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An investigation and enhancement of

thermal performance in a heat pipe and its

thermal modeling application

Yeu Yee Lee

Faculty of Engineering, Computing and Science (FECS)

Swinburne University of Technology

Sarawak Campus, Malaysia

Submitted for the degree of Doctor of Philosophy

2018

Dedicated to

my parents, siblings,

my beloved husband Alvin,

my delighted sons Finn and Fabian,

and my sweet daughter Francine.

ACKNOWLEDGEMENT

First and foremost, I would like to thank God for giving me the opportunity to undertake

this study and providing me with the strength to complete it with His grace.

In my journey towards this degree, I have found a mentor, a friend, an inspiration, and a

role model. I am deeply grateful to my principal coordinating supervisor, Prof. Alexander

Gorin, for his valuable advice and feedback. His detailed and constructive comments

helped me to improve the thesis in many ways. He was all the time available for fruitful

research discussions. His guidance and encouragement during these years are beneficial

contributions to this study. Finally, I appreciate his total confidence and the responsibility

granted me throughout this period.

I would also like to express my sincere gratitude and deep appreciation to my coordinating

supervisor, Prof. Anatoli Vakhguelt. His broad knowledge and his support throughout

this work have been of great value for me. His understanding, encouraging and personal

guidance have provided a good basis for the present thesis.

In addition, I thank my associate supervisor Adjunct Prof. Ioan Sauciuc for giving me the

opportunity and motivation to undertake this work.

My sincere thanks are due to my colleagues from Swinburne University of Technology

(Sarawak Campus), for their detailed review, constructive criticism and excellent advice

during the preparation of this thesis. Special thanks to Luk Tien Boh and Victor Bong for

helping me in the lab. I also acknowledge our lab officers and technicians for their

cooperation and friendship.

Furthermore, I wish to express my gratitude to Swinburne University of Technology

(Sarawak Campus) for my PhD studentship and the financial support in this research.

Finally, I owe my loving thanks to my family. They have lost a lot due to my research

abroad. Without their encouragement and understanding, it would be impossible for me

to finish this work.

Best Regards, Yeu Yee Lee, 2018

i

ABSTRACT Heat transfer in porous media has become increasingly important since last few decades.

The principles of heat transfer in porous media are widely used in many fields including

engineering and science. As the demand for higher heat transfer efficiency is increasing,

the use of porous media in heat pipe has vastly gained recognition. Heat pipe is the most

commonly used heat transfer device that involves the principles of conduction,

evaporation, and condensation in a porous medium. Thus, evaporation and condensation

heat transfer of porous medium play significant roles in heat pipe’s working principle.

However, there is only a handful of researches for condensation in porous media with the

effects of inertial, near-wall zone and two-phase zone. The experimental investigation of

the above-mentioned effects is complicated and remain challenging even with the

present-day advanced technology.

In this study, experimental and theoretical investigations have been done on the

evaporation and condensation heat transfer in porous media. The findings will help to

improve the performance of a heat pipe as the evaporation and condensation rates can

affect the heat transfer capacity and efficiency of the heat pipe.

Initially, experimental investigations of evaporation from porous media are conducted to

provide a deeper understanding of the mechanism heat transfer in porous media during

phase change process. An experimental setup used to study the fundamental of

evaporation mechanism in porous media is developed. The porous media is modelled by

using various sizes of brass balls, chrome steel balls, ceramic balls and river sand. The

porous media are tested at various temperatures with regards to different structures and

characteristics, such as porosity, particle size, pores size, porous layer thickness, and

particle material. Many positive results are achieved and successfully characterized

throughout this study. The experimental results obtained would enhance the thermal

performance of heat pipe. In addition, a physical model is developed for evaporation heat

transfer in porous media and fits well with experimental data.

Furthermore, the effective thermal conductivity for various porous samples is determined

experimentally. The comparison is made on the experimental results of effective thermal

conductivity and the models available. The effects of porous media parameters on

effective thermal conductivity are also studied.

ii

Next, the physico-mathematical models for film condensation on an inclined plate

embedded in porous media with the effects of inertial and near-wall region are developed.

The models developed are compared to the models and experimental data available. The

effective thermal conductivity, liquid film thickness, and convection heat transfer

coefficient were determined from experimental data available in published resources.

Finally, the theoretical model of liquid film condensation embedded in porous media with

two-phase region effect based on several assumptions was developed. The developed

model was compared to the models and experimental data available. It is found that the

model developed in this study show good agreement with both the model and

experimental results of previous researchers. The model of film condensation on an

inclined plate embedded in a porous medium with two-phase region introduces simple

analytical solutions to complex problems.

The model developed for film condensation on an inclined plate embedded in a porous

medium with two-phase region effect, as well as the modified solutions for film

condensation on an inclined plate embedded in a porous medium with inertial and near-

wall region effects, have formed the main novelty of this study. Overall, this study

contributes towards enhancing the thermal performance of heat pipe. It could lead to the

development of smaller yet efficient heat pipe. It allows control of “dry-outs” in the

evaporation section and “flooding” in the condensation section of heat pipes.

iii

DECLARATION

I declare that this thesis contains no material that has been accepted for the award of any

other degree or diploma and to the best of my knowledge contains no material previously

published or written by another person except where due reference is made in the text of

this thesis.

