperature distribution

over relative location between cubic and round-strut tetradecahedral sample at a three different

heat fluxes. Heating from one side, cooling from the other, results. ............................................ 30

Figure 3-7: Comparison between heat transfer in samples (a) with zero heat loss to surrounding,

and (b) with heat loss to the surroundings. ................................................................................... 31

Figure 3-8: Schematics for sample segmentations for heat loss calculation. ............................... 33

Figure 3-9: Temperature distribution over sample length for the third set of experiments. ......... 35

Figure 3-10: Thermal conductivity of the laser-sintered stainless steel block over applied heat

flux for the first set of experiments. Data sheet values are taken from the EOS Stainless Steel 17-

4 data sheet [37]. ........................................................................................................................... 36

Figure 3-11: Comparison of the effective thermal conductivity over applied heat flux for the

cubic and round-strut tetradecahedral heat exchangers, and the round-strut tetradecahedral

structure without walls. ................................................................................................................. 37

Figure 3-12: Heat transfer direction through (a) Parallel Model, and (b) Series Model. ............. 40

Figure 3-13: Comparison of the effective thermal conductivity for different porosities between

predictions of various analytical models. ...................................................................................... 43


predictions of various analytical models and the experimental results. ........................................ 45

Figure 4-1: Schematic of experimental apparatus. ....................................................................... 48

Figure 4-2: Variation of experimentally measured pressure gradient with average fluid velocity

in channels with cubic, round-strut tetradecahedral and thin-strut tetradecahedral cells. ............ 50

xi

Figure 4-3: Friction factor variation with Reynolds number for channels with cubic, round-strut

tetradecahedral and thin-strut tetradecahedral. ............................................................................. 53

Figure 4-4: Increase in air temperature from the inlet to the outlet of a) cubic b) round-strut

tetradecahedral, and c) thin-strut tetradecahedral heat exchangers with air flow rates varying

from 10 to 90 L/min for applied heat flux in the range of 3.2 to 0.8 kW/m2. ............................... 55

Figure 4-5: Rate of heat transfer to air flowing through cubic, round-strut tetradecahedral and

thin-strut tetradecahedral heat exchangers with varying air flow rate and total heater power of 0.8

and 2.3 kW/m2. The horizontal lines mark the total heater power of 0.8 and 2.3 kW/m2. ........... 57

Figure 4-6: Temperature variation across exit of cubic heat exchanger for constant applied heat

flux of 2.3 kW/m2 and air flow rate (a) 20 L/min, (b) 40 L/min (c) 60 L/min, and (d) 80 L/min.

Temperature scales are in °C. ....................................................................................................... 58

Figure 4-7: Temperature variation across exit of round-strut tetradecahedral heat exchanger for

constant applied heat flux of 2.3 kW/m2 and air flow rate (a) 20 L/min, (b) 40 L/min, (c) 60

L/min, and (d) 80 L/min. Temperature scales are in °C. .............................................................. 60

Figure 4-8: Temperature variation across exit of thin-strut tetradecahedral heat exchanger for


L/min, and (d) 80 L/min. Temperature scales are in °C. .............................................................. 61

Figure 4-9: Variation of heat exchanger efficiency for cubic, round-strut tetradecahedral and

thin-strut tetradecahedral channels with increasing Peclet number. ............................................. 64

Figure 4-10: Measured wall temperature and calculated air temperature variation along the length

of (a) the cubic, (b) the round-strut tetradecahedral, and (c) the thin-strut tetradecahedral heat

exchanger for an applied heat flux of 2.3 kW/m2 and air flow rates of 20 and 80 L/min. ........... 65

Figure 4-11: Local heat transfer coefficient variation along the length of (a) the cubic, (b) the

round-strut tetradecahedral, (c) the thin-strut tetradecahedral and (d) a hollow channel for 2.3

kW/m2 heat flux. ........................................................................................................................... 66

xii

Figure 4-12: Average Nusselt number (NuH) as a function of Reynolds number (ReH) for round-

strut, cubic structure, thin-strut tetradecahedral and empty channels. .......................................... 69

Figure 5-1: Unsuccessful welding of tube to the wire mesh. ........................................................ 72

Figure 5-2: Thermal skin deposition using wire-arc spray technique........................................... 73

Figure 5-3: Woven copper wire mesh screens of (a) 10 PPI, and (b) 40 PPI. .............................. 74

Figure 5-4: Backscattered electron SEM images of stainless coatings deposited at spray distances

of (a) 100 mm, (b) 150 mm, and (c) 200 mm [6]. ......................................................................... 77

Figure 5-5: SEM micrograph of coated joint [6]. ......................................................................... 79

Figure 5-6: SEM image of gap in the wire-tube joint filled by the coating material [6]. ............. 79

Figure 6-1: Heat Transfer performance charts of different heat dissipation media [14]. ............. 81

Figure 6-2: Heat transfer performance charts [43]. ...................................................................... 82

Figure 6-3: Fabricated fins after thermal spray coating of aluminum on (a) perforated sheet, and

(b) wire mesh. ............................................................................................................................... 87

Figure 6-4: Schematic diagram of the experimental setup. .......................................................... 88

Figure 6-5: Fabricated fins after sprayed using high emissivity black paint on (a) flat plate, and

(b) perforated sheet (Ø= 0.187 in (4.75 mm)). ............................................................................. 90

Figure 6-6: Temperature variation of the pipe at 15 V and 20 V (corresponding to surface heat

fluxes of 1.3 kW/m2 and 2.3 kW/m2) applied voltage for different air velocities. ....................... 91

Figure 6-7: Comparison between the variation of (NuD) with (ReD) for experimental and

theoretical model for flow over a cylinder. ................................................................................... 93

Figure 6-8: IR map of the temperature distribution of the fins (a) Flat plate, and (b) Perforated

sheet (Ø= 0.187 in (4.75 mm)). .................................................................................................... 96

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Figure 6-9: Comparison of the temperature profile at 55 V (17.7 kW/m2) with a 10 m/s flow

between the flat plate and perforated sheet (Ø= 0.187 in (4.75 mm)) .......................................... 97

Figure 6-10: Comparison between the measured surface temperature and predicted theoretical

model............................................................................................................................................. 99

Figure 6-11: The temperature profile at 60 V (21.1 kW/m2) applied voltage and for three air

velocities for perforated sheet (Ø= 0.187 in (4.75 mm)). ........................................................... 100

Figure 6-12: The temperature profile at 10 m/s air velocity and three different applied voltages

for the perforated sheet (Ø= 0.187 in (4.75 mm))....................................................................... 101

Figure 6-13: Perforated sheet tested at 55V (17.7 kW/m2) with a 10 m/s flow (a) Ø= 0.1875 in

(4.76 mm), (b) Ø= 0.125 in (3.17 mm), and (c) Ø= 0.0625 in (1.59 mm). ................................ 102

Figure 6-14: Temperature profile of the perforated fins at 55 V (17.7 kW/m2) applied voltage and

10 m/s air velocity. ...................................................................................................................... 103

Figure 6-15: Experimental temperature distribution at 55V (17.7 kW/m2) applied power with a

10 m/s air velocity (a) 10 PPI, (b) 14 PPI, and (c) 20 PPI. ......................................................... 104

Figure 6-16: Temperature profile for different wire mesh at 55 V (17.7 kW/m2) applied power

and a 10 m/s air velocity. ............................................................................................................ 105

Figure 6-17: Temperature profile of 14 PPI at 60 V (21.1 kW/m2) applied power for different air

velocities. .................................................................................................................................... 106

Figure 6-18: Temperature profile comparison between the wire mesh and perforated sheets at

55V (17.7 Kw/m2) applied power with a 10 m/s air velocity. .................................................... 107

Figure 6-19: Variation of Nusselt number (NuD) as a function of Reynolds number (ReD) based

on tube outer diameter (OD) for wire mesh and perforated sheet. ............................................. 109

Figure 6-20: Performance chart of the fabricated fins at a constant (ReD) of 5290. ................... 110

Figure 6-21: Nusselt number (NuH) variation as a function of Reynolds number (ReH). ........... 112

xiv

Figure 6-22: Comparison between the fin efficiency (ɳ) and effectiveness (ɛ) of the fins. ....... 113

Figure 7-1: Sample of heat exchangers (a) single screen 5 PPI wire mesh, (b) single screens 10

PPI wire mesh, and (c) single screens 20 PPI wire mesh. .......................................................... 118

Figure 7-2: Sample heat exchangers (a) single screens 5 PPI wire mesh, and (b) double screens 5

PPI wire mesh. ............................................................................................................................ 120

Figure 7-3: Schematic representation of the experimental setup. ............................................... 121

Figure 7-4: Schematic representation of the hot air chamber. .................................................... 122


in channels for 20 PPI and 10 PPI wire mesh screen. ................................................................. 125

Figure 7-6: Temperature rise of water flowing through the tubes (a) heat exchangers with one

wire mesh screen, and (b) heat exchangers with two wire mesh screens. .................................. 127

Figure 7-7: Variation of average air temperature at section 3 for different PPI wire mesh heat

exchangers................................................................................................................................... 129

Figure 7-8: Variation of the Overall heat transfer coefficient across different pore densities. .. 131

Figure 7-9: Nusselt number variation (Nua,D) across different pore densities at a constant water

mass flow rate of 0.015 Kg/s. ..................................................................................................... 133


Figure 7-11: IR camera surface temperature variation across heat exchangers for (a) 5 PPI, (b) 10

PPI and, (c) 20 PPI. ..................................................................................................................... 136

Figure 7-12: Schematic of eleven transverse and one longitudinal wire between two tubes. .... 137

Figure 7-13: Wire surface temperature variation along the length of one longitudinal and eleven

transverse wires, measured experimentally using IR camera, for the 5 PPI wire mesh heat

exchanger. The x and y axis are shown Figure 7-12. .................................................................. 139

xv

Figure 7-14: Wire surface temperature variation along the length of a longitudinal and six

transverse wires (T1, T2, T3, T4, T5, and T6 as shown in Figure 7-12) for the 5 PPI wire mesh

heat exchanger. Temperatures were measured experimentally using IR camera. ...................... 140

Figure 7-15: Location of longitudinal and transverse wires of wire mesh screens. ................... 141

Figure 7-16: Comparison between the measured surface temperature using IR camera and

predicted empirical model........................................................................................................... 143

Figure 7-17: Heat transfer energy balance for the fabricated heat exchangers. .......................... 144

Figure 7-18: Schematic of 3 heat exchangers connected in series. ............................................. 149

Figure 7-19: Extended surface area ratio (RA) variation as a function of NTU.......................... 150

Figure 8-1: Full assembly of a heat exchanger on top of the gas flare. ...................................... 152

Figure 8-2: Assembly process for the heat exchanger. ............................................................... 155

Figure 8-3: Fabricated bare tube section of the main heat exchanger. ....................................... 156

Figure 8-4: Fabricated section of the main heat exchanger, with one wire mesh screen attached

on front and back side of the tubes. ............................................................................................ 157

Figure 8-5: Wire mesh section after thermal skin deposition of stainless steel using wire-arc. . 158

Figure 8-6: Thermal sprayed surface of the wire mesh and the tube. ......................................... 158

Figure 8-7: Mechanical bonding of 4 PPI wire mesh to the stainless steel tube [6]. .................. 159

Figure 8-8: Front view of the fabricated heat exchanger before welding the manifolds. ........... 159

Figure 8-9: Back view of the fabricated heat exchanger after the final assembly. ..................... 160

Figure 8-10: Schematic representation of the experimental setup. ............................................. 162

Figure 8-11: Temperature drop for different hot air flow rates at a constant cold air velocity of

5.4 m/s. ........................................................................................................................................ 164

xvi

Figure 8-12: Heat transfer enchantment of the wire mesh sections compare to the plain tube. . 165


Figure 9-1: Nusselt number (NuD) variation as a function of Reynolds number (ReH). ............. 171

xvii

List of Appendices

Appendix A: Matlab Code for the Empirical Fin Model. ........................................................... 177

Appendix B: Heat Exchanger Assembly for the Hot Gas Incinerator. ....................................... 180

Appendix C: Step-by-Step Fabrication Process of the Heat Exchanger. .................................... 183

Appendix D: Location of the Thermocouples on the Surface of the Heat Exchanger. .............. 189

Appendix E: Shows a Schematic of the Fan, the Fan Performance and the Electrical Heater. .. 191

1

Chapter 1 Introduction

1.1 Introduction

Heat exchangers have been used for many years to transfer heat between different fluid streams.

Depending on the application, their performance can be improved by adding solid fins with

different geometries on their heat-conducting surface to increase the surface area between the fluid

media. There have been many attempts to optimize the shape of fins but their heat transfer and

hydraulic performance is limited by the total surface area that can be obtained in a given volume.

Open-cell porous structures such as metallic foams and wire mesh have a large surface area to

volume ratio, and have been studied extensively for heat exchanger applications. However, one of

the problems in making compact heat exchangers from open-cell porous structures is that the

porous material and the main body of the heat exchanger must be well bonded together to minimize

thermal resistance, which can be a difficult task.

In recent years, new methods of building compact heat exchangers from porous metal foams, using

technologies such as thermal spray coating, have been investigated. Thermal spray coating offers

a convenient method of bonding porous materials to metal sheets and tubes, which can be used to

make novel heat exchanger designs. Direct metal laser sintering (DMLS) is a rapid manufacturing

technology that can be used for both prototyping and mass production, which offers the possibility

of making structures with a predetermined, fully controlled internal geometry. This thesis will

explore the application of both of these methods to the fabrication of heat exchangers.

2

1.2 Literature Review

Heat exchangers are ubiquitous in industry, used wherever energy is to be transferred from a high

temperature fluid stream to another at lower temperature. There is an enormous body of literature

dealing with analysis of heat exchangers, but typically a designer wants to minimize both the size

of the heat exchanger and the work required to pump fluid through it. One method of reducing the

external dimensions of a heat exchanger is to increase the internal surface area wetted by the fluid

across which heat transfer occurs. Louvered fins, wire mesh, and other open-cell structures all

serve to increase the surface-area-to-volume ratio [1-4]. Heat transfer is further enhanced by

turbulence, induced by the complex flow path through small passages [5].

The choice of porous structures placed in the interior of heat exchangers to enhance heat transfer

is usually limited by what can be readily fabricated. Wire mesh has therefore been a favorite option

[6], since it is available in a wide variety of sizes and materials. Metal foams have attracted much

attention in recent years, as they are now being manufactured in commercial quantities and have

been shown to enhance heat transfer significantly [5, 7].

Salavati et al [7] fabricated open pore metallic foam core sandwich structures prepared by thermal

spraying of a coating on the foams that can be used as high efficiency heat exchangers due to their

high surface area to volume ratio and consequent high heat transfer.

Lu et al. [8] reviewed the thermal characteristics of metallic sandwich structures with truss and

prismatic cores used to cool the wall of a heated channel. They combined data showing the

influence of topology on the Nusselt number, Reynolds number and friction factor. Sypeck [9, 10]

studied metallic sandwich structures with truss cores and fabricated structures from perforated

aluminum alloy sheets, connecting the outer wall to the wrought metals by brazing in a vacuum

3

furnace. In an investigation by Boomsma et al. [5], metal sheets were brazed to the surfaces of

metal foams to create heat exchangers. Salimi Jazi et al. [11] and Tsolas [12] fabricated heat

exchangers by using a wire-arc spray method to deposit an Inconel 625 skin on copper and nickel

foams and measured the convection heat transfer rate. However, these porous structures are not

specifically designed to maximize heat transfer or to minimize pressure losses – they are used

because they are readily available.

Khayargoli et al. [13] investigated the effect of the microstructure of nickel and nickel-chromium

alloys metal foams on flow parameters. They found that the permeability increases as the pore size

increases which was due to increases in drag forces on the flowing fluid.

Tian et al. [14] studied fluid flow and heat-transfer during forced convection through cellular

copper lattice structures. To find the maximum heat transfer performance of the woven copper

mesh they tested several configurations. They discovered that unlike open-cell metal foams and

packed beds, the friction factor of the bonded wire screen, apart from being a function of porosity,

is also a function of orientation. They concluded that “wire-screen mesh competes favorably with

the best available heat dissipation media”. The overall thermal efficiency index of the copper

textiles-based media (mesh) was found to be approximately 3 times higher than that of copper

foam due to the high pressure drop of the copper foam.

Assaad et al. [15] created a new class of heat exchangers using wire mesh. They stacked and

sintered stainless steel woven wire mesh together and created wire mesh bricks. They machined

the bricks and cut them into thin wafers that could be combined to create porous structures. In

order to contain the working fluid inside this porous structure they deposited metal coatings on the

outer surface of the wafers using pulsed gas dynamic spraying (PGDS). They claimed, based on

4

their burst and tensile tests, that the fabricated compact wire mesh heat exchanger could withstand

internal pressure as high as 19.1 MPa.

Joen et al. [16] fabricated a single row heat exchanger consisting of aluminum metal foam covered

aluminum tubes. They placed their samples inside a wind tunnel and tested various parameters

including Reynolds number, tube spacing, foam height and the type of foam. They discovered that

increasing the foam height reduces the exterior convection resistance while increasing the pressure

drop. They also tested brazed and unbrazed samples which proved the importance of bonding and

concluded that more research is needed to develop efficient and cost-effective connection (brazing)

techniques to better connect the tube to the foam to provide solid metallic bonds.

Another factor impacting the performance of heat exchangers is the effective thermal conductivity

of both the heat exchanger structure and the fluid that flows through it. In analysis it is often

convenient to consider the solid and fluid as being one composite material in order to derive the

effective thermal conductivity of a heat exchanger. A low effective thermal conductivity in the

flow direction of the forced convection heat exchanger is desired, so that the applied heat is

transported mainly by convection and not by conduction. Researchers have developed analytical

models to predict the effective thermal conductivity of composite materials [4, 17, 18].

Zhao, Lu, Hodson and Jackson [19] examined the temperature dependence of effective thermal

conductivity of steel alloy foams for temperatures between 200- 800 K, under both vacuum and

atmospheric condition. They discovered that the transport of heat is dominated by thermal

radiation and effective thermal conductivity increase at high temperatures. They also compared

the effective thermal conductivity calculated at pressure varying from atmospheric to vacuum

conditions and established the importance of natural convection since the effective thermal

conductivity at atmospheric pressure was twice that in a vacuum.

5

Paek et al. [20] experimentally investigated thermo physical properties of different porosity

aluminum foams. They measured the effective thermal conductivity and the permeability of the

foam and found that effective thermal conductivity increases as the porosity decrease. Also, at a

fixed porosity, as the surface area in a given volume increases, flow resistance and pressure drop

increase due to a decrease of permeability. They correlated the friction factor with the permeability

based Reynolds number.

Open-cell porous materials used for heat transfer purposes must to be bonded to the external shell

of the heat exchanger in a manner that minimizes thermal resistance. Methods such as cladding,

welding, brazing, diffusion bonding and thermal spray coating have been used to connect an open-

cell structure to the body of the heat exchanger containing the flowing fluid [7-12], but these all

add to the complexity of manufacturing. In recent years, rapid manufacturing techniques have

given engineers the ability to make extremely complicated structures using additive techniques in

which three-dimensional objects are made in a single step directly from computer-based designs.

This offers the possibility of making heat exchangers with any arbitrary internal shapes: it may be

possible to optimize the shape of passages for fluid flow to maximize heat transfer while reducing

pressure losses.

6

1.3 Objectives

This thesis investigates new methods of building compact heat exchangers, using either direct

metal laser sintering (DMLS) to make channels with internal structures, or thermal spray coating

to bond wire mesh to the outside surface of tubes. This thesis aims to investigate the heat transfer

through open-cell spray coated and laser-sintered heat exchangers. The specific objectives to be

achieved are:

• Fabricate channels with internal open-cell geometries using DMLS technology.

• Study conduction heat transfer through DMLS porous structures.

• Experimentally investigate the impact of internal cell geometry on pressure drop and forced

convection heat transfer to air flowing through DMLS heat exchangers.

• Fabricate heat exchangers using thermal spraying to bond wire mesh screens or perforated

metal sheets to the outer surface of the tubes.

• Model and compare the heat transfer enhancement for different wire mesh and perforated

sheet sizes, varying their pore density, geometry and orientation.

• Fabricate an industrial size wire mesh heat exchanger and compare its performance to a

conventional plain tube heat exchanger.

7

1.4 Organization of Thesis

The first chapter starts with a general introduction to this research followed by a literature

review of porous heat exchangers.

Chapter 2 introduces the direct metal laser sintering (DMLS) fabrication process and the

geometry of the porous heat exchangers that were studied. It describes in detail the manufacturing

process and the material properties of the heat exchangers.

Chapter 3 explains the theory behind conduction heat transfer in porous structures. In this

chapter the effect of conduction for different DMLS heat exchangers was studied, and compared

to analytical models.

Chapter 4 analyzes convection heat transfer for different DMLS heat exchangers.

Convection heat transfer coefficient; are calculated and Nusselt number correlations developed.

The effect of pore geometry on hydraulic and heat transfer performance is discussed. Three

different geometries were analyzed to maximize heat transfer while minimizing pressure drop.

Chapter 5 describes the fabrication process of wire mesh heat exchangers. The wire-arc

thermal spray process was used to provide an intimate bond between wire mesh and tubes to form

water-air heat exchangers. The mechanical and material properties of the thermally sprayed wire

mesh heat exchangers are described in this chapter.

Chapter 6 describes laboratory experiments that contributed to the understanding of the

heat transfer characteristics of perforated sheets and wire mesh sheets bonded to heated tubes that

were tested inside a wind tunnel at different air velocities. The temperature distribution across the

mesh or sheet was measured using an infrared camera.

8

Chapter 7 describes the laboratory-scale water-to-air heat exchangers that were fabricated

using wire-arc thermal spray coating. Different pore densities of wire mesh were examined and

the temperature rise of water flowing through the tubes, while hot air passed over them, was

measured. Nusselt number correlations were developed for each heat exchanger.

Chapter 8 describes the process of fabricating a large thermally sprayed air-to-air heat

exchanger suitable for high temperature applications. The heat transfer enhancement due to

addition of a wire mesh was measured experimentally.

9

DMLS Heat Exchangers

2.1 Introduction

In the present study laser-sintering was used to fabricate stainless steel heat exchanger channels

filled with thin struts arranged to form either cubic or tetradecahedral. When a given space is filled

with identically shaped cells of equal volume, tetradecahedral cells (which have 14 faces, 6 square

and 8 hexagonal) are known to have the least surface area separating them, according to the well-

known “Kelvin Conjecture” [21]. Foams made by blowing gas into a liquid, contain

tetradecahedral bubbles, since surface tension minimizes their internal surface area. Heat

exchanger channels with tetradecahedral structures, therefore, have a much lower surface area than

those with cubic cells.