_________________

Yeu Yee Lee

iv

NOMENCLATURE

𝐴𝐴 Area, m2

𝑎𝑎 Thermal diffusivity, m2/s

𝑐𝑐𝑝𝑝 Specific heat capacity, J/kg.K

𝑐𝑐𝑣𝑣 Specific heat capacity at constant volume, J/kg·K

𝐶𝐶 Constant

𝒞𝒞 Concentration, mol/m3

𝐶𝐶𝑐𝑐 Coefficient of curvature

𝐶𝐶𝑢𝑢 Coefficient of uniformity

𝐸𝐸 Internal energy, J/kg

𝑑𝑑 Diameter, m

𝑑𝑑𝑑𝑑/𝑑𝑑𝑑𝑑 Temperature gradient (K/m)

𝐷𝐷𝐴𝐴𝐴𝐴 Diffusion coefficient of the molecule A in B

𝑔𝑔 Gravitational acceleration, m/s2

𝐺𝐺𝑠𝑠 Specific gravity of solids

𝑄𝑄 Heat energy, J

𝑞𝑞 Heat transfer rate, j/s or W

𝑞𝑞′′ Heat flux, W/m2

�̇�𝑞 Internal heat generation, W/m3

ℎ Mass transfer coefficient, m/s

ℎ𝑓𝑓𝑓𝑓 Latent heat of vaporization, J/kg

𝑗𝑗 Diffusive mass flux, g/m2⋅s

𝚥𝚥 ̅ Diffusive molar flux, mol/m2⋅s

𝑗𝑗𝑠𝑠 Leverett J-function

Nomenclature v

𝐾𝐾 Permeability, m2

𝐿𝐿 Length of plate or representative dimension, m

𝑚𝑚 Mass of substances, kg

�̇�𝑚 Rate of evaporation, kg/s

�̇�𝑚′′ Mass flux, kg/s⋅m2

𝑀𝑀 Molar mass, kg/mol

𝑁𝑁 Mass transfer rate, mol/s

𝑙𝑙 Porous layer thickness, m

𝐿𝐿𝑐𝑐 Characteristic length, m

𝑃𝑃 Pressure, pa or N/m2

𝑟𝑟 Radius, m

𝑟𝑟𝑐𝑐 Equivalent capillary radius, m

𝑅𝑅 Thermal resistance, K/w

𝑠𝑠 Saturation

𝑆𝑆𝑎𝑎 Surface area, m2

𝑑𝑑 Temperature, K

𝑡𝑡 Time, s

𝑈𝑈 𝑑𝑑-component velocity , m/s

𝑉𝑉 𝑦𝑦-component velocity , m/s

𝑣𝑣 Volume, m3

𝓋𝓋 Molecular volumes, m3/mol

𝑦𝑦 Mole fraction

𝛥𝛥𝛥𝛥 Enthalpy change in vaporization, J/kg

∆𝑆𝑆 Change in entropy, J

𝛥𝛥𝑑𝑑 Change in temperature, K

∇ Three-dimensional del operator

vi

Dimensionless Parameters

𝐴𝐴𝑟𝑟 Archimedes Number, 𝑓𝑓𝐿𝐿3

𝜈𝜈2�1 − 𝜌𝜌𝑣𝑣

𝜌𝜌𝑙𝑙� cos𝜑𝜑

𝐴𝐴𝑟𝑟∗ Modified Archimedes Number, 𝑓𝑓𝑔𝑔𝐿𝐿𝜈𝜈𝑙𝑙2 �1 −

𝜌𝜌𝑣𝑣𝜌𝜌𝑙𝑙� cos𝜑𝜑

𝐺𝐺𝑟𝑟 Grashof number, 𝑓𝑓𝐿𝐿3𝛽𝛽∆𝑇𝑇𝜈𝜈2

Ku Kutateladze number, 𝑟𝑟𝑖𝑖

𝑐𝑐𝑝𝑝(𝑇𝑇𝑤𝑤−𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠)

𝑁𝑁𝑁𝑁 Nusselt number, 𝛼𝛼𝛼𝛼𝜆𝜆

𝑁𝑁𝑁𝑁�� Average Nusselt number, 𝛼𝛼�𝐿𝐿𝜆𝜆

𝑃𝑃𝑟𝑟 Prandtl number, 𝜈𝜈𝑎𝑎 𝑜𝑜𝑟𝑟𝜌𝜌𝑐𝑐𝑝𝑝𝜈𝜈𝜆𝜆

𝑅𝑅� Dimensionless group, 𝜎𝜎√𝑔𝑔𝐾𝐾𝜇𝜇𝑙𝑙𝑎𝑎𝑒𝑒

𝑅𝑅𝑅𝑅 Reynold’s number, 𝑈𝑈𝐿𝐿𝜈𝜈

𝑆𝑆𝑐𝑐 Schmidt number, 𝜈𝜈

𝐷𝐷𝐴𝐴𝐴𝐴

𝑆𝑆ℎ Sherwood number, ℎ𝑚𝑚𝐿𝐿𝐷𝐷𝐴𝐴𝐴𝐴

Greek symbols

𝛼𝛼 Convection heat transfer coefficient, w/m2·K

𝛽𝛽 Coefficient of expansion of the fluid, K−1

𝜉𝜉 Constant

𝜀𝜀 Porosity

𝐾𝐾 Permeability, m2

𝜌𝜌 Density, kg/m3

𝜆𝜆 Thermal conductivity, W/m·k

𝜎𝜎 Surface tension, N/m

𝛿𝛿 Film thickness, m

Nomenclature vii

𝜇𝜇 Dynamic viscosity, kg/m·s

𝜃𝜃 Contact angle

Subscripts

∞ Ambient

𝑏𝑏 Metal ball

𝐵𝐵 Bulk

𝑐𝑐 Capillary

𝑐𝑐𝑜𝑜𝑐𝑐 Container

cond Conduction

conv Convection

e Effective

evap Evaporation

𝑓𝑓 Fluid

ℎ Heat

𝑙𝑙 Liquid

loss Loss

m Porous Medium

mass Mass

max Maximum

min Minimum

o Overall

p Particle

r Relative

s Solid

sat Saturated

viii

set Set-point

T Total

t Two-phase

𝑣𝑣 Vapour

v Void space

𝑤𝑤 Wall or surface

ix

PUBLICATIONS ARISING FROM THIS

DOCTORAL STUDY

Y.L. Yeu, H. H. J. Tan, A. Gorin, A. Vakhguelt, "Experimental Study of the Rate of

Evaporation from Porous Media of Different Matrices", Defect and Diffusion Forum, Vol.

379, pp. 171-180, 2017

Y.L. Yeu, H. H. J. Tan, A. Gorin, A. Vakhguelt, Experimental Study of the Rate of

Evaporation from Porous Media of Different Matrices, Proc. 13th International

Conference on Diffusion in Solids and Liquids (DSL 2017), Vienna, Austria, 2017.