Heat transfer and frictional drag forces increase approximately linearly with the area of contact

between a liquid and solid surface, all else remaining constant. The tetradecahedral structure

(similar to a metal foam) would be expected to have lower heat transfer efficiency than the cubic

structure (which resembles a wire mesh) if the shape of the voids does not change fluid flow

significantly. In the present study, the question is addressed whether heat transfer and drag force

varied proportionally to the wetted area, or whether the cellular tetradecahedral structures altered

the fluid flow in such a manner to have a significant effect on the heat exchanger efficiency. If the

latter is true, it may be possible to design internal geometries that maximize heat transfer while

minimizing weight and frictional losses.

The heat exchangers examined in this study were square cross-section channels with either cubic

or tetradecahedral inner structure, with a uniform heat flux applied to the outer channel walls. The

10

increase of flow temperature was used to calculate friction and convective heat transfer coefficients

at varying airflow rates. The results for channels containing either cubic or tetradecahedral cells

were compared with those for a hollow channel. The effect of varying the strut shape for

tetradecahedral cells was studied. The objective was to demonstrate that the effect of adding

internal struts is not simply to increase surface area, but that cell geometry has a significant effect

on both heat transfer and fluid flow. Laser-sintered prototypes were fabricated by my colleague

Mr. Felix Loosmann and his supervisor Professor Cameron Tropea at Technische Universirat

Dramstadt in Germany.

11

2.2 Geometric Characteristics

A porous structure is characterized by several parameters, including porosity, pore density, pore

size and strut diameter. Porosity (ε) is defined as the void volume in the porous sample divided by

its total volume. As the porosity of a sample increases, the amount of solid material of that sample

decreases. Pore density is determined by counting the number of pores crossed by a randomly

drawn line and measured in pores per inch (PPI). The dimensions of a pore are specified by the

pore size (dp), which defines the size of a unit cell, and strut diameter (df).

(a) (b)

Figure 2-1: Unit cell geometry (a) cubic, and (b) tetradecahedral.

Figure 2-1 shows the two unit cell geometries that were used to produce the 10 PPI cubic (Figure

2-1a) and tetradecahedral (Figure 2-1b) heat exchanger prototypes respectively. Both geometries

have a strut diameter (df) of 1 mm. In order to construct a 10 PPI cubic heat exchanger, the distance

between the centerlines of two adjacent struts was set to 2.54 mm (0.1 in). Another way of

constructing a tetradecahedral structure is to subtract a sphere from a 14-sided block of material.

12

The result of that subtraction was a tetradecahedral structure with a variation of the strut diameter.

In addition, the struts were not cylindrical in shape and the shape of the unit cell was much closer

to shapes found, for example, in alumina metal foams (Figure 2-2).

Figure 2-2 : Unit cell geometry of the thin-strut tetradecahedral geometry.

(a) (b) (c)

Figure 2-3: Unit cell geometry (a) cubic, (b) round-strut tetradecahedral and (c) thin-strut

tetradecahedral.

13

Figure 2-3 shows the unit cell geometries that were used to produce heat exchanger channels. They

will be referred to as cubic (Figure 2-3a), round-strut tetradecahedral (Figure 2-3b) and thin-strut

tetradecahedral (Figure 2-3c) heat exchangers. The thin-strut tetradecahedral geometry has a non-

uniform strut diameter (df), roughly triangular, that resembles those found in metal foams. The

mass of the thin-strut tetradecahedral structures is significantly lower than that of round-strut

tetradecahedral structure.

14

2.3 Fabrication of DMLS Heat Exchangers

In the present study, a new method of building compact heat exchangers, using direct metal laser

sintering (DMLS), was investigated. This technology can be used for both prototyping and mass

production and enables heat exchangers with a predetermined, fully controlled internal geometry

to be built. In DMLS a 3D CAD model was created and imported into the laser-sintering machine.

Figure 2-4: Schematic of DLMS manufacturing procedure [38].

15

The fabrication process, as shown in Figure 2-4, starts by first preheating the building chamber,

after which the recoater blade moves metal powder from the dispensing platform onto the building

platform. Next, a laser beam melts the powder at the places where solid sections are desired by the

CAD model, before the recoater blade moves a new material layer onto the building platform.

Once all the layers are finished and the building chamber cooled slowly to room temperature to

minimize internal stresses, parts are removed. The heat produced by the laser beam to melt the

material powder can be transported out of the part faster if support structures are used to act as a

heat sink.

2.3.1 Fabrication of Heat Exchanger Channels

Three stainless steel heat exchangers were manufactured containing either cubic (Figure 2-5a),

round-strut tetradecahedral (Figure 2-5b) or thin-strut tetradecahedral (Figure 2-5c) cells. Heat

exchangers were manufactured in several sections to avoid any warping or bending, which can

occur if the part is too long. The dimensions of the three differed slightly to get an integral number

of cells across the channel width in each case. For the purpose of comparison, two hollow heat

exchanger channels were also fabricated, one from a solid stainless channel and the other laser-

sintered. Both hollow channels had the same dimensions, with 25.4 mm square cross-sections and

1.7 mm thick walls.

16

(a)

(b)

(c)

Figure 2-5: Channel section (a) cubic, (b) round-strut tetradecahedral, and (c) thin-strut

tetradecahedral.

17

The cubic, round-strut tetradecahedral and thin-strut tetradecahedral channel sections were

fabricated using direct laser-sintering system (Model EOSINT M270, EOS GmbH, Krailling,

Germany) and EOS Stainless Steel 17-4 powder (Model SS_17-4_M270, EOS GmbH, Krailling,

Germany).

(a) (b)

(c)

Figure 2-6: Heat exchanger channels (a) end view of cubic channel (b) end view of round-strut

tetradecahedral channel, and (c) thin-strut tetradecahedral.

18

Figure 2-6 shows end views of completed cubic (Figure 2-6a), round-strut tetradecahedral (Figure

2-6b) and thin-strut tetradecahedral channel (Figure 2-6c) sections. One section of the cubic

channel weighed 151 g, while the round-strut tetradecahedral channel section weighed 103 g, and

the thin strut tetradecahedral channel was significantly lighter, weighing only 71 g. Using this

method, the mass of the tetradecahedral structure was minimized resulting in a mass-optimized

structure. The results for the thin-strut tetradecahedral cells was compared with the conventional

cubic and tetradecahedral channels. The objective of investigating the novel tetradecahedral

structure was to optimize the shape of internal struts to minimize the mass while transporting the

same amount of heat.

Figure 2-7 shows the internal structure of the round-strut tetradecahedral channel with one wall

removed. As can be seen from the figure, the struts are uniform throughout the structure and are

in complete contact with the wall of the heat exchanger.

Figure 2-7: Round-strut tetradecahedral channel with side face removed.

19

To assemble the four sections and form a complete channel, the offsets at the ends of each section

were machined off and sections were welded together (Figure 2-8). Two stainless steel flanges

were manufactured and welded to both ends. In order to measure the pressure drop across the

porous structure two stainless steel tubes were connected as wall taps to the first and last channel

sections, respectively. The cubic channel was approximately 295 mm long, the round-strut

tetradecahedral 299 mm long and the thin-strut tetradecahedral 292 mm long.

Figure 2-8: Complete assembly of the heat exchanger with four sections welded together.

2.3.2 Material Properties

The surfaces and cross sections of the channels were examined using scanning electron microscopy

(SEM) and energy dispersive x-ray spectroscopy (EDS) (TM3000, Hitachi High-Technologies

Canada Incorporated, Toronto, ON, Canada) to analyze the porosity, oxide content, roughness and

the material composition. The inner surface of the channel was rough, as shown by the SEM

micrograph in Figure 2-9a, due to the DMLS fabrication process that sinters powder particles. The

rough surface of the porous structure and the wall surface may enhance near wall flow turbulence

[22].

20

An average oxide content of 4% was measured at the outer surface of the heat exchanger wall

using EDS. Figure 2-9b shows a cross-section through the heat exchanger wall, which was found

having negligible porosity and to be impervious to gas penetration.

(a)

(b)

Figure 2-9: SEM images of (a) channel wall surface, and (b) cross section of the channel wall.

21

The location where the struts were connected to the wall of the heat exchanger were also analyzed,

as shown in Figure 2-10. In heat exchangers fabricated using DMLS the geometry is predetermined

and the designer have full control over the connection and internal geometry of the heat exchanger.

Using DMLS, the wall and the struts were built as one solid structure which results in a superior

connection between all of the struts and the wall of the heat exchanger, with no thermal resistance

at the interface of strut and the wall.

Figure 2-10: Connection between the strut and the channel wall of the heat exchanger.

In order to check the uniformity of the material composition and the connection at the strut and

the wall connection point, the square area on Figure 2-10 was chosen and four areas (P1, P2, P3,

and P4) were analyzed as shown in Figure 2-11. The composition of the channel walls was

analyzed at several points using EDS, which confirmed that the composition of the steel

22

corresponded to that provided by the manufacturer, the main alloying elements being Cr (15-17.5

wt%), Ni (3-5 wt%), and Cu (3-5 wt%) with traces of Mn, Si, Mo and Nb.

Figure 2-11: EDS analysis of the coating micro structure at the connection point between the

struts and the wall.

23

Conduction Heat Transfer in DMLS Heat

Exchangers

3.1 Test Samples, Experimental Apparatus and Results

The geometry of the struts was uniform throughout the length of each channel section, as shown

in Figure 3-1, where the wall of a round-strut tetradecahedral section (Figure 3-1a) was removed

to check the uniformity of the geometry and to investigate the effective thermal conductivity of

the round-strut tetradecahedral structure without the influence of outer walls.

(a)

24

(b)

Figure 3-1: Tetradecahedral structure (a) one partially removed wall, and (b) without walls.

Three sets of experiments were conducted (Figure 3-2); the first set aims to determine the thermal

conductivity of a laser-sintered stainless steel solid block (Figure 3-2a). The second set to

determine the effective thermal conductivity of cubic and round-strut tetradecahedral heat

exchangers (Figure 3-2b) and the last set to investigate the conduction heat transfer in the round-

strut tetradecahedral structure without the surrounding walls (Figure 3-2c).

25

(a) (b) (c)

Figure 3-2: Schematic overview over the four different experimental setups.

Figure 3-3 shows the experimental apparatus that is used to measure the thermal conductivity of

the laser-sintered solid material. A solid block of stainless steel (28 mm x 28 mm x 50 mm) with

known material parameters (k = 16 W/mK, ρ = 8000 kg/m3) is connected to a laser-sintered

stainless steel block of identical dimensions resulting in a test sample of the dimensions (28 mm x

28 mm x 100 mm). High thermal conductive paste (Omegatherm 201, Omega Company, Stamford,

CT) was used to minimize the thermal resistance between the solid blocks. Eight K-type

thermocouples with junction diameters of 0.6 mm were fixed onto the blocks, four on each block

with a spacing of 10 mm. Thermal conductive paste was also applied to ensure a good thermal

connection between the thermocouples and the block surface.

26

(a) (b)

Figure 3-3: Experimental apparatus to determine the thermal conductivity of laser-sintered

stainless steel (a) a block manufactured with common methods on the left side and a block sintered

using DMLS on the right side, and (b) a schematic of the experimental setup.

A copper heater 9.5 mm x 26.3 mm x 26.3 mm in dimension, which consisted of three holes

containing three high-temperature cartridges heater (3614K34, McMASTER-CARR), was

attached to the bottom square section of the stainless steel block to apply a constant heat flux

varying between 10.6 kW/m2 to 27.2 kW/m2. A copper cooling jacket was attached to the top

square section of the laser-sintered block to cool the surface and increased the temperature

difference between the top and the bottom of the test section. The apparatus was surrounded by a

50 mm thick layer of aluminum silicate insulation (Zircar ceramics, AXHTM) with an average

thermal conductivity of 0.08 W/mK.

27

Figure 3-4 shows the temperature distribution along the solid stainless steel blocks for the first set

of experimental investigations. The measured temperature of stainless steel block from 0 mm to

50 mm and laser-sintered stainless steel block from 50 mm to 100 mm. The measured temperatures

show a linear trend for each applied heat flux. The conduction of heat is considered to be linear

and dominated by a one dimensional heat conduction from the heater block to the cooler block.

Hence, ks= (q"-q"loss)/m can be used to calculate the thermal conductivity of the laser-sintered

stainless steel block, with q" being the heat flux at 50 mm, q" loss being the heat flux to the

surrounding and m being the slope of the measured temperature distribution of the laser-sintered

stainless steel block.

Figure 3-4: Temperature distribution over sample length for the first set of experiments.

0 10 20 30 40 50 60 70 80 90 100

20

40

60

80

100

120

140

160

180

200

220

Location, (cm)

Surf

ace

Tem

per

ature

, (

ºC)

10.6 kW/m2

18.9 kW/m2

27.2 kW/m2

28

The second set of experiments was designed to determine the effective thermal conductivity of the

fabricated cubic and round-strut tetradecahedral heat exchangers. The experimental apparatus

(Figure 3-5) fabricated to run, these experiments consists of a water cooling jacket on one side and

a block heater on the other side of the sample.

Seven K-type thermocouples with junction diameters of 0.6 mm were fixed on the top outer surface

of the channel with high thermal conductivity paste, with the first one positioned at z = 18 mm and

with a 37 mm spacing between thermocouples, to measure the local wall temperature. All seven

thermocouples were connected to a National Instruments data acquisition (DAQ) system and

recorded in a computer equipped with Lab View Signal Express v.3.0 (National Instrument

Corporation, Austin, TX). The same copper heating unit, which was used in the first set of

experiments, was used for this experiment. The apparatus is surrounded by a 50 mm thick layer of

aluminum silicate insulation (Zircar ceramics, AXHTM).

29

Figure 3-5: Experimental apparatus, which is used for the third and fourth set of experiments, to

measure the temperature distribution for different heat fluxes with cooling at one side of the

samples and heating on the opposite site, respectively.

Figure 3-6 shows the measured temperatures on the outer surface of round-strut tetradecahedral

and the cubic heat exchanger, respectively. The cubic and tetradecahedral samples are heated on

one end and cooled at the other, see Figure 3-5 for more information about the experimental

apparatus. The experiment was conducted for three different heat fluxes 9.8 kW/m2, 15.3 kW/m2

and 22.1 kW/m2. At location 0, the temperature of the heater block is shown and the temperature

at location 1 is the temperature of the cooling block. The temperatures measured for the cubic and

30

round-strut tetradecahedral heat exchanger are similar. The measured temperatures are not linearly

distributed.

Figure 3-6: Comparison of experimental results for the outer surface temperature distribution over

relative location between cubic and round-strut tetradecahedral sample at a three different heat

fluxes. Heating from one side, cooling from the other, results.

If the heat transfer for samples shown in Figure 3-6 is modeled as 1-D conduction and the heat

loss to the surroundings is zero (𝑞𝑙𝑜𝑠𝑠" = 0) as shown in Figure 3-7a for a material with a constant

thermal conductivity then

0 0.2 0.4 0.6 0.8 1

0

50

100

150

200

250

Relative location, X

Tem

per

ature

,T (

°C)

Round-Strut Tetradecahedral, 22.1 kW/m2

Cubic, 22.1 kW/m2


Cubic, 15.3 kW/m2


Cubic, 9.8 kW/m2

31

𝑞𝑥=0" = 𝑞𝑥=1

"

-k 𝜕𝑇

𝜕𝑥| 𝑥 = 0

= -k 𝜕𝑇

𝜕𝑥|𝑥 = 1

𝜕𝑇

𝜕𝑥| 𝑥 = 0

= 𝜕𝑇

𝜕𝑥|𝑥 = 1

(3-1)

which would result in a constant slope line of temperature and relative location.

(a)

(b)

Figure 3-7: Comparison between heat transfer in samples (a) with zero heat loss to surrounding,

and (b) with heat loss to the surroundings.

32

If the heat transfer is modeled as 1-D conduction and the heat loss to the surrounding is larger than

zero (𝑞𝑙𝑜𝑠𝑠" > 0) as shown in Figure 3-7b for a material with a constant thermal conductivity then

𝑞𝑥=0" > 𝑞𝑥=1

"

-k 𝜕𝑇

𝜕𝑥| 𝑥 = 0

> -k 𝜕𝑇

𝜕𝑥|𝑥 = 1

abs ( 𝜕𝑇

𝜕𝑥| 𝑥 = 0

) > abs ( 𝜕𝑇

𝜕𝑥|𝑥 = 1

)

𝜕𝑇

𝜕𝑥| 𝑥 = 0

< 𝜕𝑇

𝜕𝑥|𝑥 = 1

(3-2)

which results in a sharper rate of change of temperature and relative location in the beginning of

the sample (x = 0) compare to the end of the sample (x = 1).

To estimate the heat loss to the surrounding; the sample was divided into 3 segments as shown in

Figure 3-8. The amount of heat loss in each segment is calculated individually. The total heat loss

from the sample can be obtained from the summation of heat loss in each segment. The grey line

demonstrate the rate of change of temperature with respect to location. Temperature points (P1,

P2, and P3) which are at the center of each segment were measured using thermocouples.

Conservation of energy for each segment yields

𝑞𝑙𝑜𝑠𝑠 1 |𝑋 = 0.375

𝑋 = 0.125+ 𝑞𝑙𝑜𝑠𝑠 2 |

𝑋 = 0.625

𝑋 = 0.375+ 𝑞𝑙𝑜𝑠𝑠 3 |

𝑋 = 0.875

𝑋 = 0.625= 𝑞𝑙𝑜𝑠𝑠,𝑡𝑜𝑡𝑎𝑙

𝑞𝑥=0.125 = 𝑞𝑙𝑜𝑠𝑠 1 + 𝑞𝑥=0.375

𝑞𝑥=0.375 = 𝑞𝑙𝑜𝑠𝑠 2 + 𝑞𝑥=0.625

(3-3)

33

𝑞𝑥=0.625 = 𝑞𝑙𝑜𝑠𝑠 3 + 𝑞𝑋=0.875

Substituting Fourier's law of conduction to the equation (3-3)

{

−𝑘 A𝐶𝑟𝑜𝑠𝑠 (

𝜕𝑇

𝜕𝑥| 𝑥 = 0.125

−𝜕𝑇

𝜕𝑥| 𝑥 = 0.375

) = 𝑞𝑙𝑜𝑠𝑠 1

−𝑘 A𝐶𝑟𝑜𝑠𝑠 ( 𝜕𝑇

𝜕𝑥| 𝑥 = 0.375

−𝜕𝑇

𝜕𝑥| 𝑥 = 0.625


−𝑘 A𝐶𝑟𝑜𝑠𝑠 ( 𝜕𝑇

𝜕𝑥| 𝑥 = 0.625

−𝜕𝑇

𝜕𝑥| 𝑋 = 0.875


(3-4)

Figure 3-8: Schematics for sample segmentations for heat loss calculation.

34

The temperature measurement for the cubic structure at 22.1 kW/m2 (Figure 3-6) were substituted

into Equation (3-4)

{

𝑘 A𝐶𝑟𝑜𝑠𝑠

( 413 °C − 240 °C) = 𝑞𝑙𝑜𝑠𝑠 1 = 0.34 𝑊 ≡ 47% 𝑜𝑓 𝑇𝑜𝑡𝑎𝑙 𝐿𝑜𝑠𝑠

𝑘 A𝐶𝑟𝑜𝑠𝑠 ( 240 °C − 134 °C) = 𝑞𝑙𝑜𝑠𝑠 2 = 0.21 𝑊 ≡ 29% 𝑜𝑓 𝑇𝑜𝑡𝑎𝑙 𝐿𝑜𝑠𝑠

𝑘 A𝐶𝑟𝑜𝑠𝑠( 134 °C − 49.0 °C) = 𝑞𝑙𝑜𝑠𝑠 3 = 0.17 𝑊 ≡ 24% 𝑜𝑓 𝑇𝑜𝑡𝑎𝑙 𝐿𝑜𝑠𝑠

(3-5)

The heat loss in each segment is not equal. The loss is reduced when moving from the hot side of

the segment (x = 0.125) to the cold side of the segment (x = 0.875) because the average temperature

of the segment reduces. The heat loss of each segment should be proportional to the temperature

differential between surface of the sample and the ambient. The total heat loss was approximately

5% of the total heat transfer to the heat exchanger.

The same experimental setup as shown by Figure 3-5, was used to measure the effective thermal

conductivity of the tetradecahedral structure (Figure 3-1b) by replacing the heat exchanger channel

with the round-strut tetradecahedral structure Figure 3-9. With the outer surface walls filling

around 15% of the cross sectional area, experimental investigation of the inner structure is

necessary to fully understand the heat conduction mechanism within laser-sintered stainless steel

heat exchangers. These temperature measurements were used to calculate the effective thermal

conductivity of the round-strut tetradecahedral structure.

35

Figure 3-9: Temperature distribution over sample length for the third set of experiments.

Figure 3-10 shows the calculated thermal conductivity of the laser-sintered stainless steel block

for three different heat fluxes. Furthermore, thermal conductivity values provided by EOS GmbH

[37] for a temperature of 293.15 K and for a temperature of 473.15 K are shown by dotted lines.

The calculated thermal conductivity values are in good agreement with the values provided by

EOS GmbH [37]. Only a small variation of the thermal conductivity with different applied heat

fluxes is observed. A thermal conductivity value of 14 W/mK is used for the solid in analytical

predictions of the effective thermal conductivity of the round-strut tetradecahedral and cubic

samples.

300

350

400

450

500

550

0 0.2 0.4 0.6 0.8

Tem

per

ature

, T

(°C

)

Relative Location, X

9.8 kW/m2

15.3 kW/m2

22.1 kW/m2

36

Figure 3-10: Thermal conductivity of the laser-sintered stainless steel block over applied heat flux

for the first set of experiments. Data sheet values are taken from the EOS Stainless Steel 17-4 data

sheet [37].

The results of the effective thermal conductivity for all three applied heat fluxes and both heat

exchangers are shown in Figure 3-11. The round-strut tetradecahedral heat exchanger provides

less conductive heat transfer than the cubic one due to the difference in porosity and the effective

thermal conductivity being inversely proportional to the temperature. The calculated effective

thermal conductivities are small in comparison to the conductivity of the solid material, which is

14 W/mK for laser-sintered stainless steel (Figure 3-10). The calculated effective thermal

conductivities for different heat fluxes do not vary significantly and the differences are within the

error range of the experimental error.

0 10 20 30

0

2

4

6

8

10

12

14

16

18

20

Applied Heat Flux, (kW/m2)

Ther

mal

Conduct

ivit

y, (

W/m

K)

Laser Sintered Block

37

Figure 3-11 shows the huge impact of the walls on the effective thermal conductivity for the round-

strut tetradecahedral structure. The experimentally derived effective thermal conductivity values

for the round-strut tetradecahedral inner structure is about a third of the effective thermal

conductivity values, which are based on the experimental results for the round-strut tetradecahedral

sample with outer walls. The porosity values for both structures without walls are different from

the calculated porosity considering with walls, 0.89 and 0.75 for tetradecahedral and cubic

structure respectively.

Figure 3-11: Comparison of the effective thermal conductivity over applied heat flux for the cubic

and round-strut tetradecahedral heat exchangers, and the round-strut tetradecahedral structure

without walls.