Y.L. Yeu, A. Vakhguelt, A. Gorin, An Experimental Study of Evaporation in Porous

Media, Proc. World Hybrid Technologies and Energy Conference (World Hybrid 2013),

Kuching, Malaysia, 2013.

Y.L. Yeu, A. Vakhguelt, Fundamental Study of Evaporation Heat Transfer in Porous

Media, Proc. 3rd International Conference of Institution of Engineering and Technology

(IETBIC)”, Brunei Darussalam, pp. 25, 2012.

Y.L. Yeu, A. Vakhguelt, An Experimental Study in the Fundamentals of Evaporation

from Porous Structure, Proc. 10th International Heat Pipe Symposium, Tamsui, New

Taipei City, Taiwan, pp. 54 - 60, 2011.

Vakhguelt A., Bong V., Yeu E., Study of Evaporation Mechanism using Porous Media,

Drying and Evaporation, Proc. 19th Int Cong. Chemical and Process Engineering, Prague,

Czech Republic, 2010.

Y.L. Yeu, N.S. Victor Bong, A. Vakhguelt, Evaporation Mechanism in Porous Medium,

Proc. 4th World Engineering Congress, Kuching, Malaysia, PP. 201-208, 2010.

x

TABLE OF CONTENTS

ACKNOWLEDGEMENT .............................................................................................. i

ABSTRACT .................................................................................................................... i

DECLARATION .......................................................................................................... iii

NOMENCLATURE ...................................................................................................... iv

PUBLICATIONS ARISING FROM THIS DOCTORAL STUDY ............................. ix

TABLE OF CONTENTS ............................................................................................... x

LIST OF FIGURES ...................................................................................................... xv

LIST OF TABLES .................................................................................................. xxviii

1. INTRODUCTION ................................................................................................... 1

1.1 Historical Development of Heat Pipes ................................................................... 2

1.2 Fundamental Working Principles of Heat Pipes .................................................... 4

1.3 Porous Media ......................................................................................................... 6

1.4 Evaporation in Porous Media ................................................................................. 8

1.5 Condensation in Porous Media .............................................................................. 9

1.6 Research Objectives and Contributions ............................................................... 10

1.7 Outline of the Thesis ............................................................................................ 12

2. LITERATURE REVIEW ..................................................................................... 14

2.1 Fundamental Definition in Heat and Mass Transfer ............................................ 14

2.1.1 Conduction Heat Transfer ............................................................................ 14

2.1.2 Convection Heat Transfer............................................................................. 16

2.1.3 Evaporation Heat Transfer ........................................................................... 17

2.1.4 Evaporation Mass Transfer .......................................................................... 20

2.2 Effective Thermal Conductivity ........................................................................... 23

Table of Content xi

2.3 Porous Media in Heat Pipe ................................................................................... 32

2.4 Evaporation Heat Transfer in Porous Media ........................................................ 34

2.5 Investigation on Porous Media and Wick Structure ............................................. 38

2.5.1 Various Wick Structure Characteristics ....................................................... 39

2.5.2 Bi-porous Wick Structure.............................................................................. 41

2.5.3 Microgroove Wick Structures ....................................................................... 41

2.6 Parametric Study of Evaporation Heat Transfer from Porous Media .................. 42

2.6.1 Particle Size .................................................................................................. 43

2.6.2 Pore Size .................................................................................................. 46

2.6.3 Porous/Wick Thickness ............................................................................ 50

2.6.4 Porosity ......................................................................................................... 53

2.7 Boiling in Porous Media ...................................................................................... 55

2.8 Film Condensation ............................................................................................... 61

2.9 Film Condensation in Porous Media .................................................................... 64

2.9.1 Liquid Film ................................................................................................... 69

2.9.2 Inertial Effect ................................................................................................ 73

2.9.3 Near-Wall Region Effect ............................................................................... 78

2.9.4 Two-phase region effect ................................................................................ 80

2.10 Summary ............................................................................................................ 88

3. METHODOLOGY OF EXPERIMENTAL STUDIES ...................................... 90

3.1 Experimental Setup for the Study of Evaporation from Porous Media ............... 90

3.2 Experimental Setup for the Effective Thermal Conductivity Investigation ....... 101

3.3 Experimental Working Procedure for Investigation of Effective Thermal

Conductivity ............................................................................................................... 105

3.4 Experimental Procedure for the Study of Evaporation from Porous Media ...... 107

3.5 Materials used to create porous structures ......................................................... 111

xii

3.6 Instrumentation and software used for data acquisition ..................................... 113

3.6.1 Heater Control Sub-system ......................................................................... 115

3.6.2 Water Temperature Logging sub-system .................................................... 116

3.6.3 Mass Logging Sub-system........................................................................... 117

3.6.4 Ambient Temperature and Humidity Logging Sub-System ......................... 119

4. RESULTS OF EFFECTIVE THERMAL CONDUCTIVITY ........................ 120

4.1 Results of Effective Thermal Conductivity ........................................................ 120

4.2 The effect of different nature/type of solid particles on effective thermal

conductivity ................................................................................................................ 132

4.3 Effect of particle size on effective thermal conductivity ................................... 133

5. EVAPORATION FROM POROUS MEDIA: EXPERIMENTAL RESULTS

AND PHYSICAL MODELS ...................................................................................... 135

5.1 Preliminary Experimental Results and Performance Analysis of the Experimental

Setup ........................................................................................................................... 135

5.1.1 Water Temperature ..................................................................................... 137

5.1.2 Ambient conditions ..................................................................................... 141

5.1.3 Porous structure ......................................................................................... 142

5.1.4 Summary ..................................................................................................... 146

5.2 Experimental Results for the Study of Evaporation from Porous Media ........... 147

5.3 Temporal Temperature Distribution of the Water Temperature ........................ 148

5.4 Temperature History across the Porous Samples ............................................... 157

5.5 Ambient Temperature Profile and Ambient Relative Humidity ........................ 164

5.6 Evaporation Rates from Porous Media .............................................................. 167

5.7 Water Level Change During Evaporation in Porous Media .............................. 180

5.8 Effect of Particle Size on Rate of Evaporation .................................................. 181

5.9 Effect of Porosity on Rate of Evaporation ......................................................... 193

5.10 Physical Model of Evaporation from Porous Media ........................................ 197

Table of Content xiii

6. FILM CONDENSATION ON AN INCLINED PLATE EMBEDDED IN A

POROUS MEDIUM ................................................................................................... 203

6.1 Classical solution of film condensation on an inclined plate embedded in a

porous medium ........................................................................................................... 204