0 5 10 15 20 25 30

0

1

2

3

4

5

6

Applied Heat Flux, (kW/m2)

Eff

ecti

ve

Ther

mal

Conduct

ivit

y, (

W/m

K) Cubic

Round-Strut Tetradecahedral

Round-Strut Tetradecahedral Structure

38

3.2 Heat Transfer Characteristics

3.2.1 Theory

Important factors influencing the thermal performance of porous structures are the porosity, pore

density, pore size, and fiber diameter of the open-cell porous media. Porosity (ε) is defined as the

void volume in the porous sample divided by its total volume. As the porosity of a sample

increases, the amount of solid material of that sample decreases, which decreases the strength of

the sample. Pore density is measured in pores per inch (PPI) by counting the number of pores per

linear inch. The dimensions of a pore are specified by the pore size (dp), which defines the size of

a unit cell, and fiber diameter (df).

Conduction of heat is described by the equation:

𝜕𝑇

𝜕𝑡− ∇(𝛼∇𝑇) =

�̇�

𝐶𝑝 ∗ 𝜌 (3-6)

where α is the thermal diffusivity, cp is the specific heat capacity and ρ is the density of the

material. All experiments were conducted at steady state, and material parameters were assumed

constant and isotropic. Assuming heat conduction is one-dimensional, Equation (3-6) simplifies to

∆𝑇

𝐿≈𝑑𝑇

𝑑𝑥= −

𝑞"

𝑘 (3-7)

where the heat flux 𝑞" =𝑞

𝐴 , q is the applied heat and A = A solid + A fluid is the total conducting area

of the channel. L is the length of the channel and ∆𝑇 is the corresponding temperature difference.

Equation (3-7) is applicable for a block of material, but not for a composite material, such as the

laser-sintered porous prototypes. In the case where heat exchanger channels are filled with air, heat

39

is conducted almost exclusively through the laser-sintered stainless steel, yielding Equation (3-8),

which is used to calculate the effective thermal conductivity in the present study.

𝑘𝑒𝑓𝑓 = 𝑞"𝐿

∆𝑇=𝑞"𝐴𝑠𝑜𝑙𝑖𝑑𝐴𝑠𝑜𝑙𝑖𝑑

𝐿

∆𝑇= (1 − ɛ)

𝑞

𝐴𝑠𝑜𝑙𝑖𝑑 𝐿

∆𝑇 (3-8)

3.2.2 Analytical Models

Analytical models are used to predict the effective thermal conductivity of multiphase or

composite materials. In addition, analytical models allow the modeling of heat transfer and flow

through heat exchangers, which simplifies numerical investigations. All analytical models, which

are presented in the following, assume a certain spatial distribution of a fluid phase and solid phase

within a given sample. In addition, the porosity and thermal conductivity of each material

participating in the composite sample is taken into account. The participating materials in the

present study are air (𝑘𝑓 = 0.0254 W/mK) and stainless steel (𝑘𝑠 =14 W/mK).

The series model shown in Figure 3-12b predicts that the effective thermal conductivity

𝑘𝑒𝑓𝑓 = 1

ɛ𝑘𝑓+ (1 − ɛ)/𝑘𝑠

(3-9)

is the harmonic average of the thermal conductivities of the solid and gas phases, weighted by the

porosity. It assumes that both materials are oriented horizontally to the direction of the temperature

gradient, e.g. the heat flux with fluid and solid phases alternating. This combination leads to a

material that has neither a direct solid path nor a direct fluid path from the hot side to the cold side

of the first sample. The Series Model is regarded as being the lower bound of the thermal

conductivity and is dominated by the thermal conductivity of the fluid phase. The Serial Model

40

was first introduced by Reuss [29] in the field of elasticity and transferred to heat conduction by

Egli [28], Wiener [32]. In contrast, the Parallel Model as shown in Figure 3-12a [28, 32, 33]

(arithmetic mean weighted by porosity)

𝑘𝑒𝑓𝑓 = ɛ𝑘𝑓 + (1 − ɛ)𝑘𝑠 (3-10)

assumes a material distribution, which consists of equally-sized layers that are oriented vertically

to the direction of the temperature gradient. Direct solid paths of minimal length exist between hot

and cold side of the test sample. Hence, the Parallel Model is considered as being the upper bound

of the possible effective thermal conductivity and it is dominated by the thermal conductivity of

the solid phase. Both these models define the bounds of possible effective thermal conductivity

values.

(a)

(b)

Figure 3-12: Heat transfer direction through (a) Parallel Model, and (b) Series Model.

The Effective Medium Theory (EMT)

(1 − ɛ)𝑘𝑠 − 𝑘𝑒𝑓𝑓

𝑘𝑠 + 2𝑘𝑒𝑓𝑓+ ɛ

𝑘𝑓 − 𝑘𝑒𝑓𝑓

𝑘𝑓 + 2𝑘𝑒𝑓𝑓= 0

(3-11)

41

assumes a random distribution of both phases within the sample and was introduced by Bruggeman

[35]. A different attempt to model the effective thermal conductivity is to regard the distribution

of one phase as being regularly shaped. The Maxwell-Eucken Model [36]

𝑘𝑒𝑓𝑓 = 𝑘𝑓2𝑘𝑓 + 𝑘𝑠 − 2(𝑘𝑓 − 𝑘𝑠)(1 − ɛ)

2𝑘𝑓 + 𝑘𝑠 + (𝑘𝑓 − 𝑘𝑠)(1 − ɛ)

(3-12)

is such a model which assumes that the solid phase is spherical and that the solid phase is covered

by the fluid phase, which is continuous. In the given form, it is only valid for high porosity values.

Leach [17] formulated two models with the Cubic Series Parallel Model (CSP)

𝑘𝑒𝑓𝑓 = 𝑘𝑠 (1 − ɛ23) +

𝑘𝑠ɛ23

𝑘𝑓 + (𝑘𝑠 − 𝑘𝑓)ɛ13

(3-13)

being the lower bound like the Serial Model and the Cubic Parallel Serial Model (CPS)

𝑘𝑒𝑓𝑓 = 𝑘𝑠𝑘𝑠 − (𝑘𝑠 − 𝑘𝑓)ɛ

23

𝑘𝑠 − (𝑘𝑠 − 𝑘𝑓)(ɛ23 − ɛ)

(3-14)

being the upper bound like the Parallel Model. Both Cubic Cell Models (CCM) assume that the

fluid phase fills cubical shaped cells of solid. The main difference between the two Cubic Cell

Models is the treatment of cell corners. The Cubic Cell Models are expected to predict the effective

thermal conductivity of the Cubic heat exchanger well, as the unit cell is quite similar. Boomsma

and Poulikakos [34] introduced an analytical model based on the assumption that the solid phase

consists of tetradecahedral shaped cells and is filled with the fluid phase. The Tetrahedral Unit

Cell (TUC) model

42

𝑘𝑒𝑓𝑓 =√2

2(𝑅𝐴 + 𝑅𝐵 + 𝑅𝐶 + 𝑅𝐷)

where,

𝑅𝐴 = 4𝑑

(2𝑒2 + 𝛱𝑑(1 − 3))𝑘𝑠 + (4 − 2𝑒2 − 𝛱𝑑(1 − 𝑒))𝑘𝑓

𝑅𝐵 = (𝑒 − 2𝑑)2

(𝑒 − 2𝑑)𝑒2𝑘𝑠 + (2𝑒 − 4𝑑 − (𝑒 − 2𝑑)𝑒2)𝑘𝑓

𝑅𝐶 = (√2 − 2𝑒)2

2𝛱𝑑2(1 − 2𝑒√2)𝑘𝑠 + 2(√2 − 2𝑒 − 𝛱𝑑2(1 − 2√2𝑒))

𝑅𝐷 =2𝑒

𝑒2𝑘𝑠 + (4 − 𝑒2)𝑘𝑓

𝑑 = √√2(2 − (

58) 𝑒

3√2 − 2ɛ

𝛱(3 − 4𝑒√2 − 𝑒)

e =0.339

(3-15)

is similar to the Cubic Cell models, but uses a tetradecahedral as a unit cell. The TUC Model is

sensitive to the value of е. Consequently, the TUC Model is only applicable for porosities within

the range 50% to 98%, and the value for e, which is suggested by Boomsma and Poulikakos[34]

and is used by this paper to compare the prediction of the effective thermal conductivity with other

results. The TUC Model uses the same unit cell as the tetradecahedral heat exchanger and is

expected to estimate the effective thermal conductivity of the tetradecahedral heat exchanger

adequately. All of the above mentioned analytical models are used by this study to predict the

43

effective thermal conductivity of both heat exchangers, and the predictions are compared to the

experimental results.

3.2.3 Analysis and Discussion


predictions of various analytical models.

Figure 3-13 summarizes the predictions of various analytical models. The Parallel Model Equation

(3-10) marks the upper bound, whereas the Serial Model Equation (3-9) is the lower bound of the

possible effective thermal conductivity values. The Tetradecahedral Unit Cell model (TUC), the

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

2

4

6

8

10

12

14

Porosity

Eff

ecti

ve

Ther

mal

Conduct

ivit

y, (

W/m

K)

Serial Model

Parallel Model

Maxwell-Eucken Model

Tetrahedral Unit Cell Model

Cubic Series Parallel Model

Cubic Parallel Serial Model

44

Effective Medium Theory model (EMT) and the Maxwell-Eucken model (MEM) are only valid

for porosity values higher than 0.5. The reason for that limitation are model assumptions. For

smaller values of porosity, the TUC is not porous any longer, while the EMT and MEM are

descending from solid being covered by fluid, towards, fluid being covered by solid. Small to no

difference is observed for the MEM and the EMT, despite the difference in material distribution,

for porosity values above 0.75. Both models were not designed for the prediction of the effective

thermal conductivity of open porous media, as presented by this study.

On the other hand, the Cubic Cell models, Cubic Parallel Series model (CPS) and Cubic Series

Parallel model (CSP) are based on a regular structure, which is patterned in space. The three laser-

sintered heat exchangers are designed in a similar manner. Hence, it is expected that CSP and CPS

are able to predict the effective thermal conductivity of the presented heat exchangers. In addition,

the TUC is expected to be accurate for porosity values above 0.6.

45


predictions of various analytical models and the experimental results.

The effective thermal conductivity for the round-strut tetradecahedral inner structure is derived

from experimental results and shown in Figure 3-14. The Tetrahedral Unit Cell (TUC) model

Equation (3-15) is not able to predict the effective thermal conductivity values, while the Cubic

Series Parallel Model (CSP) Equation (3-13) and Cubic Parallel Serial Model (CPS) Equation

(3-14), are able to predict them for porosity values less than 0.5. Researchers use porosity values

above 0.7 in the field of forced convection heat exchangers. Smaller porosity values lead to a very

high loss of pressure, while the additional surface area does not offer any benefits for heat transfer

[39].

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

2

4

6

8

10

12

14

Porosity

Eff

ecti

ve

Ther

mal

Conduct

ivit

y, (

W/m

K) Tetrahedral Unit Cell Model

Cubic Series Parallel Model

Cubic Parallel Serial Model

Round-Strut Tetradecahedral Structure

46

3.3 Conclusion

An investigation on the effective thermal conductivity for two different laser-sintered channels and

a round-strut tetradecahedral structure has been conducted. Both channels have an ideal bonding

between the wall and the inner structure and are dense. Furthermore, it was shown that the

investigated samples almost conduct no heat with the effective thermal conductivity being small

compared to the thermal conductivity of the solid inside the samples, with the round-strut

tetradecahedral sample conducting even less heat. However, the effective thermal conductivity

that was derived from the experimental results of the channels is not characteristic of the inner

structures. The conduction heat transfer in the round-strut tetradecahedral structure without the

surrounding walls was also investigated. The results were compared to predictions of the effective

thermal conductivity by analytical models. Cubic Series Parallel Model (CSP) and Cubic Parallel

Serial Model (CPS) were able to predict the change of the effective thermal conductivity with a

variation of the fiber diameter porosity values, while the Tetrahedral Unit Cell (TUC) Model can

be used to predict the effective thermal conductivity for porosity values above 0.6. The measured

effective thermal conductivity of the round-strut tetradecahedral structure was in a good agreement

with Cubic Parallel Serial Model (CPS).

47

Convection Heat Transfer in DMLS Heat

Exchangers

4.1 Experimental Apparatus

The experimental apparatus fabricated to test heat exchangers consists of a compressed air supply

and instruments to control and measure air pressure, flow rate, and temperature (Figure 4-1). The

laboratory air supply provides a maximum flow rate of 1.6 x 10-3 m3/s (100 L/min at standard

temperature and pressure) at a pressure of 620 kPa (90 psi). The compressed air pressure was set

by a pressure regulator (Model R37221-600, Ingersoll-Rand plc, Dublin, Ireland) and a mass flow

controller (Model FMA5542, Omega Company, Stamford, CT) regulated the airflow rate through

the heat exchanger channel. The inlet (Tin) and outlet (Tout) temperatures were measured by type-

K thermocouple probes (Model TJ36-CASS-032-G-6, Omega Company, Stamford, CT), which

were located in T-junctions placed before and after the diverging and converging inlet and outlet

manifolds (Figure 4-1) that were also manufactured using DMLS.

Air pressures were read at the mid-point of the first and fourth channel section (at z = 37 mm and

221 mm, where z is the distance measured from the beginning of the channel). The pressure drop

was measured using a digital manometer (Model HHP-103, Omega Company, Stamford, CT) set

to a maximum range of 498 Pa with an accuracy of 0.2% of full scale.

Eight K-type thermocouples with junction diameters of 0.6 mm were fixed on the top outer surface

of the channel, with the first one positioned at z = 18 mm and 37 mm spacing between

thermocouples. To ensure good contact between the thermocouples and the surface, a high thermal

conductivity paste (Omegatherm 201, Omega Company, Stamford, CT) was applied. All 10

thermocouples were connected to a National Instruments Data Acquisition (DAQ) system and

48

recorded in a computer equipped with Lab View Signal Express v.3.0 (National Instrument

Corporation, Austin, TX). A 12.7 mm diameter x 2439 mm long rope heater (Model FGH051-080,

Omega Company, Stamford, CT) was wrapped uniformly around the heat exchanger and

surrounded by a fiberglass mat insulation (Micro-Flex, John Manville Corporation, Denver, CO)

with an average thermal conductivity of 0.038 W/mK.

Figure 4-1: Schematic of experimental apparatus.

A high temperature infrared camera (IR) (FLIR SC5000, FLIR Systems Inc., Wilsonville, OR)

was used to observe temperature variations across the cross-sections of the heat exchangers while

they were operating. To take infrared images, the converging exit section of the heat exchanger

was removed and the IR camera positioned in front of it. In order to ensure uniform emissivity

over the strut surfaces, they were coated with black, high-temperature thermally conductive paint

with an emissivity of 0.95. A constant heat flux of 2.3 kW/m2 was applied to cubic, round-strut

tetradecahedral and thin-strut tetradecahedral heat exchangers while airflow rates were varied from

20 L/min to 80 L/min.

49

4.2 Hydraulic Characteristics

Figure 4-2 presents the pressure drop measurements at different flow velocities through cubic,

round-strut tetradecahedral and thin-strut tetradecahedral cell heat exchangers. It can be seen that

the pumping power required is highest for the cubic cells while the thin-strut tetradecahedral

resulted in the lowest pressure drop. The mean inlet air temperature was kept constant at 21ºC.

Leong and Jin [23] compared the pressure drop through metal foams, which are usually modeled

as having tetradecahedral pores, to the pressure drop through wire-screens [24, 25], which have

pores with square cross-section. They also found that frictional losses were much higher for the

wire screens than for the foams. They attributed the difference to the different structures, with the

inter-connected cells of the foam providing less resistance to flow than the wire screens.

50


in channels with cubic, round-strut tetradecahedral and thin-strut tetradecahedral cells.

The pressure gradient for fluid flow through a porous medium is often expressed using Darcy’s

law [26].

𝛥𝑃

𝐿=µ

𝐾𝑢 +

𝜌𝐶𝐹

√𝐾𝑢2

(4-1)

where ∆P is the pressure difference across the length of the channel, µ and ρ the dynamic viscosity

and density, and u the average velocity, determined by dividing the volume flow rate of air by the

0

1000

2000

3000

4000

5000

0 1 2 3

Pre

ssure

Gra

die

nt,

ΔP

/m (

Pa/

m)

Fluid Velocity, u (m/s)

Cubic


Thin-Strut Tetradecahedral

51

open cross-sectional area of the channel. The permeability (K) and Forchheimer coefficient (𝐶𝐹)

are properties of the porous media that are determined experimentally.

Equation (4-1) was non-dimensionalize by defining the Darcy friction factor f

𝑓 =2𝛥𝑃

𝐿

𝐻

𝜌𝑢2

(4-2)

where H is the internal height of the square cross-section channel which is the hydraulic diameter

of the square channel. Substituting Equation (4-1) in Equation (4-2)

𝑓𝐷𝑎1/2

2=

1

𝑅𝑒𝐾+ 𝐶𝐹 (4-3)

with 𝐷𝑎 =𝐾

𝐻2 and 𝑅𝑒𝐾 =

𝜌𝑢√𝐾

µ . The Reynolds number 𝑅𝑒𝐾 is based on the characteristic

length scale √𝐾 and Da is the Darcy number [26].

Values of K and CF for the three structures, listed in Table 1, were determined by using a least

squares fit of Equation (4-1) to the data in Figure 4-2. The permeability of the thin-strut

tetradecahedral was higher than the permeability of the cubic and round-strut tetradecahedral

structures. Both conventional cubic and round-strut tetradecahedral heat exchangers had the same

strut diameter (1 mm), but since the porosity of the conventional round-strut tetradecahedral

structure was higher it had a higher permeability (K). The Forchheimer coefficient (𝐶𝐹) is a

measure of the total resistance to flow due to fluid drag, and since the tetradecahedral channel had

a surface area that was only half that of the cubic structure its CF value was correspondingly

smaller. The thin-strut tetradecahedral channel had a surface area that was smaller than that of the

cubic and round-strut tetradecahedral structure and its CF value was correspondingly smaller.

52

Table 4-1: Structural comparison between the cubic, round-strut tetradecahedral and thin-strut

tetradecahedral heat exchanger channels.

Cubic

Round-Strut

Tetradecahedral

Thin-Strut

Tetradecahedral

Internal surface area (m2) 0.0618 0.0346 0.0198

Mass per section (g) 151 103 71

Porosity 0.64 0.77 0.837

Permeability K (m2) 1.16 x 10-7 1.61 x 10-7 5.28 x 10-7

Forchheimer coefficient 𝑪𝑭 0.17 0.068 0.049

In order to predict the pressure drop for the fabricated heat exchangers, Equation (4-3) was fitted

to the experimental data shown in Figure 4-2.

Cubic: 𝑓𝐷𝑎1/2

2=

1

Re𝐾+ 0.17 (4-4)

Round-Strut Tetradecahedral: 𝑓𝐷𝑎1/2

2=

1

Re𝐾+ 0.068 (4-5)

Thin-Strut Tetradecahedral: 𝑓𝐷𝑎1/2

2=

1

Re𝐾+ 0.049 (4-6)

These relations are illustrated graphically in Figure 4-3, together with the experimental data.

53

Figure 4-3: Friction factor variation with Reynolds number for channels with cubic, round-

strut tetradecahedral and thin-strut tetradecahedral.

0.01

0.1

1

10

1 10 100

fDa0

.5

ReK

Cubic



Eq. (4-4)

Eq. (4-5)

Eq. (4-6)

54

4.3 Heat Transfer Characteristics

Internal structures in a heat exchanger channel promote convection, but they also increase the

cross-sectional area for axial heat conduction and the surface area for radiation. Heat supplied to

the walls of the heat exchanger is transferred by conduction and radiation both radially towards

the center of the channel and axially along the length of the tube. At low airflow rates a significant

portion of the total heat applied may be lost by heat conduction to the piping at the ends of the heat

exchanger channel instead of being transferred to the air flowing through it.

The heat exchangers were tested at nine different air flow rates ranging from 8.3x10-5 to 1.3x10-3

m3/s (10 to 90 L/min) and at four different heater voltages ranging from 30 to 60 V (giving uniform

wall heat flux varying from 0.8 to 3.2 kW/m2). The inlet air mean temperature and pressure were

21ºC and 130 kPa. Experiments were performed at steady state and readings were taken when the

thermocouple outputs had stabilized.

To measure heat transfer to the air passing through the heat exchanger the temperature rise from

the inlet to the outlet of the heat exchangers was measured as a function of flow rate as shown in

Figure 4-4 for cubic (Figure 4-4a), round-strut tetradecahedral (Figure 4-4b) and thin-strut

tetradecahedral (Figure 4-4c) heat exchangers. The temperature difference decreased with

increasing flow rate, with the cubic heat exchanger producing a slightly greater temperature rise

for the same applied heat flux and air flow rate. The cubic structure has an internal surface area

roughly twice that of the round-strut tetradecahedral heat exchanger which would lead us to expect

higher absolute heat transfer rate. The cubic structure has an internal surface area three times of

the thin-strut tetradecahedral heat exchanger, which leads to the expectation of a higher absolute

heat transfer rate. The thin-strut tetradecahedral heat exchanger produced the lowest temperature

rise (Figure 4-4c).

55

(a) (b)

(c)

Figure 4-4: Increase in air temperature from the inlet to the outlet of a) cubic b) round-strut

tetradecahedral, and c) thin-strut tetradecahedral heat exchangers with air flow rates varying from

10 to 90 L/min for applied heat flux in the range of 3.2 to 0.8 kW/m2.

0

40

80

120

160

200

0 20 40 60 80 100

Tem

per

ature

Ris

e, Δ

T (

°C)

Air Volumetric Flow Rate, ὺ (L/min)

3.2 kW/m²

2.3 kW/m²

1.5 kW/m²

0.8 kW/m²

0

40

80

120

160

200

0 20 40 60 80 100

Tem

per

ature

Ris

e, Δ

T (

°C)


3.2 kW/m²

2.3 kW/m²

1.5 kW/m²

0.8 kW/m²

0

40

80

120

160

200

0 20 40 60 80 100

Tem

per

ature

Ris

e, Δ

T (

°C)


3.2 kW/m²

2.3 kW/m²

1.5 kW/m²

0.8 kW/m²

56

To calculate the efficiency of the heat exchangers the increase in enthalpy of air passing through

them was calculated:

𝑄 = �̇�𝑐𝑝,𝑎(𝑇𝑖𝑛 − 𝑇𝑜𝑢𝑡), (4-7)

where �̇� is the mass flow rate of air, cp,a its specific heat and Tin and Tout the air inlet temperature

and outlet temperature of the heat exchanger respectively.

Figure 4-5 shows values of Q as a function of air flow rate for the case of both 2.3 kW/m2 and 0.8

kW/m2 heat flux for all three heat exchangers. The total power input to the heat exchangers in all

three cases is indicated by the horizontal lines. Three heat exchangers transferred approximately

the same amount of energy from the heaters to the air, in spite of their different structures. As the

airflow rate increased more of the heat supplied by the heater was transported out of the channels

by the air. Heat not transferred to the air was either lost to the surroundings through the insulation

or conducted to the tubes connected to the end of the heat exchangers.

57

Figure 4-5: Rate of heat transfer to air flowing through cubic, round-strut tetradecahedral and thin-

strut tetradecahedral heat exchangers with varying air flow rate and total heater power of 0.8 and

2.3 kW/m2. The horizontal lines mark the total heater power of 0.8 and 2.3 kW/m2.

To observe the effect of the internal structure of the heat exchangers on conduction heat transfer,

infrared images of the internal struts were taken at the outlet of the channel, with end-caps

removed. Figure 4-6 shows sample images for flow rates varying from 20-80 L/min in the cubic

heat exchanger with an applied wall heat flux of 2.3 kW/m2. The temperatures at the center and

edge of the channel cross-section are indicated. At the highest flow rate of 80 L/min (Figure 10d)

the edges of the heat exchanger tube were at the highest temperature (62°C), while at the center

the temperature was a little lower, about 60°C.

0

20

40

60

80

100

120

0 20 40 60 80 100

Hea

t T

ransf

er R

ate,

Q (

W)


Cubic @ 3281 W/m2

Round-Strut Tetradecahedral @ 3281 W/m2

Thin-Strut Tetradecahedral @ 3281 W/m2

Cubic @ 820 W/m2

Round-Strut Tetradecahedral @ 820 W/m2

Thin-Strut Tetradecahedral @ 820 W/m2

3281 W/m2

820 W/m2

58

Figure 4-6: Temperature variation across exit of cubic heat exchanger for constant applied heat

flux of 2.3 kW/m2 and air flow rate (a) 20 L/min, (b) 40 L/min (c) 60 L/min, and (d) 80 L/min.

Temperature scales are in °C.

The temperature drop across the cross-section of the heat exchanger demonstrated that heat was

being conducted to the interior of the cubic mesh. Under these conditions the heat exchanger

transferred over 90% of the heater power to the air (see Figure 4-5). The temperature was lower at

the top of the channel than at the bottom as a result of natural convection increasing the flow near

the upper surface and decreasing it along the lower surface. As the air flow rate decreased to 60

59

L/min (Figure 4-6c) the temperature became more uniform across the channel, indicating little heat

transfer.

At the lowest flow rate, 20 L/min (see Figure 4-6a), the temperature gradient was reversed: the

highest temperature of 139°C was at the center of the grid and decreased to the walls of the channel

that were at approximately 129°C. Heat was no longer being transmitted from the walls to the air

at the end of the channel, which explains why the air transported out less than 50% of the heater

power (see Figure 4-5). The temperature distribution was symmetrical about the center of the

channel, showing that convection heat transfer was small compared to conduction.

The round-strut tetradecahedral heat exchanger exhibited similar behavior, as shown in Figure 4-7.

At a low flow rate of 20 L/min the highest temperature was at the center of the channel and

decreased towards the walls (Figure 4-7a). Increasing the flow rate to 80 L/min reversed the

temperature gradient (Figure 4-7c). At the higher flow rates the center of the round-strut

tetradecahedral channel is significantly cooler than that of the cubic channel (compare Figure 4-6d

with Figure 4-7d).

The thin-strut tetradecahedral heat exchanger also exhibited similar behavior, as shown in Figure

4-8. At a low flow rate of 20 L/min the highest temperature was not at the center of the channel

but it was lower than the walls (Figure 4-8a). Increasing the flow rate to 80 L/min reversed the

temperature gradient (Figure 4-8c). At the higher flow rates the center of the thin-strut

tetradecahedral channel is significantly cooler than that of the cubic channel (compare Figure 4-6d

with Figure 4-8d) but close to that of round-strut tetradecahedral (compare Figure 4-7d with Figure

4-8d). As can be seen from Figure 4-8, while increasing the flow rate to 80 L/min the center of the

channel of the thin-strut tetradecahedral (Figure 4-8) became cooler faster than round-strut

tetradecahedral (Figure 4-7) and that of the cubic channel (Figure 4-6).

60

Figure 4-7: Temperature variation across exit of round-strut tetradecahedral heat exchanger for


L/min, and (d) 80 L/min. Temperature scales are in °C.

61

Figure 4-8: Temperature variation across exit of thin-strut tetradecahedral heat exchanger for

constant applied heat flux of 2.3 kW/m2 and air flow rate (a) 20 L/min, (b) 40 L/min, (c) 60 L/min,

and (d) 80 L/min. Temperature scales are in °C.

Heat is transferred into the channel by conduction along the metal struts and carried out by

convection through the air. When an air stream is heated through a characteristic temperature

difference ∆T the heat transfer rate due to convection is given by:

62

𝑄𝑐𝑜𝑛𝑣 = �̇�𝑐𝑝,𝑎∆𝑇 (4-8)

The rate of heat conduction along the struts over the same temperature difference is given by

𝑄𝑐𝑜𝑛𝑑 = 𝑘𝑠𝐴𝑠∆𝑇

𝐻 (4-9)

where ks is the thermal conductivity of the solid, As the cross-sectional area of conduction and the

channel height H is taken as a characteristic length. The ratio of the convective to conduction heat

flux gives a dimensionless Peclet number:

𝑃𝑒 =𝑄𝑐𝑜𝑛𝑣𝑄𝑐𝑜𝑛𝑑

=�̇�𝑐𝑝,𝑎𝐻

𝑘𝑠𝐴𝑠 (4-10)

The solid area across any cross-section is related to the porosity ε by the relation:

𝜀 = 1 −𝐴𝑠𝐴𝑡

(4-11)

where At is the total cross-sectional area of the channel. For a channel with a square cross-section,

At = H2. Substituting this in Equation (4-10) gives

𝑃𝑒 =�̇�𝑐𝑝,𝑎

(1 − 𝜀)𝐻 (4-12)

Assuming that for stainless steel 𝑘𝑠= 16 W/mK, that H =25 mm, and with the porosity values given

in Table 4-1, Pe for all three heat exchanger channels were calculated. Figure 4-9 shows the

variation of heat exchanger efficiency, defined as the fraction of the total heater power transferred

to the air flowing through the heat exchanger, with Peclet number. The efficiency is a function of

Pe alone, irrespective of the heat flux applied. At a given flow rate Pe is smaller for the cubic

channel, since it has lower porosity (𝜀). Convection is a more dominant heat transfer mechanism

63

for the thin-strut tetradecahedral, and round-strut tetradecahedral than the cubic channel, compared

to conduction, since it has greater porosity, explaining why its interior is cooler at the same airflow

rate (compare Figure 4-6d to Figure 4-7d). At a flow rate of 50 L/min Pe is 10. Convection is an

order of magnitude greater than conduction at flow rates above this value, and carries heat away

from the interior faster than it can be conducted in, so that the interior remains cooler than the

walls as seen in Figure 4-6d and Figure 4-7d. At lower flow rates heat cannot be transported away

by air more rapidly than it is conducted in, and the interior of the channel starts to overheat (see

Figure 4-6a, and Figure 4-7a). The heat exchanger efficiency, therefore, decreases at low flow

rates (Pe < 10).

64

Figure 4-9: Variation of heat exchanger efficiency for cubic, round-strut tetradecahedral and

thin-strut tetradecahedral channels with increasing Peclet number.

Since the heater was wrapped uniformly around the channel, a uniform heat flux was applied to

the heat exchanger walls. For a constant heat flux an energy balance gives that the air temperature

increases linearly with position along the length of a heated channel [27], so the value of the local

air temperature at a given axial distance from the inlet was calculated by interpolating between the

inlet and outlet air temperature. Figure 4-10 shows measured surface temperatures and calculated

air temperatures for cubic (Figure 4-10a), round-strut tetradecahedral (Figure 4-10b) and thin-strut

tetradecahedral (Figure 4-10b) channels at two different flow rates (20 L/min and 80 L/min) and

an applied heat flux of 2.3 kW/m2.

0

20

40

60

80

100

0 10 20 30 40

Act

ual

Hea

t E

xch

anger

Eff

icie

ncy

, η

(%)

Peclet Number, Pe

Cubic



65

(a) (b)

(c)

Figure 4-10: Measured wall temperature and calculated air temperature variation along the length

of (a) the cubic, (b) the round-strut tetradecahedral, and (c) the thin-strut tetradecahedral heat

exchanger for an applied heat flux of 2.3 kW/m2 and air flow rates of 20 and 80 L/min.

20

60

100

140

180

220

0 50 100 150 200 250 300

Tem

per

ature

, (°

C)

Axial Distance from Inlet, x (mm)

20

60

100

140

180

220

0 50 100 150 200 250 300

Tem

per

ature

, T

(°C

)


20

60

100

140

180

220

0 50 100 150 200 250 300

Tem

per

ature

, T

(°C

)Axial Distance from Inlet, x (mm)

Air

20 80

Wall

L/min

Air

20 80

Wall

L/min

Air

20 80

Wall

L/min

66

(a) (b)

(c) (d)

Figure 4-11: Local heat transfer coefficient variation along the length of (a) the cubic, (b) the

round-strut tetradecahedral, (c) the thin-strut tetradecahedral and (d) a hollow channel for 2.3

kW/m2 heat flux.

0

10

20

30

40

50

60

0 50 100 150 200 250 300

Hea

t tr

ansf

er C

oef

fici

ent,

h (

W/m

2K

)


80 L/min

60 L/min

40 L/min

20 L/min

0

10

20

30

40

50

60

0 50 100 150 200 250 300

Hea

t tr

ansf

er C

oef

fici

ent,

h (

W/m

2K

)Axial Distance from Inlet, x (mm)

80 L/min

60 L/min

40 L/min

20 L/min

0

10

20

30

40

50

60

0 50 100 150 200 250 300

Hea

t tr

ansf

er C

oef

fici

ent,

h (

W/m

2K

)


80 L/min

60 L/min

40 L/min

20 L/min

0

10

20

30

40

50

60

0 50 100 150 200 250 300

Hea

t tr

ansf

er C

oef

fici

ent,

h (

W/m

2K

)


80 L/min

60 L/min

40 L/min

20 L/min

67

A local convective heat transfer coefficient h was defined for a section of the channel by using

an energy balance

𝑄𝑐𝑜𝑛𝑣 = ℎ𝐴𝑠𝑓(𝑇𝑠−𝑇𝑓) (4-13)

where Asf is the internal surface area of the channel section (the area wetted by the fluid), Ts is the

local wall temperature, measured by thermocouples attached to the channel, and Tf the calculated

bulk mean fluid temperature. Figure 4-11 shows calculated values of local heat transfer

coefficients at various axial positions for cubic, round-strut and thin-strut tetradecahedral heat

exchangers and a hollow channel. For the cubic channel, (Figure 4-11a) heat transfer coefficients

increased with flow rate, reaching a value of approximately 20 W/m2K at a flow rate of 80 L/min.

The value of h did not change very much with axial position. For the round-strut tetradecahedral

channels (Figure 4-11b) heat transfer coefficients were higher, reaching over 50 W/m2K. Thin-

strut tetradecahedral resulted in similar heat transfer coefficients than round-strut tetradecahedral.

The maximum values were closest to the inlet, and then decreased sharply to reach a constant value

at approximately 125 mm (about 5 times channel height H), indicating fully developed flow [25].

Average heat transfer coefficients ℎ̅ for all three channels were calculated as follows:

ℎ̅ =𝛥𝑥

𝐿 ∑ℎ(𝑥) (4-14)

where L is the length of the channel and Δx is the spacing between thermocouples, which is

approximately 37 mm. Equation (4-15) non-dimensionalized the average heat transfer coefficient,

using the channel height H as a length scale

𝑁𝑢𝐻 =ℎ̅𝐻

𝑘 (4-15)

68

Nusselt numbers were plotted as a function of flow Reynolds number, defined as

𝑅𝑒𝐻 =𝜌𝐻𝑢

𝜇

(4-16)

The variation of 𝑁𝑢𝐻 with 𝑅𝑒𝐻 is presented in Figure 4-12. All the data for each channel collapsed

onto a single line. The results for cubic, round-strut and thin-strut tetradecahedral channels were

compared with the results for both an empty steel channel and laser-sintered empty channel. Since

the flow inside the empty channel was a developing flow, the fully developed Nusselt number

equation could not be used for the comparison in this case. 𝑁𝑢𝐻 increased by factors of 4 and 2

for round-strut tetradecahedral and cubic structure respectively compared to the empty channels,

whose heat transfer did not differ significantly. The enhancement of 𝑁𝑢𝐻 was higher for the round

and thin-strut tetradecahedral than the cubic structure, even though it exhibited a lower pressure

drop (Figure 4-2). The thin-strut tetradecahedral heat structure resulted in a similar enhancement

of 𝑁𝑢𝐻 than the conventional round-strut tetradecahedral structure. The thin-strut tetradecahedral

structure resulted in the lowest pressure drop compare to the other two structure, a competitive

enhancement of 𝑁𝑢𝐻 while having the lowest weight. A detailed study of flow through the

different internal structures will be required to understand why their heat transfer properties differ.

69

Figure 4-12: Average Nusselt number (NuH) as a function of Reynolds number (ReH) for round-

strut, cubic structure, thin-strut tetradecahedral and empty channels.

0

10

20

30

40

0 1000 2000 3000 4000

Nuss

elt

num

ber

, N

uH

Reynolds number, ReH



Cubic

Empty Channel

Empty Channel Laser Sintered

70

4.4 Conclusion

Laser-sintering was used to fabricate heat exchanger channels with complex internal structures.

Three channels were built, two containing cubic and round-strut tetradecahedral cells with

identical strut diameters and one with thin-strut tetradecahedral cells. The round-strut

tetradecahedral channel had 56% of the surface area and 68% of the weight of the cubic channel,

yet gave higher permeability, lower friction factor and lower pressure drop. The round-strut and

thin-strut tetradecahedral channels also gave much higher local heat transfer coefficients than the

cubic channel, with a 100% higher Nusselt number. The thin-strut tetradecahedral channel yielded

higher permeability, lower friction factor and lower pressure drop compared to the cubic and

round-strut tetradecahedral channels. The thin-strut tetradecahedral structure had the lowest mass

per section of 71 g compare to 151 g and 103, and highest porosity of 0.84 compared to 0.64 and

0.77 of cubic and round-strut tetradecahedral structures respectively. All three structures had much

higher NuH than empty channels.

Heat transfer in the investigated channels was by both conduction and convection. In was found

that the Peclet number must be large (>10) for convection to be sufficiently rapid to carry away

heat conducted to the interior. At lower values of Pe the interior struts become hotter than the walls

of the channel. Heat was no longer conducted in and heat exchanger efficiency decreases.

Convection was a more dominant heat transfer mechanism for the thin-strut tetradecahedral, and

round-strut tetradecahedral than the cubic channel, compared to conduction, due to their higher

porosity.

71

Wire-Arc Thermal Sprayed Heat Exchangers

5.1 Introduction

Porous structures such as metal foam and wire mesh can act as fins to enhance heat transfer in heat

exchangers due to their light weight, large surface area to volume ratio, high strength to weight

ratio. Wire mesh may not have as large a surface area to volume ratio as other porous structures

like metallic foams but are available in a much wider variety of materials and are also more cost

effective. In this study wire mesh was used as the porous structure for the fabrication of stainless

steel tube heat exchangers since it is available in materials that are much more resistant to

oxidation.

The porous structures must be in good thermal contact with the surface of the tubes, through which

fluid passes, to reduce thermal resistance and ensure high heat transfer. Brazing and welding have

been in use for many years to join metallic substrates together. Brazing is expensive since it

requires a vacuum furnace to heat the substrate. For successful welding both parts should melt at

the same time which did not happen. The wire mesh melts and evaporates much faster than the

tube Figure 5-1.

72

Figure 5-1: Unsuccessful welding of tube to the wire mesh.

Better welded connections can be achieved using larger wire mesh diameters but there are only

commercially available with very small pore density, 1 PPI which was not suitable for this study.

There is a need for more efficient and economical method of connecting the wire mesh to the tube

since heat transfer depends on a good bond between the two.

Wire-arc spray coating is a technique to deposit metallic coatings on substrates as shown in Figure

5-2. In this technique two electrically conductive wires are fed into a spray gun, where they

generate an arc by applying a voltage between their tips. The arc melts both wires and a jet of

compressed air is used to atomize the liquid metal and accelerate molten particles toward the

substrate to be coated. The accelerated particles solidify after hitting the substrate and form a

coating. Other thermal spray techniques such as high velocity oxy-fuel spraying and plasma

spraying are available commercially to create dense coatings.

73

Figure 5-2: Thermal skin deposition using wire-arc spray technique.

In this study wire-arc spray was used to provide a bond between the wire mesh and the tube due

to its low cost and ability to produce thick coatings. A wire-arc spraying process was used due to

its low operational cost and high efficiency compared to other thermal spraying processes, which

made it a good candidate for mass production of heat exchangers.

74

5.2 Geometric Characteristic

Metallic wire mesh (Figure 5-3) are porous structures consisting of an array of metals forming

square, rectangular or circular pore patterns. Wire mesh screens are manufactured in a variety of

pore sizes, wire diameters and wire types and are categorized based on the type of connection

between wires as welded, woven, crimped or molded. Tube heat exchangers were modified using

wire mesh structures in order to enhance the heat transfer performance of the heat exchanger by

increasing its external surface area. Wire mesh enhances the heat transfer of the heat exchanger in

a manner similar to solid plate fins, but due to their porosity, the pressure drop across them is

significantly lower. The ideal wire mesh PPI should have a high ratio of surface area to occupied

volume without reducing air penetration. Additionally, the size of the pore should be large enough

to permit thermal spray particles to penetrate and provide sufficient mechanical bonding between

the mesh and the tube, reducing the thermal resistance and ensuring high thermal contact.

(a)

(b)

Figure 5-3: Woven copper wire mesh screens of (a) 10 PPI, and (b) 40 PPI.

75

5.3 Fabrication of Wire-Arc Thermal Sprayed Heat Exchangers

A twin wire-arc spraying system (ValuArc, Sulzer Metco Inc., Westbury, NY) was used to spray

Alloy Metcoloy 2 wires on the tube-wire mesh joints to create a metallic bond between tubes and wire

mesh at ambient conditions. Optimized parameters, from the work of Rezaey et al. [6], pertaining to

wire mesh heat exchangers using wire-arc spraying were employed. They analyzed the in-flight

characteristics of the molten droplets measured using the DPV-2000 spray monitoring system (DPV-

2000 particle diagnostic monitoring system, Tecnar Automation Ltd., St-Bruno, Quebec, Canada) to

analyze in-flight characteristics of the molten droplets and effect of spraying distance on their size,

temperature, and velocity when they hit the substrate surfaces. Results of these experiments were

correlated with coating properties.

It is important to minimize the amount of porosity in the thermal sprayed coatings since it has a

significant effect on their mechanical and physical properties and would reduce the thermal

conductivity of the layer between the tubes and wire mesh. Porosity also reduces the tensile strength

of the thermally sprayed coatings, which would result in reduction in the resistance of the coating to

thermal stresses at the time of heat exchanger start up and shut down.

Backscattered electron images of coatings deposited at spraying distances of 100,150, and 200 mm

are shown in Figure 5-4. The light gray metal splats, the intermediate contrast oxide regions at the

splat boundaries, and the black pores can be readily discerned. The gray phase in the back scattered

electron SEM micrographs shown in Figure 5-4 was identified as oxides by EDS analysis. SEM

micrographs of the coating between the wire and tube were analyzed to find the porosity and oxide

content and the results are shown in Table 5-1.

76

The optimum spraying distance of 0.15 m (6 in) was used to minimize the porosity and oxide content,

while maintaining sufficient adhesion strength to obtain satisfactory heat conduction, and mechanical

connections at the interface of the tube and the wire mesh.

Table 5-1: Porosity, oxide content, and adhesion strength of the coatings sprayed under different

conditions [6].

Sample Porosity*

(%)

Oxide Content*

(%)

Adhesion Strength**

(MPa)

1 (100mm) 4 ± 1 5 ± 0.5 18 ± 1

2 (150mm) 2 ± 0.4 7 ± 1 24 ± 2

3 (200mm) 6 ± 1

8 ± 1 20 ± 1

* Standard deviation calculated based on 8 SEM image analysis for each sample.

** Standard deviation calculated based on 5 measurements for each sample.

77

(a)

(b)

(c)

Figure 5-4: Backscattered electron SEM images of stainless coatings deposited at spray distances

of (a) 100 mm, (b) 150 mm, and (c) 200 mm [6].

78

In-flight characteristics of the molten droplets were also measured using the DPV-2000 system to

investigate the effect of spraying distance on their size, temperature, and velocity when they hit

the substrate surfaces. Wire-arc spraying parameters selected for fabricating heat exchangers are

listed in Table 5-2.

Table 5-2: Wire-arc thermal spray parameters for deposition of stainless steel coating [6].

Gun ValuArc

Wire Feed Rate (m/min) 7

Voltage (V) 31

Inlet Pressure (psi) 85

Air Flow Rate (SCFM) 60

Spraying Distance (m) 0.15

Using these parameters, a superior mechanical was achieved between the wire and tube, as shown

in Figure 5-5. The gap between the wire and the tube, shown at higher magnification in Figure 5-6,

was completely filled by coating material, forming a good path for heat conduction.

79

Figure 5-5: SEM micrograph of coated joint [6].

Figure 5-6: SEM image of gap in the wire-tube joint filled by the coating material [6].

80

Preliminary Investigation of Flow over Perforated Sheet

and Wire Mesh Fins

6.1 Introduction

Fins have been conventionally used to enhance heat transfer. The use of porous materials has been

proposed as a way to increase the surface area of the heat exchanger that at the same time reduces

the weight of the system and increases the efficiency of heat exchange. There is an enormous body

of literature dealing with analysis of heat exchangers but few researchers have investigated the

heat transfer performance of wire mesh as a heat transfer enhancer for heat exchanger applications.

Armour and Cannon [40] studies fluid flow through woven screens measuring the pressure drop

across different types of woven metal screens and developing a general correlation for pressure

drop. Varshney and Saini [41] used wire mesh screen for solar air heated applications where they

packed the air duct with wire mesh screens to enhance heat transfer. They concluded that heat

transfer enhancement depends strongly on the geometrical parameters of the wire mesh matrix.

Li et al. [42] used wire mesh at the inlet of a channel to create turbulent flow and enhance heat

transfer. They looked into different types of wire mesh and varied the Reynolds while measuring

the heat transfer enhancement. The effective heat transfer enhancement was also compared to the

low pressure loss due to the presence of wire mesh. The heat transfer enhancement was attributed

to the presence of wire mesh as a turbulence generator.

81

Figure 6-1: Heat Transfer performance charts of different heat dissipation media [14].