6.1.1 Temperature distribution along the porous layer ....................................... 208

6.1.2 Determination of liquid film thickness ........................................................ 210

6.1.3 Determination of the effective thermal conductivity ................................... 217

6.2 Modified solution for film condensation on an inclined plate embedded in a

porous medium with inertial effects ........................................................................... 220

6.3 Modified solution for film condensation on an inclined plate embedded in a

porous medium with inertial effects and the near-wall region effects ....................... 222

6.4 Thin Film Condensation in Porous Media ......................................................... 228

6.4.1 Comparison of experimental data to predicted values ............................... 231

7. TWO-PHASE REGION EFFECT ON FILM CONDENSATION ON AN

INCLINED PLATE EMBEDDED IN A POROUS MEDIUM ............................... 233

7.1 Mathematical Formulation for film condensation on an inclined plate embedded in

a porous medium with two phase region effect .......................................................... 234

7.2 Comparison to models developed by other researchers. ...................................... 248

7.3 Comparison of experimental data to other models ............................................... 251

8. CONCLUSIONS AND RECOMMENDATIONS ............................................ 258

8.1 Conclusions ........................................................................................................ 258

8.2 Recommendations of Future Studies .................................................................. 260

REFERENCES ........................................................................................................... 262

APPENDICES ......................................................................................................... xxxiii

A. Detailed summary table of results obtained from the Evaporation heat transfer

in porous medium................................................................................................. xxxiv

B. Data of water temperatures obtained from LabVIEW Signal Express software

lii

xiv

C. Data of water mass changes obtained from RS key software .....................xcvi

D. Specification of Dvorovenko’s (1997) Test Samples ................................... cxx

E. Summary Table of Calculated Results for Film Condensation Heat Transfer of

Freon-12 on Inclined Plate Embedded in the Porous Medium .......................... cxxiv

F. Matlab Code ................................................................................................. clviii

G. Thermophysical Properties of Saturated Freon-12 (CCL2F2) .................. clxiv

xv

LIST OF FIGURES Figure 1.1 Schematic diagram of a conventional heat pipe ............................................. 5

Figure 1.2 The variation of the matrices of porous medium with (a) no sphere particles;

(b) large sphere particles; and (c) small sphere particles .................................................. 7

Figure 2.1 One-dimensional heat transfer by conduction (diffusion of energy) ............ 15

Figure 2.2 Model development pathways for molecular diffusion problems (Welty et al.,

2014) ............................................................................................................................... 22

Figure 2.3 A porous medium that comprise of series composite wall ........................... 24

Figure 2.4 A porous medium that comprises the parallel composite wall ..................... 24

Figure 2.5 Comparison between proposed model and data for porous media filled with

water (Florez et al., 2013) ............................................................................................... 26

Figure 2.6 Effective thermal conductivity vs. porosity for experimental data and values

calculated through literature models for porous media saturated with water (Florez et al.,

2013) ............................................................................................................................... 26

Figure 2.7 Comparison of effective thermal conductivity predicted by various analyses

of the experimental data of Nozad et al. (1985) (Kaviany, 2012)................................... 30

Figure 2.8 Comparison of the permeability and the capillary pumping for different wick

structure (Sauciuc et al., 2000) ........................................................................................ 40

Figure 2.9 Mean temperature of the heating block vs. imposed heat flux at ∆𝛥𝛥 =

4.0mm. (Cao et al., 2002) ............................................................................................... 48

Figure 2.10 Heat transfer coefficient vs. imposed heat flux at ∆𝛥𝛥 = 4.0mm. (Cao et al.,

2002) ............................................................................................................................... 48

Figure 2.11 Heat transfer coefficient with vaa rying heat flux of different mesh size and

pool boiling (Li and Peterson, 2006b) ............................................................................ 49

Figure 2.12 Wick thickness effect on the evaporating heat transfer coefficients (rb =

0.635mm; 𝜀𝜀 = 43%; LH = 0.01m; working fluid = water)(Hanlon and Ma, 2003) ........ 51

xvi

Figure 2.13 Effect of wick thickness on (a) the vapour temperature (Tv), (b), (c) and (d)

the pressure drop for OD=12.7mm, OD=20mm and OD=30mm respectively for

difference evaporator lengths. (Di Marco et al., 2014) ................................................... 52

Figure 2.14 Steady-state maximum temperature rise of the heat pipe temperature with

porosity for different wick structures (Hassan and Harmand, 2015). ............................. 54

Figure 2.15 Maximum heat pipe pressure difference at steady state with porosity for

different wick structures (Hassan and Harmand, 2015). ................................................. 54

Figure 2.16 Heat transfer from capillary wicking structure surfaces (Faghri, 1995) ..... 55

Figure 2.17 Heat transfer from a submerged wick (Faghri and Zhang, 2006) ............... 56

Figure 2.18 Coordinates and nomenclature for a thin vapour layer adjacent to a heated

vertical surface in a permeable medium. (Parmentier, 1979) ......................................... 57

Figure 2.19 Schematic diagram of a water-saturated porous bed with the two-phase zone

(Bau and Torrance, 1982a).............................................................................................. 59

Figure 2.20 Film boiling in porous media on a vertical wall (Cheng and Verma, 1981,

Faghri and Zhang, 2006) ................................................................................................. 61

Figure 2.21 Condensation formed on the surface. Dropwise condensation (left) and

Film condensation (Right). ............................................................................................. 62

Figure 2.22 Condensation curves for steam. (Tanasawa, 1991, Amanifard et al., 2007)

......................................................................................................................................... 62

Figure 2.23 Coordinate systems for film condensation along a wedge (n = 0) and a cone

(n = 1) (Cheng, 1981) ...................................................................................................... 66

Figure 2.24 Variation of the Nusselt number with the Jacob number for θ = 30 ° and ω

= 0.2 and various values of the anisotropic permeability ratio (Sanya et al., 2014) ...... 70

Figure 2.25 Effect of the derivation from the Darcy flow regime (Nakoryakov and

Gorin 1994) ..................................................................................................................... 77

Figure 2.26 Heat transfer with consideration for the inertial effects (Nakoryakov and

Gorin 1994) ..................................................................................................................... 78

Figure 2.27 Film condensation embedded in porous media for gravity-capillary

dominated (𝐵𝐵𝑜𝑜 ≃ 1) and capillary dominated(𝐵𝐵𝑜𝑜 < 1) flows ...................................... 81

List of Figures xvii

Figure 3.1 Schematic diagram of the experimental set up for the study of evaporation

from porous media .......................................................................................................... 91

Figure 3.2 Photo of actual experimental set up for the study of evaporation from porous

media ............................................................................................................................... 92

Figure 3.3 Cast Aluminium Heater with an integrated K-type thermocouple ............... 95

Figure 3.4 Uneven heat distribution on the top surface of the aluminium container

(Left) and an improved heat distribution with the use of a sand bath (Right) was

observed through the thermal imaging device. ............................................................... 96

Figure 3.5 Even heat distribution on the surface of the (Left) heater and (Right)

aluminium container was achieved using the aluminium thick block. ........................... 97

Figure 3.6 Heat sink compound to reduce contact resistance between two surfaces. (a)

RS Heat Sink Compound and (b) Wakefield Thermal Compound. ................................ 98

Figure 3.7 Fairly even heat distribution observed in the aluminium container ............. 98

Figure 3.8 Superwool 607 paper thermal insulation sheet ............................................. 99

Figure 3.9 Temperature control system with temperature controller, solid state relay

(SSR) and pulse width modulation (PWM). ................................................................. 100

Figure 3.10 (a) Temperature-Humidity Sensors chip and (b) Temperature-Humidity

logging system .............................................................................................................. 101

Figure 3.11 Thermal network of heat transfer in porous medium ............................... 102

Figure 3.12 Equipment used to determine the thermal conductivity of the materials 103

Figure 3.13 Schematic diagram of Armfield linear heat conduction accessory (model:

HT 11). .......................................................................................................................... 104

Figure 3.14 Decagon KD2 Pro Thermal Properties Analyser...................................... 104

Figure 3.15 Points of temperature distribution in composite solids............................. 106

Figure 3.16 Heat transfer through composite wall (test section) ................................. 107

Figure 3.17 Thermocouples position............................................................................. 109

Figure 3.18 View of surface area change as the water level drops .............................. 110

Figure 3.19 Various sizes of Brass balls used in the experiment ................................. 112

xviii

Figure 3.20 Overview of the data acquisition and control system ............................... 113

Figure 3.21 Block diagram of heater control sub-system ............................................ 115

Figure 3.22 Pulse-width modulation driver ................................................................. 116

Figure 3.23 Block diagram of the water temperature logging sub-system .................. 116

Figure 3.24 NI 9211 Thermocouple input module with NI USB 9162 Hi-Speed USB

Carrier ........................................................................................................................... 117

Figure 3.25 Block diagram of the mass logging sub-system ....................................... 117

Figure 3.26 A&D GF-10K Electronic balance ............................................................ 118

Figure 3.27 WinCT Data Communication RsKey software interface ......................... 118

Figure 3.28 Block diagram of the ambient temperature and humidity logging sub-

system............................................................................................................................ 119

Figure 4.1 Physical contact points between brass balls and heated surface ................. 122

Figure 4.2 Temperature distribution along the simple plane wall of uniform material

(Brass) and constant cross sectional area (0.00049m2). ................................................ 126

Figure 4.3 Temperature distribution along the composite wall of Brass – Ceramic –

Brass .............................................................................................................................. 126

Figure 4.4 Temperature distribution along the composite wall of Brass – Dry River

Sand (0.6-1.2mm) – Brass ........................................................................................... 127

Figure 4.5 Temperature distribution along the Composite Wall of Brass – Dry River

Sand (1.2-2.4mm) – Brass ........................................................................................... 127

Figure 4.6 Temperature distribution along the composite call of Brass – Dry River

Sand (2.4-4.8mm) – Brass ........................................................................................... 128

Figure 4.7 Temperature distribution along the composite call of Brass – Brass 2mm

balls (Randomly packed) – Brass ............................................................................... 128

Figure 4.8 Temperature distribution along the composite wall of Brass – Brass 3mm




List of Figures xix



Figure 4.11 Temperature distribution along the composite wall of Brass – Brass

2,3,4,5mm balls (Randomly packed) – Brass ............................................................ 130

Figure 4.12 Comparison between literature models and experimental data for a porous

structure made up of Brass Ball 2mm. .......................................................................... 131

Figure 4.13 Comparison of thermal conductivity for Brass Balls samples.................. 134

Figure 5.1 Transient temperature response of the water temperature(Yeu and Vakhguelt,

2011) ............................................................................................................................. 138

Figure 5.2 Thermal resistance for initial experiment setup (Yeu and Vakhguelt, 2011)

....................................................................................................................................... 139

Figure 5.3 The balls arrangement for Mix all sample during the preliminary test ...... 141

Figure 5.4 The relation between evaporation rate and relative humidity (Yeu and

Vakhguelt, 2011) ........................................................................................................... 141

Figure 5.5 The relations between evaporation rate and room temperature (Yeu and

Vakhguelt, 2011). .......................................................................................................... 142

Figure 5.6 The relations between porosity and evaporation rate at different heater

temperatures for Loose Random Packing Test Samples. .............................................. 144

Figure 5.7 Graph of evaporation rate for simple cubic samples with ball size of 20mm,

heater temperature of 60°C and porous layer thickness of 40mm (Yeu et al., 2010). .. 144

Figure 5.8 The evaporated water mass for the first hour at steady state. (single sizes

samples with loose random packing)(Yeu and Vakhguelt, 2011). ............................... 145