Tian et al. [14] studied fluid flow and heat-transfer during forced convection through cellular

copper lattice structures. Heat was applied the bottom of the test samples by a heating pad. To find

the maximum heat transfer performance of the woven copper mesh they tested several

configurations. They discovered that unlike open-cell metal foams and packed beds, the friction

factor of the bonded wire screen, apart from being a function of porosity, is also a function of

orientation. They concluded that wire-screen mesh can compete with the available heat dissipation

media.

82

Venugopal, Balaji and Venkateshan [43] experimentally studied the pressure drop and heat transfer

in a vertical duct filled with metallic porous structures. The test section consisted of two identical

porous structures on both side of a plate-heater. A large increase in average Nusselt number, by a

factor of up to 4.52, was observed with a material with 0.85 porosity. The porous media model

they developed shows a similar thermo-hydrodynamic performance to that seen in metallic foams.

Figure 6-2: Heat transfer performance charts [43].

83

Kurian, Balaji and Venkateshan [44] studied the heat transfer enhancement due to packed wire

mesh screens. They filled a horizontal channel with wire screens to create a porous block. The

results were comparable with heat transfer enhancement of metallic foam structures. Previous

researchers have used wire mesh screens to produce a block of porous structure in order to study

its pressure drop and heat transfer performance. In this study, single wire mesh screens were used

to enhance heat transfer.

A simple method of increasing the heat transfer surface area has been developed by using a twin

wire-arc thermal spray system to generate a dense, high strength coating that bonds perforated

sheet and wire mesh to the outside surfaces of fins which was explained in the previous chapter.

In this study, as the first step toward understanding the performance of these porous structures, the

heat transfer from perforated sheet; and wire mesh was experimentally investigated. Experiments

were done in which electrically heated fins were placed inside a wind tunnel with the air velocity

varying between 0 to 20 m/s. To understand the heat transfer enhancement, the temperature

distribution of the porous structures was measured using a high temperature infrared camera for

different applied voltages and at different velocities. Several fin designs were fabricated and tested

using 0.06, 0.12 and 0.18 in (1.52, 3.05 and 4.57 mm) perforated sheet hole diameter, and 10, 14

and 20 PPI wire mesh to understand the heat transfer enhancement due to convection in each case.

It was possible to produce significant increases in the heat transfer from the plain tube by

connecting porous screens to the outer surface of the tubes.

84

6.2 Fabrication of Wire-Arc Thermal Sprayed Fins

For this study, one flat plate, three perforated aluminum sheets with 0.06, 0.12 and 0.18 in (1.52,

3.05 and 4.57 mm) hole diameter and three aluminum wire mesh sheets with pore density of 10,

14 and 20 PPI were used as shown in Table 6-1 and Table 6-2. The ideal wire mesh pore size or

hole diameter for perforated sheets should correspond to a high ratio of surface area to volume,

without reducing air penetration. Additionally, the size of the pore should be large enough to

permit thermal spray particles to penetrate, and provide sufficient mechanical bonding between

the mesh and the tube, reducing thermal resistance and ensuring good thermal contact. The screen

dimensions were identical for both wire mesh and perforated sheet, 76 mm x 76 mm. As the hole

diameter decreased from 0.18 in (4.57 mm) Perfo (a) to 0.06 in (1.54 mm) Perfo (c), the number

of the holes increased which resulted in the reduction of the open area from 51% to 30%.

Table 6-1: Perforated sheet specifications.

Fin

Opening

Size

Open

Area

Center-to-Center

Spacing

Number

of Holes

Porosity

Surface Area

of the Fin

Perfo (a)

0.18 in

(4.57 mm)

51 %

0.25 in

(6.35 mm)

144 0.41

8.82 in2

(5690 mm2)

Perfo (b)

0.12 in

(3.05 mm)

40 %

0.19 in

(4.83 mm)

256 0.32

10.8 in2

(6968 mm2)

Perfo (c)

0.06 in

(1.54 mm)

30 %

0.11 in

(2.79 mm)

715 0.22

12.6 in2

(8129 mm2)

85

Wire mesh is available in different pore densities, specified as pores per inch (PPI), and

experiments were conducted with 10 PPI, 14 PPI and 20 PPI wire mesh (Table 6-2). As the opening

size decreased from 0.075 in (1.9 mm) to 0.034 in (0.86 mm), which resulted in the increase in the

number of pores per inch of the wire mesh, the percentage of the open area decreased from 56%

to 46%.

Table 6-2: Wire mesh fin specifications.

PPI Opening Size

Open

Area

Wire Diameter Porosity

Surface Area of

the Fin

10

0.075 in

(1.90 mm)

56%

0.025 in

(0.63 mm)

0.90

7.07 in2

(4561 mm2)

14

0.051 in

(1.29 mm)

51%

0.02 in

(0.51 mm)

0.92

7.92 in2

(5110 mm2)

20

0.034 in

(0.86 mm)

46%

0.016 in

(0.41 mm)

0.94

9.05 in2

(5837 mm2)

Aluminum was sprayed using wire-arc spray system on the sample shown in Table 6-3 where

aluminum perforated and wire mesh screens were fastened to a 9.5 mm outer diameter, 6.4 mm

inner diameter and 83.8 mm long aluminum tube. A dense coating was deposited on samples as

shown in Figure 48. The area over which the porous structures were in contact with the tube were

covered by the sprayed aluminum coating, with strong mechanical bonding between the coating,

tube and the wire mesh.

86

Table 6-3: Summary of the porous structures used in the study.

Flat plate Perforated Sheet Wire Mesh

Ø= 0.187 in (4.75 mm) 10 PPI

Ø= 0.125 in (3.17 mm) 14 PPI

Ø= 0.0625 in (1.59 mm) 20 PPI

87

(a)

(b)

Figure 6-3: Fabricated fins after thermal spray coating of aluminum on (a) perforated sheet, and

(b) wire mesh.

88

6.3 Experimental Apparatus and Methods

An existing horizontal bench-mounted wind tunnel (Plint & Partners TE-93) with 127 mm x 127

mm square cross-section was retrofitted with a custom made working section to allow for modular

placement of a cartridge heater and specimen within the forced air stream as shown in Figure 6-4.

The working section itself is fully customizable with interchangeable polycarbonate and aluminum

panels. Aluminum honeycomb (0.5 in (12.7 mm) diameter) flow strengthener sheets were placed

both upstream and downstream of the working section to enhance the homogeneity of the flow

inside the wind tunnel.

A sliding orifice plate at the discharge of the fan allows the wind tunnel flow rate to be throttled

between 0 m/s to 30 m/s; flow velocities up to 20 m/s can be measured at any vertical position via

a top side port with hot-wire anemometer (Model HHF42, Omega Company, Stamford, CT).

Figure 6-4: Schematic diagram of the experimental setup.

89

Air temperature was measured with a K-type thermocouples with junction diameters of 0.6 mm

placed in the air stream and air velocity was recorded with a hot-wire anemometer (Model HHF42,

Omega Company, Stamford, CT) with a range of 0 to 20 m/s and a resolution of 0.1 m/s placed

inside the testing section as shown in Figure 6-4. To avoid disturbing incoming air flow during

experiments, the anemometer was removed and the port sealed once the wind tunnel ramped up

and the air velocity had come to steady state. To measure the ambient air temperature, two

thermocouples were placed in the approaching air stream, with one at the intake silencer baffle of

the wind tunnel and another at the frontal area of the test section. Measurements from these two

thermocouples were monitored to maintain a constant incoming air temperature of approximately

20 °C during the experiments. All fins were tested in parallel to the incoming air flow

configuration.

Three-inch long electrical heaters (3618K403, High-Temperature Cartridge Heaters, McMaster-

Carr) were used to provide a constant heat input to the fins during the experiments. To measure

the applied heat flux; the first step was to calculate the derated wattage provided by the heater

using the following equation given by the manufacurer

(𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑉𝑜𝑙𝑡𝑎𝑔𝑒

𝑅𝑎𝑡𝑒𝑑 𝑉𝑜𝑙𝑡𝑎𝑔𝑒)2 ∗ 𝑊𝑎𝑡𝑡𝑎𝑔𝑒 𝑎𝑡 𝑟𝑎𝑡𝑒𝑑 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 = 𝐷𝑒𝑟𝑎𝑡𝑒𝑑 𝑊𝑎𝑡𝑡𝑎𝑔𝑒 (6-1)

where operation voltage is the voltage provided by the power supply, rated voltage was given at

120 V by the supplier and wattage at rated voltage was also given at 200 W by the manufacturer.

The tube surface temperature was measured using five type K thermocouples attached with 0.5 in

(12.7 mm) spacing to the surface of the tube. The temperature distributions of the surface of the

perforated sheet and wire mesh were acquired via an infrared (IR) camera. An IR camera was

positioned in front of the wind tunnel upstream the fin as shown in Figure 6-4. All fins were

90

sprayed with high emissivity black paint (Figure 6-5), rated for high temperature use, to increase

the emissivity of the surface to 0.95 and make it uniform.

(a) (b)

Figure 6-5: Fabricated fins after sprayed using high emissivity black paint on (a) flat plate, and

(b) perforated sheet (Ø= 0.187 in (4.75 mm)).

91

6.4 Results and Discussion

In this section the results for the plain tubes are presented first, followed by the results of the

perforated sheet and wire mesh fins and a comparison between the two.

6.4.1 Plain Tube

The performances of the plain tubes was investigated for three different air velocities of 3.7 m/s,

10 m/s, 15 m/s and at two different applied heater voltage of 15 and 20 V (corresponding to surface

heat fluxes of 1.3 kW/m2 and 2.3 kW/m2). Figure 6-6 demonstrates the tube’s surface temperature

at different velocities. By increasing the velocity the heat transfer coefficient increased and

therefore surface temperature dropped.

Figure 6-6: Temperature variation of the pipe at 15 V and 20 V (corresponding to surface heat

fluxes of 1.3 kW/m2 and 2.3 kW/m2) applied voltage for different air velocities.

10

20

30

40

50

60

70

80

0 2 4 6 8 10 12 14 16

Tem

per

ature

, (°

C)

Velocity, (m/s)

20V

15V

92

The heat transfer from the plain tube (Q Tube) was calculated and compared to the widely acceptable

theoretical mode [45] for flow over a cylinder

Nu = 0.683𝑅𝑒0.466𝑃𝑟1/3 for Re = 40 to 4000

Nu = 0.193𝑅𝑒0.618𝑃𝑟1/3 for Re = 4000 to 40,000

(6-2)

The convective heat transfer coefficient, ℎ𝑎 , was calculated using Equations (6-3) and Equation

(6-4)

ℎ𝑎 =𝑄𝑡𝑢𝑏𝑒

𝐴 ( 𝑇 − 𝑇∞) (6-3)

𝑁𝑢𝐷 = ℎ𝐷

𝑘 (6-4)

where A is the surface area of the tube, T is the surface temperature, T∞ is the air temperature, D is

the diameter of the tube and 𝑘 is the thermal conductivity of air at the film temperature of Tf = (T

+ T∞)/2.

The Reynolds number was calculated using the following equation

𝑅𝑒𝐷 =

𝑉𝐷

𝜈 (6-5)

where 𝑉 is the velocity of air and 𝜈 is the kinematic viscosity of air.

The experimental and theoretical models for flow over the plain tube are plotted in Figure 6-7 as

the variation of 𝑁𝑢𝐷 with 𝑅𝑒𝐷 based on tube diameter as the length scale.

93

Figure 6-7: Comparison between the variation of (NuD) with (ReD) for experimental and

theoretical model for flow over a cylinder.

Assuming the heat loss to the surrounding is zero (𝑞𝑙𝑜𝑠𝑠 = 0) from the conservation of energy

𝑞ℎ𝑒𝑎𝑡𝑒𝑟 = 𝑞𝑡𝑢𝑏𝑒

𝑉2

𝑅= ℎ𝑖𝑑𝑒𝑎𝑙 𝐴 ( 𝑇 − 𝑇∞)

(6-6)

0

10

20

30

40

50

60

70

0 2000 4000 6000 8000 10000 12000

Nuss

elt

Num

ber

, N

uD

Reynolds Number, ReD

Theoretical Model

Experimental Results (15 V)

Experimental Results (20 V)

94

The ideal heat transfer coefficient, assuming no heat losses due to conduction through the base of

the heater, is

ℎ𝑖𝑑𝑒𝑎𝑙 =

𝑉2

𝑅𝐴 ( 𝑇 − 𝑇∞)

(6-7)

In the experiment the heat loss to the surrounding is not zero (𝑞𝑙𝑜𝑠𝑠 > 0) therefore

𝑞ℎ𝑒𝑎𝑡𝑒𝑟 = 𝑞𝑡𝑢𝑏𝑒 + 𝑞𝑙𝑜𝑠𝑠

𝑉2

𝑅= ℎ𝑒𝑥𝑝 𝐴 ( 𝑇 − 𝑇∞) + 𝑞𝑙𝑜𝑠𝑠

ℎ𝑒𝑥𝑝 =

𝑉2

𝑅 − 𝑞𝑙𝑜𝑠𝑠

𝐴 ( 𝑇 − 𝑇∞)

(6-8)

Therefore, the measured heat transfer coefficient from the experiment (ℎ𝑒𝑥𝑝) is smaller than that

expected in the ideal case when there are no losses. The results presented in Equation (6-8)

confirms that the fin exhibits loss and therefore calculated Nusselt numbers are lower than the

theoretical value. The percentage of 𝑞𝑙𝑜𝑠𝑠 to the heat input varies between 8 to 12%. Considering

a black surface radiation and a constant surface temperature of 350K, the radiative heat transfer is

less than 1% of the total heat transfer. The radiative heat transfer is negligible due to low surface

temperature.

6.4.2 Perforated Sheet Fins

The performance of the perforated sheet fins was investigated for three different air velocities of

3.7 m/s, 10 m/s, 15 m/s and at three different applied heater voltages of 55, 60 and 65 V

95

(corresponding to surface heat flux of 17.7, 21.1 and 24.7 kW/m2 based on the outer surface area

of the tube). To ensure that steady state was reached during the experiment, the wind tunnel was

operated for 30 minutes for each applied voltage. The experiments were performed at steady state,

and the readings were taken when the thermocouple outputs were stabilized. The initial step was

to compare the performance of the flat plate to the perforated sheet and analyze the temperature

distribution along the surface of both structures. Figure 6-8 demonstrates the comparison between

the flat plate and the perforated sheet for a 55 V heater voltage and at 10 m/s air velocity. Air

velocity and the voltage applied to the heater were kept constant while fin temperature distribution

was analyzed.

For the flat plate, due to its non-porosity, the air could not pass through the plate and was forced

to pass through the 1 in (25.4 mm) gap between the edge of the fin and the test section wall.

Analysis of the temperature distribution, presented in Figure 6-8, demonstrated a greater heat

transfer from the perforated sheet than the flat plate. Flat plate fin resulted in a higher surface

temperature compare to the perforated sheet. This could be explained since the flat plate has a

nonporous structure which results in an air velocity drop and consequently lower convection heat

transfer rate.

96

(a)

(b)

Figure 6-8: IR map of the temperature distribution of the fins (a) Flat plate, and (b) Perforated

sheet (Ø= 0.187 in (4.75 mm)).

97

Figure 6-9: Comparison of the temperature profile at 55 V (17.7 kW/m2) with a 10 m/s flow

between the flat plate and perforated sheet (Ø= 0.187 in (4.75 mm)).

To better understand the surface temperature distribution along both fins, the temperature

distribution was mapped as a function of fin length as shown in Figure 6-9. The x axis represents

the distance along either the flat plate or the perforated sheet, which were 3 in (76.2 mm) wide and

were bonded at their centers so that the fin length was 1.5 in (38.1 mm).

The perforated sheet gave much higher heat transfer and consequently lower fin tip temperature of

26°C compare to 41°C for the flat plate. The perforated sheet also exhibited a maximum

temperature of 69°C on the surface of the tube compared to 74°C for the solid plate. The sudden

drop in temperature near the centerline of the solid plate shows that bonding with the tube was not

98

perfect. As seen in Table 6-3, holes were drilled in the flat plate to allow the thermal spray coating

to penetrate and connect it to the tube. Better bonding may improve heat transfer from the tube.

The temperature variation along a fin with an insulated tip is given by [45]

𝑇(𝑥) − 𝑇∞𝑇𝑏 − 𝑇∞

= cosh𝑚(𝐿 − 𝑥)

cosh𝑚𝐿

𝑚 = √ℎ𝑝

𝑘𝐴𝑐

(6-9)

where x is the distance from the fin base, 𝐴𝑐 the cross sectional area of the fin, ℎ the convection

heat transfer coefficient, 𝑝 the perimeter, 𝑇𝑏 the temperature of the fin base and 𝐿 the length of the

fin.

Figure 6-10 shows a comparison between the experimental temperature measurements and the

theoretical temperature variation in which the heat transfer coefficient was adjusted to get the best

agreement between the two. The convection heat transfer coefficients which best fitted the

theoretical model to the experimental results were h =115 W/m2K for the solid plate and h =170

W/m2K for the perforated sheet. The model deviated from the experimental measurements near

the base where the plates were attached to the tube because the contact was not perfect. The higher

heat transfer coefficient of the perforated sheet was a result of the penetration of air through the

holes in it.

99

Figure 6-10: Comparison between the measured surface temperature and predicted theoretical

model.

Figure 6-11 Shows the temperature profile at 60 V for the perforated sheet (Ø= 0.187 in (4.75

mm)) at different air velocities.

20

30

40

50

60

70

80

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Tem

per

ature

, (°

C)

Length, (inch)

Flat Plate Theoretical [45]

Flat Plate Experiment

Perforated Sheet Experiment

Perforated Sheet Theoretical [45]

100

Figure 6-11: The temperature profile at 60 V (21.1 kW/m2) applied voltage and for three air

velocities for perforated sheet (Ø= 0.187 in (4.75 mm)).

The maximum temperature of 115°C, which was in the middle of the fin, decreases to 66°C as the

velocity was increased from 3.7 to 15 m/s. The heat transfer coefficient varied from 61 to 224

W/m2K for 3.7 to 15 m/s respectively. To investigate the effect of change in heat flux on the surface

temperature, the air velocity was kept constant at 10 m/s while the heat flux was varied from 17.7

kW/m2 to 24.7 kW/m2 (corresponding to voltages from 55 V to 65 V) as shown in Figure 6-12. As

the applied voltage increased from 55 V to 65 V, the maximum temperature increased from 69°C

to 84°C. Some fluctuations are present in the experimental temperature profile due to the presence

of holes on the perforated sheet.

20

30

40

50

60

70

80

90

100

110

120

0 0.5 1 1.5 2 2.5 3

Tem

per

ature

, (°

C)

Length, (inch)

3.7 m/s

10 m/s

15 m/s

101

Figure 6-12: The temperature profile at 10 m/s air velocity and three different applied voltages for

the perforated sheet (Ø= 0.187 in (4.75 mm)).

Figure 6-13 shows the surface temperature distribution for the perforated sheet fins which was

recorded using an IR camera. The fin with the highest percentage of open area Perfo (a) (Figure

6-13a) resulted in the hottest tube temperature, which means the lowest heat transfer from the

surface of the perforated sheet to the surroundings. At this point it is clear that there should be an

optimized opening size that maximizes the heat transfer without producing a large pressure drop

across the fin. To better understand the surface temperature distribution along fins, the temperature

distribution was mapped as a function of the fin’s length as shown in Figure 6-14. The heat transfer

coefficient varied from 170 to 231 W/m2K for Ø= 0.1875 in to Ø= 0.0625 respectively. The fin

with the smallest hole diameter resulted in a better heat transfer and consequently the lowest tube

temperature of 57°C compare to 70°C of the perforated sheet with 0.18 in (4.57 mm) hole diameter.

20

30

40

50

60

70

80

90

0 0.5 1 1.5 2 2.5 3

Tem

per

ature

, (°

C)

Length, (inch)

55V

60V

65V

102

(a)

(b)

(c)

Figure 6-13: Perforated sheet tested at 55V (17.7 kW/m2) with a 10 m/s flow (a) Ø= 0.1875 in

(4.76 mm), (b) Ø= 0.125 in (3.17 mm), and (c) Ø= 0.0625 in (1.59 mm).

103

Figure 6-14: Temperature profile of the perforated fins at 55 V (17.7 kW/m2) applied voltage and

10 m/s air velocity.

6.4.3 Wire Mesh Fins

Figure 6-15 shows the surface temperature distribution of the three wire mesh fins for a constant

air velocity of 10 m/s and applied voltage of 55 V (17.7 kW/m2). The 10 PPI wire mesh fin had

the highest percentage of open area (56%), resulting in the lowest tube temperature compared to

the 20 PPI wire mesh fin that has the lowest open area (46%). 20 PPI wire mesh resulted in the

smallest heat transfer from the surface of the perforated sheet to the surroundings. The IR results

20

30

40

50

60

70

80

0 0.5 1 1.5 2 2.5 3

Tem

per

ature

, (°

C)

Length, (inch)

Perfo (a)

Perfo (b)

Perfo (c)

104

demonstrated that the worst connection exists for 20 PPI wire mesh since the thermally sprayed

particles could not effectively penetrate between the pores (Figure 6-15). As the pore size increases

from 20 PPI to 10 PPI, the quality of the connection increased between the wire mesh and the tube

since the particles could penetrate between the pores to connect the mesh to the tube. To better

understand the surface temperature distribution along three fins, the temperature distribution was

mapped as a function of the fin’s length as shown in Figure 6-16.

(a) (b) (c)

Figure 6-15: Experimental temperature distribution at 55V (17.7 kW/m2) applied power with a

10 m/s air velocity (a) 10 PPI, (b) 14 PPI, and (c) 20 PPI.

105

The fin with the largest pores, 10 PPI, resulted in better heat transfer rate and consequently lower

tube temperature of 71°C compare to 82°C of the 20 PPI mesh. The maximum surface temperature

seems to increase with the porosity. Smaller pores clog easily during the thermal spraying process

and therefore prevent good bonding of tube with the fin (Figure 6-15c). In addition, as it is shown

in Figure 6-16, the lowest temperature was almost the same for 10 & 20 PPI, which means the 20

PPI configuration transfers as much heat as 10 PPI due to its high wire mesh surface area. 14 PPI

mesh resulted in the highest fin temperature of 23°C on the end of the fin.

Figure 6-16: Temperature profile for different wire mesh at 55 V (17.7 kW/m2) applied power and

a 10 m/s air velocity.

15

25

35

45

55

65

75

85

95

0 0.5 1 1.5 2 2.5 3

Tem

per

ature

, (°

C)

Length, (inch)

10 PPI

14 PPI

20 PPI

106

14 PPI wire mesh sheet fin was further investigated by varying the air velocity while keeping the

applied voltage constant, as shown in Figure 6-17. The maximum temperature of 128°C, which is

in the middle of the fin, decreases to 71°C as the air velocity was increased from 3.7 to 15 m/s.

Figure 6-17: Temperature profile of 14 PPI at 60 V (21.1 kW/m2) applied power for different air

velocities.

To better compare the performance of wire mesh to perforated sheet the surface temperature

distribution for the three perforated sheets and 10 PPI wire mesh was plotted in Figure 6-18. The

temperature distribution was mapped as a function of the fins. 10 PPI wire mesh resulted in the

15

35

55

75

95

115

135

0 0.5 1 1.5 2 2.5 3

Tem

per

ature

, (°

C)

Length, (inch)

3.7 m/s

10 m/s

15 m/s

107

highest surface temperature of 71°C but it had the lowest temperature profile across the measured

line. The low surface temperature of the wire mesh is due to its high permeability compare to

perforated sheets. Wire mesh is the best configuration as the temperature quickly drops and a

reduced fin size of approximately 1.5 inch (38.1 mm) would be sufficient since the fin temperature

reaches the ambient air temperature.

Figure 6-18: Temperature profile comparison between the wire mesh and perforated sheets at 55V

(17.7 Kw/m2) applied power with a 10 m/s air velocity.

20

30

40

50

60

70

80

0 0.5 1 1.5 2 2.5 3

Tem

per

ature

, (°

C)

Length, (inch)

Perfo (a)

Perfo (b)

Perfo (c)

Woven wire mesh

108

6.5 Heat Transfer Characterization

The total heat transfer from the tube and fins is a combination of heat transfer from the plain tube

and from the porous structure connected to the tube. To calculate the enhancement due to the

porous structure, the heat transfer from the tube was subtracted from the total heat transfer as

shown in Equation (6-10). The tube temperature was applied to previously found relationship of

plane tube and then the heat transfer from the tubes, 𝑄𝑡𝑢𝑏𝑒, was calculated

𝑄𝑡𝑜𝑡𝑎𝑙 = 𝑄𝑚𝑒𝑠ℎ + 𝑄𝑡𝑢𝑏𝑒 (6-10)

𝑄𝑚𝑒𝑠ℎ = 𝑄𝑝𝑒𝑟𝑝 + 𝑄𝑝𝑎𝑟𝑎 (6-11)

The heat transfer from the wire mesh 𝑄𝑚𝑒𝑠ℎ consistd of the heat transfer from the wires which

were perpendicular to the tube (𝑄𝑝𝑒𝑟𝑝) and wires which were parallel to the tube (𝑄𝑝𝑎𝑟𝑎) as shown

in Equation (6-11). To calculate 𝑄𝑚𝑒𝑠ℎ the wires were considered as long pin fins using the

following equation [45]

𝑄𝑝𝑒𝑟𝑝 = √ℎ𝑎𝑃𝑓𝑘𝑓𝐴𝑓.𝑐 (𝑇𝑏 − 𝑇∞) tanh(𝑚𝐿)

𝑚 = √ℎ𝑎𝑃𝑓/𝑘𝑓𝐴𝑓.𝑐

(6-12)

𝑄𝑝𝑎𝑟𝑎 = ℎ𝑎 𝐴𝑓.𝑐 ( 𝑇𝑏𝑛 − 𝑇∞) (6-13)

where 𝑃𝑓 and 𝐴𝑓.𝑐 are the perimeter and cross-sectional area of the fin respectively, L is the length,

𝑘𝑓 the thermal conductivity and 𝑇𝑏𝑛 is the base temperature of the wire in the nth row, which was

measured using the IR camera. The wire mesh heat transfer is calculated by subtracting the heat

109

transfer of plain tube from the total heat transfer. The heat transfer coefficient was calculated by

substituting Equation (6-12) and (6-13) to Equation (6-11). The heat transfer coefficient for the

perforated sheet and the flat plate were also estimated with long fin equations.

Figure 6-19 shows the Nusselt number (𝑁𝑢𝐷) variation with the change of Reynolds

number (𝑅𝑒𝐷) for both the 14 PPI wire mesh and 0.18” hole diameter perforated sheet. 14 PPI

mesh fin resulted in a higher 𝑁𝑢𝐷 at different 𝑅𝑒𝐷 than the perforated sheet.

Figure 6-19: Variation of Nusselt number (NuD) as a function of Reynolds number (ReD) based

on tube outer diameter (OD) for wire mesh and perforated sheet.

0

20

40

60

80

100

120

140

160

0 2000 4000 6000 8000 10000

Nuss

elt

Num

ber

, N

uD

Reynolds Number, ReD

14 PPI Mesh

0.18" Perforated

110

Figure 6-20: Performance chart of the fabricated fins at a constant (ReD) of 5290.

All the fins were also compared at a constant 𝑅𝑒𝐷 of 5290 as shown in Figure 6-20. In general all

wire mesh fins had higher 𝑁𝑢𝐷 than perforated sheet fins. The highest 𝑁𝑢𝐷 corresponds to the 10

PPI wire mesh which has the largest pore size. The 𝑁𝑢𝐷 reduced when wire mesh pore size was

decreases to 20 PPI. The flat plate fin has the lowest 𝑁𝑢𝐷 at a given 𝑅𝑒𝐷.

The perforated sheet structure creates large resistance to the air flow because the solid portion of

the perforated sheet is perpendicular to the direction of the flow. This air blockage creates

stagnation (low velocity) regions that have low heat transfer coefficient and reduce the overall heat

transfer performance of perforated sheets compared to wire mesh screens.

10 PPI

Mesh

14 PPI

Mesh

20 PPI

Mesh 0.06"

Perforated 0.12"

Perforated0.18"

Perforated

Flat sheet

0

20

40

60

80

100

120

140

160

180

200

Nuss

elt

Num

ber

, N

uD

111

By comparing the 𝑁𝑢𝐷for three different hole size perforated sheets of 0.18”, 0.12” and 0.06” with

non-perforated surface area ratio of 49%, 60% and 70% (Table 6-1), It was concluded that 0.06”

diameter hole perforated sheet has the highest 𝑁𝑢𝐷. This value is the direct contribution of the

non-perforated surface area (Table 6-1). In other words, the perforated sheet with 70% surface area

ratio had the highest heat transfer area among those three perforated sheets, independent of the

hole size. Values are tabulated as follows

Table 6-4: Comparison between the variation of NuD and Anon-perf.

Hole Diameter 𝑨𝒏𝒐𝒏−𝒑𝒆𝒓𝒇

𝑨𝒕𝒐𝒕𝒂𝒍 𝑵𝒖𝑫

𝑵𝒖𝑫𝑨𝒏𝒐𝒏−𝒑𝒆𝒓𝒇𝑨𝒕𝒐𝒕𝒂𝒍

0.06” 70% 63 90

0.12” 60% 49 82

0.18” 49% 41 84

The experimental data suggest that 𝑁𝑢𝐷 is proportional to the non-perforated surface area.

𝑁𝑢𝐷 ∝ 𝐴𝑛𝑜𝑛−𝑝𝑒𝑟𝑓

𝐴𝑡𝑜𝑡𝑎𝑙

(6-14)

These results confirms that the higher heat transfer in the 0.06” hole diameter perforated sheet is

due to its higher surface area.

112

Figure 6-21: Nusselt number (NuH) variation as a function of Reynolds number (ReH).

Data found in literature was for a stack of wire meshes, as shown in Figure 6-21. Li et al. [42]

obtained 𝑁𝑢𝐻 based on channel height of 10 mm as characteristic length for copper wire screens

and Venugopal, Balaji and Venkateshan [43] have also looked into stacks of perforated sheets and

presented their results based on channel height. Calculated results were also converted to 𝑁𝑢𝐻 base

on the hydraulic diameter of the wind tunnel for the sake of comparison. The values of 𝑁𝑢𝐻 found

in the experiment were in agreement by the results of Li et al. [42] and Venugopal, Balaji and

Venkateshan [43]. The difference between the calculated experimental results and the results found

in the literature can be due to the existence of bypass flow around porous screens.

1

10

100

1000

10000

1 10 100 1000 10000 100000 1000000

Nuss

elt

Num

ber

, N

uH

Reynolds Number, ReH

14 PPI Wire Mesh

0.18" Perforared Sheet

Venugopal, Balaji and Venkateshan (0.92 Porosity) [43]



Li et al. (copper wire screens) [42]

113

The performance of the fins was further analyzed based on their fin efficiency and effectiveness

as shown in Figure 6-22. Fin Efficiency (ɳ) and Effectivness (ɛ) were calculated using the

following equations [45]

Fin Efficiency, longfin (ɳ ) =

QfinQfin,max

=1

mL (6-15)

Fin Effectivness, longfin (ɛ) = QfinQno,fin

= √𝑘𝑃

ℎ𝐴 (6-16)

Figure 6-22: Comparison between the fin efficiency (ɳ) and effectiveness (ɛ) of the fins.

30

40

50

60

70

80

90

100

0 0.2 0.4 0.6 0.8 1

Fin

Eff

ecti

vnes

s, ɛ

Fin Efficiency, ɳ

20 PPI Mesh

14 PPI Mesh

0.18" Perforated

0.12" Perforated

10 PPI Mesh

0.06" Perforated

114

The results from Figure 6-22 indicate that wire mesh fins were more effective than perforated sheet

fins. As can be seen from Figure 6-18, the temperature of the wire mesh dropped much faster and

reached the ambient air temperature faster than the perforated sheet. This finding indicates that the

same heat transfer could have been achieved with a shorter fin length. The high fin efficiency can

also be explained using Figure 6-18. The maximum surface temperature was much lower for the

perforated sheet fin than the wire mesh. The wire mesh was not as efficient as perforated sheet

which resulted in a lower overall heat transfer from the hot tube. By increasing wire or plate

thickness 𝑚 in Equation (6-15) decreases, therefore fin efficiency increases. The heat exchangers

and experimental setup for the next chapter was designed to further enhance the understanding of

heat transfer in wire mesh heat exchangers. The temperature distribution along each wire needs to

be analyzed to better understand the enhancement due to the wires which were perpendicular to

the primary wires, which were also connected to the body of the tube heat exchanger.

115

6.6 Conclusion

In this chapter the heat transfer characteristics of the perforated and wire mesh porous structures

have been investigated. Aluminum fins were fabricated by connecting aluminum wire mesh,

perforated sheet and flat plate to aluminum tubes using wire-arc thermal spray coating. The results

indicated the importance of the quality of contact between tubes and porous structure. The porous

structures with high open area allowed good penetration of the coating material into the gap between

wire and tube surface, and thus providing good adhesion and thermal conduction. The fins were tested

inside a wind tunnel and their surface temperature was measured. Significant increase in heat transfer

were achieved by attaching wire mesh or perforated sheet to the plain tube. All fins resulted in larger

heat transfer rate than the flat plate. The performance of the wire mesh fins was affected by pore

density that affects air penetration. The extended surfaces of the perforated sheet and wire mesh

enhanced heat transfer from the tube to the surrounding air inside the wind tunnel. Wire mesh is the

best configuration as the temperature quickly drops and a reduced fin size of approximately 1.5 in

(38.1 mm) would be sufficient since the fin temperature reaches the ambient air temperature and

there is no need for a 3 in. Wire mesh fins were more effective than perforated sheet fins but less

efficient.

116

Water-to-Air Wire Mesh Heat Exchangers

7.1 Introduction

The purpose of this study was to fabricate a high temperature gas to liquid wire mesh heat

exchanger, and to measure heat transfer through the wire mesh. The wire mesh screens were

bonded to the outer surface of tubes using thermal spraying. Experiments were done in which

water cooled 5, 10, and 20 pores per inch (PPI) wire mesh heat exchangers were placed inside a

chamber with an air temperature of 320 ± 20°C at the test section. To measure the heat transfer

enhancement, compared to a plain tube heat exchanger, the temperature rise of the water between

the inlet and outlet of the heat exchanger was measured for three different water flow rates, varying

from 500 to 900 mL/min. A high temperature infrared camera was used to study the surface

temperature, investigate the wire mesh fin efficiency and effectiveness, and to investigate the

connection between the wire mesh and the tube.

117

7.2 Fabricated Heat Exchangers

7.2.1 Wire Mesh

Woven wire mesh screens with pore densities of 5, 10, and 20 PPI were used to make heat

exchangers. The ideal wire mesh pore density should correspond to a high ratio of surface area to

occupied volume, without reducing air penetration. Additionally, the size of the pores should be

large enough to permit thermal spray particles to penetrate, and provide sufficient mechanical

bonding between the mesh and the tube, reducing the thermal resistance and ensuring high thermal

contact. The screen dimensions were identical for all tested samples with the dimensions of 152

mm x 203 mm (𝐿𝑚 x 𝑊𝑚) in an attempt to investigate and compare the efficiency and effectiveness

of the extended surface area of porous materials for the same occupied area.

7.2.2 Fabrication Process

Six heat exchangers were fabricated by bonding stainless steel tubes and wire mesh screens using

a thermal spray process. Each heat exchanger was composed of four tubes with 6.3 mm (0.25 in)

diameter outer diameter, 178 mm (7 in) length, and 0.25 mm (0.01 in) wall thickness; with 57 mm

(2.25 in) center to center tube spacing. The first three heat exchangers were fabricated by thermal

spraying a 5, 10, or 20 PPI wire mesh screen on top of the tubes, respectively, as shown in Figure

7-1. A second set of heat exchangers was fabricated by connecting one wire mesh screen on top,

and another on the bottom, of the tubes as shown in Figure 7-2b. The thermal contact resistance

between the wire mesh and the tube surface is low since the wire mesh is simply placed on top of

the tube to simplify the manufacturing process. The thermal contact resistance would have

increased if the wire mesh was wrapped around the tube to increase the contact area between them.

118

(a)

(b)

(c)

Figure 7-1: Sample of heat exchangers (a) single screen 5 PPI wire mesh, (b) single screens 10

PPI wire mesh, and (c) single screens 20 PPI wire mesh.

119

Stainless steel tubes were connecting to each other by six 90 degree elbow compression fittings in

order to form a path for the coolant. The important parameters of the fabricated heat exchangers

used in this study are summarized in Table 7-1.

Table 7-1: Parameters of the wire mesh heat exchangers.

Samples

Pore

Density

(PPI)

Pore Size

(m²)

Open

Area

(%)

Number

of

Screens

Wire

Diameter

(m)

Mesh

Surface

Area,

𝑨𝒎 (m²)

Total

Surface

Area,

A Total (m²)

Porosity

Heat Ex

1 N/A N/A N/A 0 N/A N/A 0.014 N/A

Heat Ex

2 5 1.5x10-5 59 1 1.2x10-3 0.045 0.059 0.81

Heat Ex

3 10 3.8x10-6 59 1 5.8x10-4 0.045 0.059 0.91

Heat Ex

4 20 4.7x10-7 29 1 5.8x10-4 0.094 0.108 0.91

Heat Ex

5 5 1.5x10-5 59 2 1.2x10-3 0.09 0.104 0.81

Heat Ex

6 10 3.8x10-6 59 2 5.8x10-4 0.09 0.104 0.91

Heat Ex

7 20 4.7x10-7 29 2 5.8x10-4 0.188 0.202 0.91

Each wire of the screen mesh is modeled as a cylinder. The mesh surface area calculations were

performed by accounting for the number of layers in the x and y directions, the wire diameters, and

the dimensions of the mesh. The total surface area (𝐴𝑇𝑜𝑡𝑎𝑙) is the sum of the mesh surface area

(𝐴𝑚) and the tube surface area (𝐴𝑡). The tube surface area is simply the surface area of the tube

without the wire mesh screen. In order to ensure a uniform emissivity over the surface of all heat

exchangers, they were painted with layers of black, high temperature, thermally conductive paint

with emissivity of 0.95, as shown in Figure 7-2.

120

(a)

(b)

Figure 7-2: Sample heat exchangers (a) single screens 5 PPI wire mesh, and (b) double screens 5

PPI wire mesh.

121

7.3 Experimental Apparatus and Methods

The experimental apparatus consisted of an open loop water system and a hot gas chamber. The

coolant flow passing through the tube was maintained by a water circulation loop. A schematic

representation of the experimental setup and the hot air chamber are shown in Figure 7-3 and

Figure 7-4, respectively. The high temperature air chamber was designed to create a steady high

temperature environment to test the fabricated heat exchangers. The channel was positioned

vertically and an experimental rig was designed and fabricated to hold the structure. The test

section, which was designed to hold the heat exchanger perpendicular to the direction of the hot

gas flow, consisted of an inlet and outlet connection to bring water into and out of the heat

exchanger.

Figure 7-3: Schematic representation of the experimental setup.

122

The secondary chamber was designed with the same dimensions as the main test section to permit

a uniform high temperature air flow to reach the heat exchanger, and to avoid recirculation of the

outer air to the test section.

Figure 7-4: Schematic representation of the hot air chamber.

The heat exchanger is located in the test section (Section 3), perpendicular to the direction of the air

flow. The hot air passing through the chamber was supplied by an electrical air heater (F076029,

SKORPION™ AIR HEATERS, OSRAM SYLVANIA, Exeter, NH). The velocity flow field

inside the wind tunnel was measured using a pitot tube (P06A Pitot Static Probe, FlowKinetics,

123

Texas) with an accuracy within ±0.24% of full scale velocity. Water flowed through a damper and

pressure regulator to prevent the flow rate from fluctuating. A valve was placed before the flow meter

to adjust the flow and the flow rate measured a flow meter, with a range of 0.1 to 1 L/min with an

accuracy of 1% of full scale, before the water entered the heat exchanger. The water flow circulated

through the heat exchanger while air was forced over it. Two type-K thermocouple probes were

attached to the inlet and the outlet of the heat exchangers to measure the inlet (𝑇𝑖) and outlet (𝑇𝑜)

water temperatures. An IR camera was used to record the heat exchanger surface temperature during

the experiment. The average air temperature was measured using 15 Type-K thermocouples at

section 3, located before the heat exchanger.

124

7.4 Pressure Drop Through Wire Mesh Screens

The hydraulic performance of wire mesh screens alone, without any tubes, and the effect of spacing

between screens on the air pressure drop were also investigated. The experimental apparatus used

to test the wire mesh samples consists of a horizontal wind tunnel with a square chamber of 127

mm x 127 mm cross section. An aluminum flow straightener was used downstream of the

experimental test section to achieve a uniform flow. The velocity flow field inside the channel was

measure using a hot wire anemometer (Model HHF42, Omega Company, Stamford, CT) with a

range of 0 to 20 m/s, and a resolution of 0.1 m/s. The pressure drop was measured using a digital

manometer (Model HHP-103, Omega Company, Stamford, CT) set to a maximum range of 498

Pa (2 inH2O) with an accuracy of 0.2% of full scale at the beginning and end of the test sections.

Two different pore densities of 20 PPI and 10 PPI stainless steel were chosen, while a fixed width

and height of 127 mm was used for all the samples. The effect of providing distance between wire

mesh screens on the pressure drop were also analyzed providing 13 mm and 25 mm (0.5 and 1 in)

spacing between wire mesh screens.

As the wire mesh pore size increases from 20 PPI to 10 PPI, air flow resistance through the wire

mesh decreases, which results in higher air penetration through the mesh and increase in

permeability as shown in Figure 7-5.The permeability and air flow resistance of the wire mesh

plays an important role in hydraulic characteristic of wire mesh heat exchanger.

125


in channels for 20 PPI and 10 PPI wire mesh screen.

0

100

200

300

400

500

600

700

800

900

1000

0 5 10 15 20 25

Pre

ssure

Dro

p , Δ

P (

Pa)

Velocity, V (m/s)

20 PPI - 0.5" Space

20 PPI - 1" Space

10 PPI - 0.5" Space

10 PPI - 1" Space

126


The performance of the fabricated stainless steel heat exchangers was investigated for three different

water flow rates in the range of 0.5 – 0.9 L/min and an air temperature of 320 ± 20°C. Fabricated wire

mesh heat exchangers outperformed the bare tube heat exchanger, as seen in Figure 7-6, which

demonstrates the effectiveness of the wire mesh as a heat transfer enhancer.

(a)

2

4

6

8

10

12

14

0.4 0.5 0.6 0.7 0.8 0.9 1

Tem

per

ature

Ris

e, (℃

)

Water Volume Flow Rate, (L/min)

plain tube

5 PPI

10 PPI

20 PPI

127

(b)

Figure 7-6: Temperature rise of water flowing through the tubes (a) heat exchangers with one wire

mesh screen, and (b) heat exchangers with two wire mesh screens.

As seen in Figure 7-6a, single screen wire mesh heat exchangers resulted in an 84% higher

temperature rise compared to the plain tube heat exchanger. When comparing the performance of the

2 screen wire mesh heat exchanger. 2 screen 10 PPI wire mesh outperformed the other heat

exchangers (Figure 7-6b). For both 10 PPI and 5 PPI heat exchangers, having two wire mesh screens

was better than one. Air penetrated more easily through the 5 and 10 PPI than the 20 PPI wire mesh,

since the pore sizes were much larger. High pore density wire mesh caused extra resistance to air

flow, which reduced forced convection heat transfer. For the case where a heat exchanger was built

using two screen wire mesh (Figure 7-2b) the heat transfer performance increased by 130 %, 105 %,

and 76 % for 10, 5 and 20 PPI wire mesh respectively, compared to the plain tube heat exchanger.

2

4

6

8

10

12

14

0.4 0.5 0.6 0.7 0.8 0.9 1

Tem

per

atu

reR

ise,

(℃

)

Water Volume Flow Rate, (L/min)

plain tube

2 sheets 20 PPI

2 sheets 10 PPI

2 sheets 5 PPI

128

Heat transfer was always enhanced since the extended wires were used to increase the overall surface

area, and also increase the convective heat transfer.

To better understand this variation in surface temperature, the average air temperature before the

heat exchanger is shown in Figure 7-7. The average air temperature was measured by positioning

sixteen K-type thermocouples with junction diameters of 0.6 mm in the air stream before the heat

exchanger and averaging their temperatures at steady state. The air temperature increased as the

pore density of the mesh increased from 5 PPI to 20 PPI. Double screen heat exchangers resulted

in a higher temperature rise compared to the plain tube and single screen wire mesh heat

exchangers, as shown in Figure 7-6.

The air accumulates behind the heat exchangers because of the pressure drop due to the porous

geometry of the wire mesh. The pressure drop test across wire mesh in the wind tunnel experiment

further proved the variation in air penetration through these structures. In the case where heat

exchangers were fabricated using only one wire mesh screen on average, the wire mesh surface

temperatures were 300°C, 312°C and 327°C for 5, 10 and 20 PPI wire mesh, respectively.

129

Figure 7-7: Variation of average air temperature at section 3 for different PPI wire mesh heat

exchangers.

5 PPI,

1 Screen

10 PPI,

1 Screen

20 PPI,

1 Screen

5 PPI,

2 Screen

10 PPI,

2 Screen

20 PPI,

2 Screen

Plain

Tube

260

270

280

290

300

310

320

330

340

Air

Tem

per

ature

, (̊C

)

130


7.6.1 Non-Dimensional Parameters

The following experiments were conducted by measuring the temperature rise of the water

between the inlet and outlet of the heat exchanger for three different water flow rates, from 500 to

900 mL/min. In these experiments water cooled heat exchangers were placed inside a high

temperature chamber with an air temperature of 320 ± 20°C and average air velocity of 1 m/s.