Figure 5.9 The evaporated water mass for the first hour at steady state. (mix sizes

samples with loose random packing)(Yeu and Vakhguelt, 2011). ............................... 145

Figure 5.10 Chrome steel balls rusted during the heating process ............................... 146

Figure 5.11 Temporal temperature distribution of the water temperature at a different

position for all test samples ........................................................................................... 149

xx

Figure 5.12 Temporal temperature distribution of the water temperature at different

position for River sand (with a grain size of 0.6 – 1.2mm, 1.2 – 2.4mm, and 2.4 –

4.8mm) and Ceramic Carbon Balls samples ................................................................. 149


position for Non-porous sample sets ............................................................................. 150


position for Brass2rp1 sample sets (2mm Brass Balls with random packing and porous

thickness of 1.9cm) ....................................................................................................... 150


position for Brass4hcp1 sample sets (4mm Brass Balls with hexagonal closed packing

and porous thickness of 1.95cm) ................................................................................... 151


position for Brass5sc1 sample sets (5mm Brass Balls with simple cubic packing and

porous thickness of 1.9cm) ........................................................................................... 151


position for Brass4rp2 sample sets (4mm Brass Balls with random packing and porous

thickness of 2.93cm) ..................................................................................................... 152


position for Brassmrp2 sample sets (2,3,4,5 mm Brass Balls with random packing and



position for Brassmrp3 sample sets (2,3,4,5 mm Brass Balls with random packing and



position for Brass23rp sample sets (2,3 mm Brass Balls with random packing and



position for RS1 sample sets (River sand with a grain size of 0.6 – 1.2mm) ............... 154



List of Figures xxi




position for CCB porous sample sets (8mm ceramic carbon balls packed randomly) . 156


position for HCP porous sample sets (5mm brass balls with Hexagonal Closed packing)

....................................................................................................................................... 156


position for BCC porous sample sets (5mm brass balls with Body Cubic Cantered

packing) ......................................................................................................................... 157


position for Random porous sample sets (5mm brass balls with Random packing). ... 157

Figure 5.28 Temperature History across the Plain Media (Water only) Sample ......... 159

Figure 5.29 Temperature History across the Porous Sample of Brass2rp1 ................. 159

Figure 5.30 Temperature History across the Porous Sample of Brass4hcp1 ............... 159

Figure 5.31 Temperature History across the Porous Sample of Brass5sc1 ................. 160

Figure 5.32 Temperature History across the Porous Sample of Brass4rp2 ................. 160

Figure 5.33 Temperature History across the Porous Sample of Brassmrp2 ................ 160

Figure 5.34 Temperature History across the Porous Sample of Brassmrp3 ................ 161

Figure 5.35 Temperature History across the Porous Sample of Brass23rp ................. 161

Figure 5.36 Temperature History across the Porous Sample of RS1 ........................... 161



Figure 5.39 Temperature History across the Porous Sample of CCB.......................... 162

Figure 5.40 Temperature History across the Porous Sample of Brass5Hcp ................ 163

Figure 5.41 Temperature History across the Porous Sample of Brass5Bcc ................ 163

Figure 5.42 Temperature History across the Porous Sample of Brass5Rp .................. 163

xxii

Figure 5.43 Comparison of Steady-State Temperature Distribution for all test samples

....................................................................................................................................... 164

Figure 5.44 Ambient temperature and relative humidity for porous sample of Brass2rp1

....................................................................................................................................... 165

Figure 5.45 Ambient temperature and relative humidity for porous sample of

Brass4hcp1 .................................................................................................................... 165

Figure 5.46 Ambient temperature and relative humidity for porous sample of Brass5sc1

....................................................................................................................................... 166

Figure 5.47 Ambient temperature and relative humidity for porous sample of Brass4rp1

....................................................................................................................................... 166

Figure 5.48 Ambient temperature and relative humidity for porous sample of

Brassmrp2 ..................................................................................................................... 166

Figure 5.49 Comparison of Evaporation Rates for non-porous sample and various

porous samples every 10 minutes interval .................................................................... 167

Figure 5.50 Comparison of Evaporation Rates for Brass4hcp1 sample and Brass4rp2

sample every 10 minutes interval .................................................................................. 168

Figure 5.51 the changes of surface area with respect to the porous height. .................. 169

Figure 5.52 Liquid receding during evaporation ......................................................... 170

Figure 5.53 Comparison of Evaporated Water Mass ................................................... 171

Figure 5.54 Evaporated Water Mass for Non-porous samples .................................... 173

Figure 5.55 Evaporated Water Mass for Brass2rp1 samples ....................................... 173

Figure 5.56 Evaporated Water Mass for Brass4hcp1 samples ..................................... 174

Figure 5.57 Evaporated Water Mass for Brass5sc1 samples ....................................... 174

Figure 5.58 Evaporated Water Mass for Brass4rp2 samples ....................................... 175

Figure 5.59 Evaporated Water Mass for Brassmrp2 samples ...................................... 175

Figure 5.60 Evaporated Water Mass for Brassmrp3 samples ...................................... 176

Figure 5.61 Evaporated Water Mass for Brass23rp samples ....................................... 176

Figure 5.62 Evaporated Water Mass for RS1 samples ................................................ 176

List of Figures xxiii



Figure 5.65 Evaporated Water Mass for CCB samples ............................................... 177

Figure 5.66 Observed Liquid Water Evaporation Rate for all test samples................. 178

Figure 5.67 Water Level Changes during Evaporation ................................................ 180

Figure 5.68 Observed Liquid Water Evaporation Rate for Non-porous and Brass Balls

Porous Samples ............................................................................................................. 181

Figure 5.69 Mass changes of sample Brass2rp1 for the first hour after achieving steady

state ............................................................................................................................... 183

Figure 5.70 Mass changes of sample Brass4hcp1 for the first hour after achieving

steady state .................................................................................................................... 183

Figure 5.71 Mass changes of sample Brass5sc1 for the first hour after achieving steady

state ............................................................................................................................... 184