The water and air inlet and outlet temperatures were measured by placing thermocouples at the

corresponding inlet and outlet. The heat transfer rate of water as calculated using

�̇� = �̇� 𝑤 𝐶𝑝.𝑤 ∆ 𝑇𝑤 (7-1)

where 𝐶𝑝 is specific heat, �̇� is mass flow rate and subscript w stands for water flow loop. The

overall heat transfer coefficient U and log mean temperature ∆𝑇𝐿𝑀𝑇𝐷 were calculated using the

equations below

�̇� = 𝑈𝐴𝑡 ∆𝑇𝐿𝑀𝑇𝐷 (7-2)

∆𝑇𝐿𝑀𝑇𝐷 = ∆𝑇1 − ∆𝑇2

𝑙𝑛 (∆𝑇1 − ∆𝑇2) (7-3)

where 𝐴𝑡 is the tube outer surface area and ∆𝑇1 and ∆𝑇2 represent the temperature difference

between two fluids at the two ends (inlet and outlet) of a heat exchanger. The heat transfer

coefficient of air, ℎ𝑎, is found using the equation:

131

1

𝑈𝐴𝑡=

1

ℎ𝑤𝐴1+ 𝑙𝑛 (

𝐷2𝐷1)

2 𝑘𝑡𝐿𝑡+

1

ℎ𝑎𝐴2 (7-4)

where 𝐷1 and 𝐴1 was the inner tube’s diameter and area and 𝐷2 and 𝐴2 was the outer tube’s

diameter and area, 𝐿𝑡 is the length of the tube and 𝑘𝑡 is the thermal conductivity of the stainless

steel tube.

Figure 7-8: Variation of the Overall heat transfer coefficient across different pore densities.

To study the heat transfer coefficient, a graph is plotted with wire mesh PPI on the X axis and

overall heat transfer coefficient on the Y axis (Figure 7-8). For the case of 5 and 10 PPI wire mesh,

double screen heat exchangers outperformed single screen heat exchangers. This relation turns

reverse in 20 PPI heat exchanger, where single screen outperformed double screen wire mesh heat

exchanger.

5 PPI,

1 Screen

5 PPI,

2 Screen10 PPI,

1 Screen

10 PPI,

2 Screen

20 PPI,

1 Screen

20 PPI,

2 Screen

60

70

80

90

100

110

120

Over

all

Hea

t T

ransf

er C

oef

fici

ent,

U

(W/m

2K

)

132

The heat transfer coefficient between the water and the inner surface of the tube can be calculated

using standard correlations. The value of 𝑁𝑢𝑤 has a constant value of 4.36 for fully developed

flow since the flow inside the tube is laminar 𝑅𝑒𝑤< 2300 [45]. Reynolds and Prandtl number for

water flow in the tube can be calculated using the equations,

𝑅𝑒𝑤 = 𝑉𝑤𝐷1 𝜈𝑤

(7-5)

𝑁𝑢𝑤 = ℎ𝑤𝐷1 𝑘𝑤

(7-6)

𝑃𝑟𝑤 = 𝜇𝑤 𝐶𝑝.𝑤

𝑘𝑤 (7-7)

where 𝑉𝑤 is the velocity of water in the tube, 𝜇𝑤 the dynamic viscosity, 𝐶𝑝.𝑤 the specific heat,

𝜈𝑤 the kinematic viscosity and 𝑘𝑤 the thermal conductivity of water.

After calculating the heat transfer coefficient ha using the Equation (7-4), the Nusselt number on

the outer surface of the tube was calculated using

𝑁𝑢𝑎 =

ℎ𝑎 𝐷2𝑘𝑎

(7-8)

where 𝑘𝑎 is the thermal conductivity of air.

Figure 7-9 shows the Nusselt number (𝑁𝑢𝑎,𝐷) variation with mesh size for a constant water mass

flow rate of 0.015 Kg/s. The Nusselt numbers for both single mesh heat exchangers (1 Screen)

and double mesh heat exchangers (2 Screen) were plotted. The single mesh heat exchangers all

had similar values of Nusselt number (𝑁𝑢𝑎,𝐷), approximately 12, indicating that the flow fields

133

were similar in all cases and not strongly affected by the mesh. It is apparent that the 10 PPI double

mesh heat exchanger has the highest Nusselt number (𝑁𝑢𝑎,𝐷) followed by the 5 PPI double mesh.

The 20 PPI double mesh heat exchanger has the lowest Nusselt number (𝑁𝑢𝑎,𝐷). Increasing the

mesh surface area promotes heat transfer, but after a certain point blocking of the air flow leads to

a decrease in heat transfer.

Figure 7-9: Nusselt number variation (Nua,D) across different pore densities at a constant water

mass flow rate of 0.015 Kg/s.

Calculated results were also compared to Nusselt number (NuH) variation with the change of

Reynolds number (ReH) relations for stack wire mesh screens, H is the channel height, found in

the literature as shown in Figure 7-10. Calculated heat transfer coefficients were generally greater

than valued reported by Li et al. [42] and Venugopal, Balaji and Venkateshan [43]. This can be

5 PPI,

1 Screen

10 PPI,

1 Screen 20 PPI,

1 Screen

5 PPI,

2 Screen

10 PPI,

2 Screen

20 PPI,

2 Screen

10

11

12

13

14

15

16

17

Nu

a,D

134

explained by the fact that in this study thermal sprayed heat exchangers were used to reduce

interfacial thermal resistance.


1

10

100

1000

1 10 100 1000 10000

Nuss

elt

Num

ber

, N

uH


10 PPI, 2 Screen

5 PPI, 2 Screen

10 PPI, 1 Screen

5 PPI, 1 Screen

20 PPI, 1 Screen

20 PPI, 2 Screen





135

7.6.2 Empirical Fin Model Correlation

To observe the effect of the wire mesh on heat transfer, infrared (IR) images of the heat exchangers

were captured and analyzed. Figure 7-11 shows sample IR images for 5, 10, and 20 PPI wire mesh

heat exchangers inside the hot air chamber. The infrared images demonstrate the effectiveness of

the wire mesh fin, and also the flaws in the tube-mesh connection. The IR results demonstrated

that the worst connection exists for 20 PPI wire mesh, since the thermally sprayed particles could

not effectively penetrate through the pores. As the pore size increases from 20 PPI to 5 PPI, the

quality of the connection between the wire mesh and the tube increased since the particles could

penetrate through the pores and connect the mesh to the tube.

136

90 ⁰C 200 ⁰C 250 ⁰C 290 ⁰C 315 ⁰C

(a)

(b)

(c)

Figure 7-11: IR camera surface temperature variation across heat exchangers for (a) 5 PPI, (b) 10

PPI and, (c) 20 PPI.

137

Heat transfer to the tube is limited by to the thermal contact resistance between the wire mesh and

the tube. The analysis begins with comparing the effectiveness of the wire mesh with a long fin

and then finding contribution of the transverse wires as illustrated in Figure 7-12.

Figure 7-12: Schematic of eleven transverse and one longitudinal wire between two tubes.

The variation of temperature along the long fin with a constant cross section (Ac = constant) can

be model using the following equation

𝑇fin tip = 𝑇∞

𝑇(𝑥) = 𝑇∞ + (𝑇𝑏 − 𝑇∞)𝑒√ℎ𝑝𝐾𝐴𝑐

−𝑥

(7-9)

X

Y

138

where 𝐴𝑐 is the cross-sectional area of the fin at location x, 𝑝 is the perimeter of a fin, ℎ is the

convection heat transfer coefficient, 𝑘𝑓 is thermal conductivity of the fin, 𝑇∞ is the temperature of

the surrounding and 𝑇𝑏 is a fin base temperature.

IR camera images of 5 PPI wire mesh (Figure 7-11a) were post processed and the experimental

wire mesh and tube surface temperatures were measured. 5 PPI wire mesh was chosen since it was

easier to analyze due to the thickness of its wires. To find the contribution of transverse wires to

the overall heat transfer enhancement due to wire mesh screens, the surface temperature along a

single longitudinal wire and eleven transverse wires perpendicular to it were analyzed. Eleven

temperature probes were used to map the temperature distribution of the transverse wires and one

to map the temperature of the longitudinal wire (Figure 7-12). The temperature variation along the

longitudinal wire, located on the x-axis of schematic Figure 7-12, is plotted in Figure 7-13. The

transverse wires were located perpendicular to the longitudinal wires, with a fixed x coordinate as

shown in Figure 7-12. The y axis in Figure 7-12 was used to map the temperature distribution

along the transverse wires (Figure 7-14).

As can be seen from Figure 7-13, the temperature of the longitudinal wire increases slowly from

where the wire is connected to one tube, until it reaches its maximum half way between the cold

tubes. The temperature of the longitudinal wire eventually reached the temperature of the ambient

temperature. It was found that the transverse wires were conducting heat towards the longitudinal

wire, since the temperature of the longitudinal wire was lower at the point of overlap with the

transverse wires, Figure 7-13.

139

Figure 7-13: Wire surface temperature variation along the length of one longitudinal and eleven

transverse wires, measured experimentally using IR camera, for the 5 PPI wire mesh heat

exchanger. The x and y axis are shown Figure 7-12.

The y axis in Figure 7-12 is used to map the temperature distribution along the longitudinal and

six transverse wires (T1, T2, T3, T4, T5, and T6), which is plotted in Figure 7-14. The temperature

distribution along the longitudinal wire is shown as a vertical line in Figure 7-14.

120

140

160

180

200

220

240

260

280

300

110 130 150 170 190 210

Surf

ace

Tem

per

ature

, (̊C

)

Location Along x Axis, (mm)

Longitudinal Wire

T1

T2

T3

T4

T5

T6

T7

T8

T9

T10

T11

140

Figure 7-14: Wire surface temperature variation along the length of a longitudinal and six

transverse wires (T1, T2, T3, T4, T5, and T6 as shown in Figure 7-12) for the 5 PPI wire mesh

heat exchanger. Temperatures were measured experimentally using IR camera.

Figure 7-14 demonstrates the conductive heat transfer from transverse wires (T1, T2, T3, T4, T5,

and T6 as shown in Figure 7-12) to the longitudinal fin. The temperature of the transverse wires

were higher at their point of contact with the longitudinal wire. Since the presence of transverse

wires results in a higher heat transfer rate, the conventional straight fin model will not predict the

heat transfer from the wire mesh heat exchangers accurately.

110

130

150

170

190

210

230

250

270

290

310

323 324 325 326 327 328 329 330 331

Surf

ace

Tem

per

atu

re,

(̊C)

Location Along y Axis, (mm)

Longitudinal wireT6T5T4T3T2T1

141

Wire mesh screens as shown in Figure 7-15 were similar to longitudinal fin structures but the

temperature distribution will differ due to the presence of transverse wires perpendicular to the

longitudinal. The effect of transverse wires on the heat transfer was investigated in this study by

analyzing the surface temperature distribution of the wire mesh screen.

Figure 7-15: Location of longitudinal and transverse wires of wire mesh screens.

If l is the length of a pore and d is a fin diameter then the longitudinal surface temperature

variation of the first pore can be expressed as

𝑠 = {

𝑥

2 𝑙 + 𝑙 + 𝑑

𝑑(𝑥 − 𝑙)

0 ≤ 𝑥 < 𝑙 − 𝑑

𝑙 − 𝑑 ≤ 𝑥 < 𝑙 (7-10)

𝑻(𝒙) = 𝑻∞ + (𝑻𝒃 − 𝑻∞)𝒆−𝒎𝒔 (7-11)

142

𝒎 = √𝒉𝒑

𝑲𝑨𝒄

where s is the actual length of the wire as a function of x, and x is the location on the longitudinal

wire.

Substituting Equation (7-10) into Equation (7-11) results in the temperature variation for the

longitudinal wire for the first pore

𝑇(𝑥) = {𝑇∞ + (𝑇𝑏 − 𝑇∞)𝑒

−𝑚𝑥

𝑇∞ + (𝑇𝑏 − 𝑇∞)𝑒−𝑚 [2 𝑙+

𝑙+𝑑𝑑(𝑥−𝑙)]

0 ≤ 𝑥 < 𝑙 − 𝑑

𝑙 − 𝑑 ≤ 𝑥 < 𝑙

(7-12)

The temperature distribution of the second pore can also be analyzed by

𝑇(𝑥) = 𝑇∞ + (𝑇𝑏 − 𝑇∞)𝑒−𝑚𝑠 (𝑥)

(7-13)

𝑠 = {2𝑙 + (𝑥 − 𝑙)

4 𝑙 + 𝑙 + 𝑑

𝑑(𝑥 − 2𝑙)

𝑙 ≤ 𝑥 < 2𝑙 − 𝑑

2𝑙 − 𝑑 ≤ 𝑥 < 2𝑙

The temperature distribution along the nth pore can be calculated using

𝑇(𝑥) = 𝑇∞ + (𝑇𝑏 − 𝑇∞)𝑒−𝑚𝑠 (𝑥)

(7-14)

𝑠 = {

(𝑛 − 1)𝑙 + 𝑥

𝑛 𝑙 + 𝑙 + 𝑑

𝑑(𝑥 − 𝑛𝑙)

(𝑛 − 1)𝑙 ≤ 𝑥 < 𝑛 𝑙 − 𝑑

𝑛𝑙 − 𝑑 ≤ 𝑥 < 𝑛 𝑙

Surface measurements conducted using IR camera were used to validate Equation (7-14) as

shown in Figure 7-16. Appendix A shows the Matlab code for the empirical fin model.

143

Figure 7-16: Comparison between the measured surface temperature using IR camera and

predicted empirical model.

100

150

200

250

300

0 5 10 15 20 25

Tem

per

ature

, (°

C)

Length, X (mm)

Empirical Fin Model

Experimental Result

144

7.6.3 A Model for Prediction of Heat Exchanger Temperature Rise

The objective of this section was to obtain a model for predicting the performance of the tested

heat exchangers for various inlet flow rates and surface area. In order to predict the outlet

temperature of the heat exchangers the known inlet and outlet temperatures of the tested heat

exchangers were used as a base line. Next a non-dimensional number was extracted which was

used for obtaining (estimating) the unknown outlet temperature of the same heat exchanger with a

different flow rate.

Figure 7-17: Heat transfer energy balance for the fabricated heat exchangers.

Figure 7-17 shows the energy balance, Equation (7-15), for a small section of a heat exchanger.

From the conservation of energy

�̇�𝐶𝑝𝑇𝑥 − �̇�𝐶𝑝(𝑇𝑥 + 𝜕𝑇

𝜕𝑥𝑑𝑥) = ℎ 𝑑𝐴 (𝑇𝑠 − 𝑇∞) (7-15)

If 𝑇𝑠 = 𝑇𝑓𝑙𝑢𝑖𝑑,𝑖𝑛𝑠𝑖𝑑𝑒 = 𝑇, then

145

−�̇�𝐶𝑝𝜕𝑇

𝜕𝑥𝑑𝑥 = 𝑈 𝑃 𝑑𝑥 ( 𝑇 − 𝑇∞),𝑤ℎ𝑒𝑟𝑒 𝑑𝐴 = 𝑃 𝑑𝑥

𝜕𝑇

𝜕𝑥+ (

𝑈 𝑃

�̇�𝐶𝑝) 𝑇 = 𝑇∞

𝑈 𝑃

�̇�𝐶𝑝

(7-16)

If the form of 𝑇(𝑥) = 𝑘𝑒−𝑡𝑥 + 𝐶, then by substituting in to (7-16) the differential equation

−𝑡 𝑘𝑒−𝑡𝑥 + 𝑈 𝑃

�̇�𝐶𝑝 (𝑘𝑒−𝑡𝑥 + 𝐶) =

𝑈 𝑃

�̇�𝐶𝑝𝑇∞ (7-17)

𝑒−𝑡𝑥 (𝑘 𝑈 𝑃

�̇�𝐶𝑝− 𝑡𝑘) +

𝑈 𝑃

�̇�𝐶𝑝𝐶 = 𝑇∞

𝑈 𝑃

�̇�𝐶𝑝

Therefore

𝐶 = 𝑇∞ , 𝑎𝑛𝑑 𝑡 =𝑈 𝑃

�̇�𝐶𝑝

𝑇(𝑥) = 𝑘𝑒−𝑈 𝑃�̇�𝐶𝑝

𝑥+ 𝑇∞ (7-18)

Since 𝑃 = 𝐴𝑠𝑢𝑟𝑓

𝐿, where 𝐴𝑠𝑢𝑟𝑓 is the overall area of the mesh and the tube and 𝐿 is the length of

the tube (4 x178 mm (7 in)), then we can introduce a number of transfer units (𝑁𝑇𝑈∗) based on

water side of the heat exchanger

𝑁𝑇𝑈∗ =𝑈 𝐴𝑠𝑢𝑟𝑓

�̇�𝐶𝑝 (7-19)

Substituting Equation (7-19) into Equation (7-18)

𝑇(𝑥) = 𝑘𝑒−𝑁𝑇𝑈∗ 𝑥𝐿 + 𝑇∞ (7-20)

146

By applying the boundary conditions at x = 0 and x = L we get

𝑇𝑖𝑛 = 𝑘𝑒−𝑁𝑇𝑈∗ (0𝐿) + 𝑇∞

Therefore

𝑘 = 𝑇𝑖𝑛 − 𝑇∞

(7-21)

Also 𝑇𝑜𝑢𝑡 = (𝑇𝑖𝑛 − 𝑇∞) 𝑒−𝑁𝑇𝑈∗ (

𝐿

𝐿) + 𝑇∞ (7-22)

Therefore

𝑁𝑇𝑈∗ = 𝑙𝑛(𝑇𝑖𝑛 − 𝑇∞)

(𝑇𝑜𝑢𝑡 − 𝑇∞) (7-23)

Depending on the known variables, 𝑁𝑇𝑈∗ can be used for calculating (predicting) the outlet

temperature of the heat exchanger (𝑇𝑜𝑢𝑡), as shown in Table 7-2, or if 𝑇𝑜𝑢𝑡 is known, equation

(7-23) can be used to calculate 𝑁𝑇𝑈∗.

By comparing 𝑁𝑇𝑈∗ with the well know definition of 𝑁𝑇𝑈

𝑁𝑇𝑈 =𝑈 𝐴

�̇�𝐶𝑝 (7-24)

Which can be simplified to

𝑁𝑇𝑈 =𝑈 𝐴

�̇�𝐶𝑝 (𝑇𝑖𝑛 − 𝑇𝑜𝑢𝑡)

(𝑇𝑖𝑛 − 𝑇𝑜𝑢𝑡) 𝛥𝑇𝐿𝑀𝛥𝑇𝐿𝑀

Since 𝑈 𝐴 𝛥𝑇𝐿𝑀 = 𝑚 ̇ 𝐶𝑝 (𝑇𝑖𝑛 − 𝑇∞)

(7-25)

147

𝑁𝑇𝑈 =(𝑇𝑖𝑛 − 𝑇𝑜𝑢𝑡)

𝛥𝑇𝐿𝑀𝑇𝐷 (7-26)

𝑁𝑇𝑈 =(𝑇𝑖𝑛 − 𝑇𝑜𝑢𝑡)

(𝑇𝑖𝑛 − 𝑇𝑜𝑢𝑡)

𝑙𝑛(𝑇𝑖𝑛 − 𝑇∞)(𝑇𝑜𝑢𝑡 − 𝑇∞)

= 𝑙𝑛

(𝑇𝑖𝑛 − 𝑇∞)

(𝑇𝑜𝑢𝑡 − 𝑇∞) (7-27)

The equation (7-23) and equation (7-23) were identical therefore it was concluded that 𝑁𝑇𝑈∗ =

𝑁𝑇𝑈.

Table 7-2: Parameters of the wire mesh heat exchangers at a water mass flow rate of 0.015 Kg/s.

Sam

ple

s

Pore

Den

sity

(P

PI)

Nu

mb

er o

f S

cree

ns

𝑻𝒊𝒏

(°C)

𝑻𝒐𝒖𝒕

(°C)

𝑻∞

(°C)

𝑵𝑻𝑼∗

Eq.(7-23)

𝑻𝒐𝒖𝒕

Eq.(7-22)

Heat

Ex 1 N/A 0 19.1 22.1 265 0.0123 𝑇𝑜𝑢𝑡 = (𝑇𝑖𝑛 − 𝑇∞) 𝑒

−0.0123 + 𝑇∞

Heat

Ex 2 5 1 19.0 24.3 299 0.0191 𝑇𝑜𝑢𝑡 = (𝑇𝑖𝑛 − 𝑇∞) 𝑒

−0.0191 + 𝑇∞

Heat

Ex 3 10 1 20.0 27.4 305 0.0263 𝑇𝑜𝑢𝑡 = (𝑇𝑖𝑛 − 𝑇∞) 𝑒

−0.0263 + 𝑇∞

Heat

Ex 4 20 1 19.7 25.3 319 0.0189 𝑇𝑜𝑢𝑡 = (𝑇𝑖𝑛 − 𝑇∞) 𝑒

−0.0189 + 𝑇∞

Heat

Ex 5 5 2 20.7 26.9 320 0.0209 𝑇𝑜𝑢𝑡 = (𝑇𝑖𝑛 − 𝑇∞) 𝑒

−0.0209 + 𝑇∞

Heat

Ex 6 10 2 23.1 30.2 322 0.0240 𝑇𝑜𝑢𝑡 = (𝑇𝑖𝑛 − 𝑇∞) 𝑒

−0.0240 + 𝑇∞

Heat

Ex 7 20 2 21.8 27.1 328 0.0175 𝑇𝑜𝑢𝑡 = (𝑇𝑖𝑛 − 𝑇∞) 𝑒

−0.0175 + 𝑇∞

148

For a cases with different flow rates (�̇�) a new 𝑁𝑇𝑈∗ can be estimated using

𝑁𝑇𝑈∗𝑛𝑒𝑤 = 𝑁𝑇𝑈∗𝑜𝑙𝑑 (

�̇�𝑜𝑙𝑑

�̇�𝑛𝑒𝑤) (7-28)

Table 7-3 compares the experimentally calculated non-dimensionalize number 𝑁𝑇𝑈∗, calculated

using Equation (7-23) for a water mass flow rate of 0.0117 Kg/s to the predicated non-

dimensionalize number 𝑁𝑇𝑈∗𝑛𝑒𝑤 calculated using Equation (7-28). The calculate non-

dimensionalize numbers 𝑁𝑇𝑈∗ were in a good agreement with the predicted non- dimensionalized

number 𝑁𝑇𝑈∗𝑛𝑒𝑤.

Table 7-3: Parameters of the wire mesh heat exchangers at a water mass flow rate of 0.0117

Kg/s.