Figure 5.72 Water mass changes of sample Brass4rp2 for the first hour after achieving

steady state .................................................................................................................... 184

Figure 5.73 Mass changes of sample Brassmrp2 for the first hour after achieving steady

state ............................................................................................................................... 185

Figure 5.74 Mass changes of sample Brassmrp3 for the first hour after achieving steady

state ............................................................................................................................... 185

Figure 5.75 Mass changes of sample Brass23rp for the first hour after achieving steady

state ............................................................................................................................... 186

Figure 5.76 Water mass changes of sample Non-porous for the first hour after

achieving steady state .................................................................................................... 186

Figure 5.77 Effect of Particle Size for Brass Balls samples on Rate of Evaporation .. 187

Figure 5.78 Observed Liquid Water Evaporation Rate for River Sand and Ceramic

Carbon Balls Porous Samples ....................................................................................... 188

Figure 5.79 Water mass changes of sample RS1 for the first hour after achieving steady

state ............................................................................................................................... 188

xxiv


state ............................................................................................................................... 189


state ............................................................................................................................... 189

Figure 5.82 Effect of Particle Size for River Sand samples on Rate of Evaporation .. 190

Figure 5.83 Effect of Particle Size for River Sand samples on amount of water

evaporated in 60minutes & 120 minutes. ...................................................................... 191

Figure 5.84 Evaporated mass changes for porous samples used to test the effect of

particle size on the rate of evaporation ......................................................................... 192

Figure 5.85 Effect of porosity on the rate of evaporation for brass balls samples ....... 194

Figure 5.86 Effect of porosity on water temperature at liquid-vapor interface for brass

balls samples ................................................................................................................. 194

Figure 5.87 Effect of porosity on rate of evaporation for river sand samples ............. 196

Figure 5.88 Effect of porosity on water temperature at liquid-vapour interface for river

sand samples ................................................................................................................. 196

Figure 5.89 overview of heat pipe construction and its working principle.................. 197

Figure 5.90 Leverett J-Function versus water saturation. ............................................ 199

Figure 5.91 Comparison between experimental results with the developed models for

various brass balls sample at Tw=80°C and saturation, s ≈ 0.98. ................................ 201

Figure 5.92 Comparison between experimental results with the developed models for

various sizes of randomly packed brass balls sample at Tw=100°C and saturation, s ≈

0.96. ............................................................................................................................... 202

Figure 6.1. Schematic diagram of film condensation on an inclined plate embedded in a

porous medium. ............................................................................................................. 205

Figure 6.2 Comparison of the experimental data of Dvorovenko (1997) with the

theoretical model of Nakoryakov and Gorin (1994) for film condensation on an inclined

plate embedded in a porous medium............................................................................. 208

List of Figures xxv

Figure 6.3 Temperature profile of condensation film in a porous medium with a grain

diameter of d=1.1mm and grain porosity of ε=0.38 with plate length of (a) L=250mm,

(b) L=500mm, (c) L=750mm and (d) L=1000mm (Dvorovenko, 1997) ...................... 209


diameter of d=0.8mm and grain porosity of ε=0.38 with plate length of (a) L=250mm,

(b) L=500mm, (c) L=750mm and (d) L=1000mm (Dvorovenko, 1997) ...................... 210

Figure 6.5 Determination of liquid film thickness from the E-3f (d=1.1mm, L=750mm,

cos φ=0.01784) temperature profile graph .................................................................... 211

Figure 6.6 Determination of liquid film thickness from the E-4b (d=1.1mm, L=500mm,

cos φ = 0.45008) temperature profile graph .................................................................. 212

Figure 6.7 Relations between the liquid film thicknesses with the Rayleigh number. 215

Figure 6.8 Relations between the liquid film thicknesses with the Rayleigh number and

G-parameter................................................................................................................... 217

Figure 6.9 Correlation between effective thermal conductivity and Rayleigh Number

....................................................................................................................................... 219

Figure 6.10 Correlation between effective thermal conductivity and Rayleigh Number

for film condensation on a inclined plate with an inclination angle of 𝑐𝑐𝑜𝑜𝑠𝑠𝜑𝜑 = 0.2 ..... 219

Figure 6.11 Comparison of experimental results (Dvorovenko, 1997) with the

theoretical model for film condensation on an inclined plate embedded in a porous

medium with inertial effects.......................................................................................... 222

Figure 6.12 Film condensation in porous media with near-wall region effects ........... 223

Figure 6.13 Film condensation heat transfer of Freon-12 on inclined plate embedded in

the grain layer with near-wall region effects for samples E-4 (d=1.1mm, ε=0.38, and

L=1000mm) .................................................................................................................. 224

Figure 6.14 Film condensation heat transfer of Freon-12 on inclined plate embedded in

the grain layer with near wall region effects for samples E-4 (d=1.1mm, L=1000mm,

ε=0.38). ......................................................................................................................... 225

Figure 6.15 Comparison of experimental results with the theoretical model for film

condensation on an inclined plate embedded in a porous medium with inertial effects

....................................................................................................................................... 228

xxvi

Figure 6.16 Thin condensate film forms on the surface .............................................. 229

Figure 6.17 Void fraction distribution (Johnson and Kapner, 1990) ........................... 229

Figure 6.18 Comparison of experimental data to predicted values for thin film

condensation on an inclined plate embedded in porous media with grain size of 3.2mm.