Sam

ple

s

Pore

Den

sity

(P

PI)

Nu

mb

er o

f S

cree

ns

𝑻𝒊𝒏

(°C)

𝑻𝒐𝒖𝒕

(°C)

𝑻∞,

(°C)

𝑵𝑻𝑼∗

Eq. (7-23)

𝑵𝑻𝑼∗𝒐𝒍𝒅

Table 7-2

𝑵𝑻𝑼∗𝒏𝒆𝒘

Eq.(7-28)

Heat Ex 1 N/A 0 19.0 22.9 265 0.0156 0.0123 0.0157

Heat Ex 2 5 1 19.1 26.0 299 0.0250 0.0191 0.0245

Heat Ex 3 10 1 21.0 28.4 305 0.0264 0.0263 0.0337

Heat Ex 4 20 1 19.6 26.8 319 0.0243 0.0189 0.0242

Heat Ex 5 5 2 20 28.0 320 0.0270 0.0209 0.0268

Heat Ex 6 10 2 22.9 31.8 322 0.0302 0.0240 0.0308

Heat Ex 7 20 2 21.7 28.0 328 0.0208 0.0175 0.0224

149

We can also estimate an outlet temperature (𝑇𝑜𝑢𝑡) of a larger heat exchanger using the calculated

𝑁𝑇𝑈∗ from this chapter while considering the change of surface area as well.

𝑁𝑇𝑈∗𝑛𝑒𝑤 = 𝑁𝑇𝑈∗𝑜𝑙𝑑 (�̇�𝑜𝑙𝑑

�̇�𝑛𝑒𝑤) (𝐴𝑛𝑒𝑤𝐴𝑜𝑙𝑑

) (7-29)

Figure 7-18: Schematic of 3 heat exchangers connected in series.

If multiple heat exchangers with known 𝑁𝑇𝑈∗ were connected in series (Figure 7-18), the exit

temperature from each heat exchanger could be estimated as follow

𝑇𝑜𝑢𝑡,1 = (𝑇𝑖𝑛,1 − 𝑇∞) 𝑒−𝑁𝑇𝑈∗ + 𝑇∞

𝑇𝑜𝑢𝑡,2 = (𝑇𝑜𝑢𝑡,1 − 𝑇∞)𝑒−𝑁𝑇𝑈∗ + 𝑇∞

𝑇𝑜𝑢𝑡,3 = (𝑇𝑜𝑢𝑡,2 − 𝑇∞) 𝑒−𝑁𝑇𝑈∗ + 𝑇∞

(7-30)

150

Extended surface area ratio was defined as

𝑅𝐴 =𝐴𝑠𝑢𝑟𝑓

𝐴𝑡𝑢𝑏𝑒

(7-31)

Figure 7-19 shows the variation of NTU with different extended surface ratios. All of the cases

were compared against the bare tube heat exchanger. The highest NTU was achieved for the 10

PPI single screen heat exchanger. In other words, while single screen of 10 PPI wire mesh didn't

have the highest surface area for heat transfer but it was the most effective one by yielding the

highest NTU. It can also be noticed that the double screen 5 PPI HEX outperformed the single

screen. It is different from the pattern we observed for 10 and 20 PPI. The reason can be explained

by the fact that 5 PPI screen has larger cells and air was able to sufficiently flow over the second

screen. As a result the second layer of 5 PPI screen actually contributed to the heat transfer rather

than creating air blockage.

Figure 7-19: Extended surface area ratio (RA) variation as a function of NTU.

0

2

4

6

8

10

12

14

16

0.01 0.015 0.02 0.025 0.03

RA

NTU

10 PPI, 2 Screen

10 PPI, 1 Screen

5 PPI, 2 Screen

5 PPI, 1 Screen

20 PPI, 1 Screen

20 PPI, 2 Screen

Plain Tube

151

7.7 Conclusion

Stainless steel heat exchangers were fabricated by connecting stainless steel wire mesh screens to

stainless steel tubes using wire-arc thermal spray coating. The optimum spraying distance of 152 mm

was used to achieve a porosity of 2 %, oxide content of 6.6 %, and adhesion strength of 24 MPa for

the deposited stainless steel. Results indicated superior penetration of the coating material into the

gaps between wire mesh and tube’s outer surface, which provided strong adhesion and thermal

conduction in 10 and 5 PPI wires mesh. Fabricated heat exchangers were tested inside a hot air

chamber and heat transfer performance were also analyzed. The extended surface area of the wire

mesh enhanced the heat transfer from the hot air to the cooling water running inside the heat

exchanger. All fabricated heat exchangers resulted in a higher temperature rise than the plain tube,

with the maximum of 130 % for 2 screens, 10 PPI wire mesh, compared to the plain tube heat

exchanger. It was found that the performance of wire mesh heat exchangers depended on the pore

density of the mesh which effects the air penetration through the heat exchanger. If the pore density

was high (20 PPI), then adding the second screen to the heat exchanger resulted in the reduction

of the overall performance the heat exchanger.

Based on the surface temperature analysis of the wire mesh, it was concluded that fins cannot be

simply modeled as a plain longitudinal fin, since the heat was also being conducted from the

transverse wires which were perpendicular to the longitudinal wire. An empirical model was

developed to predict the temperature variation of the wire mesh screens. Another model was also

developed for predicting the performance of the tested heat exchangers for various inlet flow rates

and surface area.

152

Air-To-Air Wire Mesh Heat exchangers

8.1 Introduction

Gas flares are used to eliminate waste gases such as methane, which are not feasible to use or

transport. In theory, the heat of combustion can be recovered from the combustion gases using

heat exchangers for different commercial or industrial processes. By positioning a heat exchanger

(HEX) on top of the hot gas stack, as shown on Figure 8-1, the heat of combustion can be captured.

Figure 8-1: Full assembly of a heat exchanger on top of the gas flare.

153

It is difficult to manufacture heat exchangers that can withstand high combustion temperatures and

have a high enough efficiency to make them commercially viable. Waste gases exit flares at

temperatures of over 1000ºC, which exceeds the operation range of most high thermal conductivity

materials such as copper and aluminum that are typically used to fabricate heat exchangers. New,

high efficiency heat exchanger design can compensate for the low thermal conductivity of

materials, such as stainless steel and Inconel that can withstand high temperatures.

In the previous chapters, I analyzed the efficiency and effectiveness of the thermally sprayed wire

mesh porous heat exchangers on a small scale. In this study a large scale wire mesh heat exchanger

was built and compared to a plain tube heat exchanger.

154

8.2 Heat Exchanger Design

The proposed design is a modular heat exchanger which can be easily modified for different

operating conditions. The heat exchanger consists of four sections which were fabricated

separately and connected together using bolts, as seen in Figure 8-2. Wire mesh is placed only on

the top and the bottom of the tubes on the first and the third section. To analyze the performance

of the wire mesh heat exchanger (first and third section) to the plain tube heat exchanger, the

second and forth sections were built without adding wire mesh screen on the tubes. The heat

exchanger assembly was originally designed to fit onto a gas flare incinerator by simply aligning

the support section of the design to the existing flange of the incinerator. Appendix B shows a

schematic of the heat exchanger on an incinerator.

155

Figure 8-2: Assembly process for the heat exchanger.

156

8.3 Manufacturing of the Heat Exchanger

The heat exchanger has four sections that were manufactured seperately, and bolted together. Two

of the sections consists of only stainless steel tubes, and the other two has 2 sheets of 5 PPI wire

mesh attached to the tubes. Each section of the heat exchanger was 2 in (50.8 mm) high, and there

were a total of 5 tubes in each section. The tubes have an outer diameter of 1 in (25.4 mm), an

inner diameter of 0.87 in (22.1 mm), and were spaced 3.5 in (88.9 mm) apart (Figure 8-3). The

wire mesh used in the heat exchanger was of 5 PPI, and the overall size of the wire mesh was 17

in (431.8 mm) by 17 in (431.8 mm). The overall surface area of the tube, for each section, inside

the 17 in x 17 in channel, was 172280 mm2. The surface area for sections with wire mesh was

furthur enhanced by 553468 mm2 due to the presence of 2 sheets of 5 PPI wire mesh.

Figure 8-3: Fabricated bare tube section of the main heat exchanger.

157

Figure 8-4: Fabricated section of the main heat exchanger, with one wire mesh screen attached

on front and back side of the tubes.

Before a thermal sprayed skin was applied, both the tube and the wire mesh were sand blasted

before and after they were fastened together. The spray coating for the heat exchanger was done

at the CACT lab as shown in Figure 8-5 where the twin wire-arc spraying gun is visible. Figure

8-5 shows the heat exchanger after the spraying process in which wires were fully connected to

the tube’s surface along the length of the tube. A dense layer of stainless steel coating was sprayed

on the point of contact between the mesh and the tube using wire-arc thermal spraying gun, as

shown Figure 8-6. The quality and the mechanical bonding of the connection between the wire

mesh and the tube could have been furthered improved if the wire mesh was more flexible. A

flexible wire mesh that could further bend around the tube would enhance the mechanical

connection between them (Figure 8-7).

158

Figure 8-5: Wire mesh section after thermal skin deposition of stainless steel using wire-arc.

Figure 8-6: Thermal sprayed surface of the wire mesh and the tube.

159

Figure 8-7: Mechanical bonding of 4 PPI wire mesh to the stainless steel tube [6].

The stacked heat exchanger consisted of two separate water distributing tubes that supply water to

the heat exchanger units, as shown in Figure 8-8. Inlet and outlet manifolds were provided

seperately for bare tube and wire mesh sections of the heat exchanger. Appendix C shows the step-

by-step fabrication process of the heat exchanger..

Figure 8-8: Front view of the fabricated heat exchanger before welding the manifolds.

160

Figure 8-9: Back view of the fabricated heat exchanger after the final assembly.

The wire mesh heat exchanger units (section 1 & 3) shared the same inlet and outlet manifold.

161

8.4 Experimental Apparatus

The experimental apparatus consisted of a compressed air supply, an electrical heater, a heat

exchanger unit and a wind tunnel. The hot air flowed inside the tubes of the heat exchanger unit,

while cold air flowed over them and through the porous structures. A schematic representation of

the experimental setup is shown in Figure 8-10. An air electrical heater supplied hot air that passed

through the heat exchanger. The compressor fed the air to the mass flow meter (Model FMAA844A,

Omega Company, Stamford, CT) which was then supplied to the electrical heater (F076029,

SKORPION™ AIR HEATERS, OSRAM SYLVANIA, Exeter, NH). The hot air from the

electrical heater then entered the inlet of the heat exchanger unit, which was placed inside the wind

tunnel. The wind tunnel provided constant air flow, with the use of direct drive centrifugal inline

fan (DSI-135ANE, Twin City Fan and Blower, Minneapolis, MN). Cold air was blown through an

18 in (457.2 mm) diameter duct (Blo-R-Vac flexible duct, McMASTER-CARR) and over heat

exchanger. To reduce the heat loss from the heat exchanger, it was insulated with two layers of

fiber glass insulation (Micro-Flex, John Manville Corporation, Denver, CO). The heat exchanger

was painted with a black paint to provide a uniform emissivity thought the heat exchanger.

Four K-type thermocouple probes measured the hot air temperature at the inlet (𝑇𝑖) and outlet (𝑇𝑜) of

the heat exchanger, as shown in Figure 8-10 . Twelve thermocouples were attached to the surface

of the heat exchanger to record the local surface temperature of the wire mesh and the tube surface

temperature. Eight thermocouples were used to measure the average cold air temperature

downstream of the heat exchanger, and two to read the cold air temperature upstream of the heat

exchanger. A National Instruments Data Acquisition (DAQ) unit was used to record the

thermocouple signals. The DAQ was connected directly to a computer which was equipped with

Lab VIEW Signal Express v.3.0 (National Instruments Corporation, Austin, TX). The velocity

162

flow field inside the wind tunnel was measured using a hot wire anemometer (Model HHF42,

Omega Company, Stamford, CT) with a range of 0 to 20 m/s and a resolution of 0.1 m/s. Appendix

D shows the location of the thermocouples on the surface of the heat exchanger.

Appendix E shows a schematic of the fan, the fan performance specification and the electrical

heater.

Figure 8-10: Schematic representation of the experimental setup.

163

8.5 Heat Transfer Calculation

The objective of this experiment was to investigate the effect of wire mesh in increasing heat

transfer compared to a bare tube heat exchanger. The comparison was made by measuring the

temperature drop of hot air along the heat exchanger. Three hot air flow rates of 250, 350 and 450

L/min and three different cold air velocities of 3.7, 4.7 and 5.4 m/s, as shown in Table 8-1, were

used. Experiments were done in which heat exchangers were placed inside a wind tunnel with

variable speed fan.

The rate of heat extracted from the hot air can be calculated from

�̇�𝑎 = �̇� 𝑎 𝐶𝑝.𝑎 ∆ 𝑇𝑎 (8-1)

where 𝐶𝑝 is specific heat, �̇� is mass flow rate and the subscripts a stands for hot air flow loop.

Table 8-1: Cold air velocities inside the wind tunnel.

Cold Flow Average Velocity (m/s) Volume flow rate (cfm)

1 5.4 1889

2 4.7 1656

3 3.7 1298

164


The results for a constant cold air flow rate of 5.4 m/s in the wind tunnel, and for a hot air flow rate

of 250 to 450 L/min are presented in Figure 8-11. The results illustrate the temperature drop of hot

air through the heat exchanger for various flow rates. The results indicate higher temperature drop

when using wire mesh, compared to bare tube heat exchangers. In all of these cases, temperature drop

was reduced when the flow rate was reduced.

Figure 8-11: Temperature drop for different hot air flow rates at a constant cold air velocity of

5.4 m/s.

185

190

195

200

205

210

215

220

225

230

200 250 300 350 400 450 500

Tem

per

ature

Dro

p, (°

C)

Hot Gas Flow Rate, (L/min)

Mesh

Tube

165

Using Equation (8-1), the heat transfer from the hot was calculated. The increase in heat transfer

by using wire mesh was then compared with a bare tube heat exchanger, as shown in Figure 8-12.

Figure 8-12: Heat transfer enchantment of the wire mesh sections compare to the plain tube.

The improvement in the heat transfer rate was in the range 5 to 15%. The maximum increase in

heat transfer was experienced for a hot air flow rate of 450 L/min. It could also be observed that

the improvement in the heat transfer was superior for the cold air with the low air velocity of 3.7

m/s than 5.4 m/s.

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

18.00

20.00

250 300 350 400 450

Per

centa

ge

Hea

t T

ransf

er I

ncr

ease

, (%

)

Hot Gas Flow Rate, (L/min)

5.4 m/s

4.7 m/s

3.7 m/s

166


The overall heat transfer coefficient U and log mean temperature ∆𝑇𝐿𝑀𝑇𝐷 were calculated using

equations below

�̇� = 𝑈𝐴𝑡 ∆𝑇𝐿𝑀𝑇𝐷 (8-2)

∆𝑇𝐿𝑀𝑇𝐷 = ∆𝑇1 − ∆𝑇2

𝑙𝑛 (∆𝑇1 − ∆𝑇2)

(8-3)

where 𝐴𝑡 is the tube outer surface area and ∆𝑇1 and ∆𝑇2 represent the temperature difference

between two fluids at the two ends (inlet and outlet) of a heat exchanger. The heat transfer

coefficient of air ℎ𝑜𝑢𝑡 is found using the equation:

1

𝑈𝐴𝑡=

1

ℎ𝑖𝑛𝐴1+ 𝑙𝑛 (

𝐷𝑜𝑢𝑡𝐷𝑖𝑛

)

2 𝑘𝑡𝐿𝑡+

1

ℎ𝑜𝑢𝑡𝐴𝑜𝑢𝑡 (8-4)

where 𝐷𝑖𝑛 and 𝐴𝑖𝑛 are the inner tube diameter and area while 𝐷𝑜𝑢𝑡 and 𝐴𝑜𝑢𝑡 are the outer tube

diameter and area, 𝐿𝑡 is the length of the tube and 𝑘𝑡 is the thermal conductivity of the stainless

steel tube.

Reynold and Nusselt number were calculated using the equation,

𝑅𝑒𝐷,𝑜𝑢𝑡 = 𝑉𝑜𝑢𝑡𝐷𝑜𝑢𝑡

𝜈 (8-5)

𝑁𝑢𝐷,𝑜𝑢𝑡 = ℎ𝑜𝑢𝑡𝐷𝑜𝑢𝑡

𝑘 (8-6)

where 𝑉𝑜𝑢𝑡 is the velocity of air, 𝜈 the kinematic viscosity, ℎ𝑜𝑢𝑡 is the heat transfer coefficient of

the cold air, and 𝑘 the thermal conductivity of air.

167

Experimental results were compared to Nusselt number (NuH) variation with the change of

Reynolds number (ReH) relations for stack wire mesh screens in the literature as shown in Figure

8-13. The calculated heat transfer coefficients were generally lower than valued reported by Li et

al. [42] and greater than values reported by Venugopal, Balaji and Venkateshan [43].


1

10

100

1000

10000

1 10 100 1000 10000 100000 1000000

Nuss

elt

Num

ber

, N

uH






5 PPI, 2 screen

168

8.8 Conclusion

Thermally sprayed air-to-air heat exchanger suitable for high temperature applications was

fabricated. Fabricated heat exchanger was tested inside a wind tunnel and its heat transfer

performance was analyzed. Wire mesh heat exchanger resulted in a higher temperature rise than the

plain tube. The improvement in the heat transfer rate was in the range 5 to 15%. The maximum

increase in heat transfer was experienced for a hot air flow rate of 450 L/min. It could also be

observed that the improvement in the heat transfer was superior for the cold air with the low air

velocity of 3.7 m/s than 5.4 m/s. The heat transfer enhancement due to addition of a wire mesh

was measured experimentally. Experimental results were compared to Nusselt number (NuH)

variation with the change of Reynolds number (ReH) relations for stack wire mesh screens in the

literature.

169

Summary

9.1 Laser Sintered Heat Exchangers

Laser sintering process was an effective manufacturing methods for fabricating heat exchangers

and the following objectives were achieved:

• Fabricated channels containing cubic and round-strut tetradecahedral cells with identical

strut diameters and one with thin-strut tetradecahedral cells using DMLS technology.

• Enhanced the bonding and the contact area between the porous structure and the surface of

the heat exchanger while controlling the uniformity of the porous structure.

• Experimentally investigated the impact of internal cell geometry on pressure drop,

conduction and forced convection heat transfer through DMLS heat exchangers.

• Designed a thin-strut tetradecahedral geometry, which maximized the heat transfer while

minimizing the weight and friction loss.

9.2 Wire Mesh Heat Exchangers

In the second part of the thesis wire mesh heat exchangers were fabricated using thermal spraying

process to bond wire mesh screens or perforated metal sheets to the outer surface of the tubes. The

following objectives were achieved in the second part of the thesis:

• Developed a simple method of increasing the heat transfer surface area by using a twin

wire-arc thermal spray system to generate a dense, high strength coating that bonds porous

structures to the body of the heat exchanger.

170

• Concluded that a porous structures with high open area allowed for superior penetration of

the coating material into the gap between the wire mesh and the tube surface, and thus providing

good adhesion and thermal conduction.

• Investigated the heat transfer enhancement for different pore density wire mesh and

perforated sheets sizes. The experimental results indicated that a right balance between pore

density and number of screens is crucial for maximizing the heat transfer performance of the

porous heat exchangers.

• Enhanced the heat transfer performance of plain tube heat exchangers using various pore

density wire mesh and perforated sheets. It was found that the performance of the heat exchangers

depended on the air penetration between the porous structures.

• An empirical model was developed to predict the temperature variation of the wire mesh

screens.

• Fabricated an industrial size wire mesh heat exchanger and compare its performance to a

conventional plain tube heat exchanger.

• To summarize, the values of heat transfer enhancement achieved by using wire mesh as

presented in chapters 6, 7 and 8, 𝑁𝑢𝐷 and 𝑅𝑒𝐷 based on tube diameter are shown in Figure 9-1.

By fitting a trend line of best fit to these data points a general empirical relation between 𝑁𝑢𝐷 and

𝑅𝑒𝐷 is found as follow

𝑁𝑢𝐷 = 0.1731𝑅𝑒𝐷0.4364 (9-1)

171

Figure 9-1: Nusselt number (NuD) variation as a function of Reynolds number (ReH).

0

0.5

1

1.5

2

2.5

3

1 1.5 2 2.5 3 3.5 4 4.5

Log N

uD

Log NuD

14 PPI Mesh (Ch.6)

0.18" Perforared (Ch.6)

5 PPI, 1 Screen (Ch.7)





172

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177

Appendices

Appendix A: Matlab Code for the Empirical Fin Model.

clc

clear

nx=101;

x=zeros(nx,1);

s=zeros(nx,1);

T=zeros(nx,1);

Texp2=[125

128

139

150

157

173

198

215

225

231

233

236

249

262

269

272

277

282

284

285

290

293

293

294

296

296

297

299

300

301

302

302

302

303

303

304

305

305

304

];

Xexp2=[0

178

0.63

1.26

1.89

2.52

3.15

3.78

4.41

5.04

5.67

6.3

6.93

7.56

8.19

8.82

9.45

10.08

10.71

11.34

11.97

12.6

13.23

13.86

14.49

15.12

15.75

16.38

17.01

17.64

18.27

18.9

19.53

20.16

20.79

21.42

22.05

22.68

23.31

23.94

];

Xexp2=Xexp2+1.5;

l=0.00508; % pore length m

d=0.0012; % wire thickness "m"

np=5; % number of pores

length=np*l; % total length

Tinf=307+273; % Temp inf in Kelvin

Tb=115+273; % Base Temp in Kelvin

h=30; % Heat Transfer Coef

h1=h/10;

p=3.1415*d; % wire perimeter in m2

A=3.1415*d^2/4; % wire cross section area m2

k=16; % thermal condcutivity of wire

m=(h*p/k/A)^0.5;

m1=(h1*p/k/A)^0.5;

179

for i=1:nx

x(i)=length*(i-1)/(nx-1);

for j=1:(np+1)

if (x(i)>=(j-1)*l) && (x(i)<(j*l-d))

s(i)=x(i)+(j-1)*l;

elseif (x(i)>=(j*l-d)) && (x(i)<(j*l))

s(i)=2*j*l+(l+d)/d*(x(i)-j*l);

end

end

if x(i)<(l-d)

T(i)=Tinf+(Tb-Tinf)*exp(-m1*s(i));

else

T(i)=Tinf+(Tb-Tinf)*exp(-m*s(i));

end

Torig(i)=Tinf+(Tb-Tinf)*exp(-m*x(i));

end

C=T-273;

Corig=Torig-273;

xmm=1000*x;

close all;

figure

plot(xmm,C)

xlabel('Length, x in mm')

ylabel('Temperature in C')

hold on;

plot(Xexp2,Texp2,'-o','Color','black');

hold on;

plot(xmm,Corig,'-*','Color','green');

legend('show');

180

Appendix B: Heat Exchanger Assembly for the Hot Gas Incinerator.

183

Appendix C: Step-by-Step Fabrication Process of the Heat Exchanger.

189

Appendix D: Location of the Thermocouples on the Surface of the Heat

Exchanger.

191

Appendix E: Shows a Schematic of the Fan, the Fan Performance and the

Electrical Heater.

experimental investigation of heat transfer in laser ...€¦ · experimental investigation of heat...

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