....................................................................................................................................... 232

Figure 7.1 Schematic diagram of film condensation on an inclined plate embedded in a

porous medium that has two-phase region. ................................................................... 234

Figure 7.2 Leverett J-Function varies with water saturation. ...................................... 237

Figure 7.3 Relative permeability of liquid phase and vapour phase. ........................... 238

Figure 7.4 Nusselt number as function of 𝐴𝐴𝑟𝑟 ∗ 𝑃𝑃𝑟𝑟𝐾𝐾𝑁𝑁 for porosity 𝜀𝜀 = 0.38, permeability

K = 0.0005075 mm2, γ = 0.025 and 𝜉𝜉= 1. ..................................................................... 245

Figure 7.5 The effect of Kutateladze number, 𝐾𝐾𝑁𝑁. ...................................................... 246

Figure 7.6 The condensation heat transfer results for porosity 𝜀𝜀 = 0.38, permeability K

= 0.0005075 mm2, γ = 0.025 and 𝜉𝜉 = 1. ........................................................................ 246

Figure 7.7 Dimensionless heat transfer coefficient with surface tension effect for

porosity 𝜀𝜀 = 0.38, permeability K = 0.0005075 mm2,𝛾𝛾 = 0.025 and 𝜉𝜉 = 1 ................. 247

Figure 7.8 The effect of 𝛾𝛾 for porosity 𝜀𝜀 = 0.38, permeability K = 0.0005075 mm2,

L = 250mm, 𝐵𝐵𝑜𝑜 = 0.1 and 𝜉𝜉 = 1. ................................................................................. 248

Figure 7.9 Film condensation embedded in porous media with glass beads size of

900𝜇𝜇m. .......................................................................................................................... 250

Figure 7.10 Comparison of the predicted model developed by Majumdar and Tien

(1990), Plumb (1984) to the present model (with 𝜉𝜉 = 1) and experimental data with no

two-phase region effect (𝐵𝐵𝑜𝑜 ≫ 1) for film condensation on an inclined plate with a

length of 500mm embedded in porous media with a grain size of 800μm. .................. 252

Figure 7.11 Comparison of experimental results with the theoretical model for film

condensation on an inclined plate embedded in porous media with a grain size of 800μm

and plate length of 250mm............................................................................................ 253

List of Figures xxvii


diameter of d=800μm and grain porosity of ε=0.38 on an inclined plane with an angle of

cos φ=0.10343 and plate length of L=250mm (Dvorovenko, 1997). ........................... 254

Figure 7.13 Comparison of temperature difference between wall temperature and

saturation temperature with different heat flux for various samples of film condensation

on an inclined plate with angle cos φ=0.10343 embedded in porous media with grain

size of 800μm and plate length of 250mm, 500mm, 750mm and 1000mm. ................ 255

Figure 7.14 Comparison of liquid film thickness for various samples of film

condensation on an inclined plate with angle cos φ=0.10343 embedded in porous media

with grain size of 800μm and plate length of 250mm, 500mm, 750mm and 1000mm.

....................................................................................................................................... 255

Figure 7.15 Comparison of experimental data to numerical values for film condensation

on an inclined plate with inclination angle of 𝑐𝑐𝑜𝑜𝑠𝑠𝜑𝜑 = 0.10343 and length of 250mm

embedded in porous media with grain size of 800𝜇𝜇m. ................................................. 256

Figure 7.16 Film condensation on an inclined plate with inclination angle of 𝑐𝑐𝑜𝑜𝑠𝑠𝜑𝜑 =

0.10343 and length of 250mm embedded in porous media with grain size of 800𝜇𝜇m.

....................................................................................................................................... 257

xxviii

LIST OF TABLES Table 2.1 Existing mass transfer-based evaporation equations use (Singh and Xu, 1997)

......................................................................................................................................... 18

Table 2.2 Models and correlations for the effective thermal conductivity of the

composed material (Hahne et al., 1991, Bird et al., 2007, Pietrak and Wisniewski, 2015)

......................................................................................................................................... 27

Table 2.3 Experimental results of 𝜆𝜆𝑅𝑅 of various dry sands with different densities 𝜌𝜌 and

porosities 𝜀𝜀 at 20℃. (Hahne et al., 1991) ....................................................................... 31

Table 2.4 Maximum porosity for different packing arrangements ................................ 37

Table 2.5 Comparison of Permeability analysed by using Carman-Kozeny equation and

Ergun equation. ............................................................................................................... 38

Table 2.6 Porous sample developed by Mwaba et al. (2006) ........................................ 47

Table 2.7 Porous example developed by Cao et al. ( 2002)........................................... 47

Table 2.8 Typical values of Bo and 𝑅𝑅 for various fluids and porous media (Majumdar

and Tien, 1990, Vargaftik, 1975) .................................................................................... 84

Table 2.9 Relative permeability suggested by various researchers. (Chung et al., 1992,

Gudjonsdottir et al., 2015, Pruess et al., 1999) ............................................................... 86

Table 3.1 List of Materials, Apparatus, and Equipment ................................................. 92

Table 3.2 HT11 Insulated Composite Wall Specification ........................................... 105

Table 3.3 Distance of thermocouples relative to T1 ..................................................... 105

Table 3.4 Various packing types for porous structure ................................................. 108

Table 3.5 Specification of Test Samples ...................................................................... 109

Table 3.6 Thermophysical Properties of Selected Materials ....................................... 112

Table 3.7 Instrumentation and software used for data acquisition .............................. 114

Table 4.1. Experimental measurements for heat conduction in the composite solids of

Brass – test samples – Brass. ....................................................................................... 123

List of Tables xxix

Table 4.2 Comparison of measurement between Armfield HT11 and Decagon KD2 Pro

for effective thermal conductivity ................................................................................. 131

Table 4.3 Experimental Results of River Sand ............................................................. 132

Table 5.1 Specification of Simple Cubic Packing Test Samples for Preliminary Test. 136

Table 5.2 Specification of Loose Random Packing Test Samples for Preliminary Test

....................................................................................................................................... 137

Table 5.3 The void fraction and packing density value for various random packed

structure (Dullien and Brenner 2012) ........................................................................... 143

Table 5.4 A comparison between the experimental porosity and theoretical porosity for

all three matrix arrangements ........................................................................................ 148

Table 5.5 Mass fraction of liquid water in brass balls porous samples........................ 179

Table 5.6 Mass fraction of remaining water in 2 river sand and ceramic carbon balls

porous samples .............................................................................................................. 179

Table 5.7 Summary of the average evaporation rates for brass balls samples after steady

state ............................................................................................................................... 187

Table 5.8 Summary of the steady state for River sands mass versus time .................. 190

Table 5.9 The rate of evaporation for various particle size samples ............................ 193

Table 6.1 Determination of liquid film thickness from the E-3f (d=1.1mm, L=750mm,

cos φ=0.01784) samples ................................................................................................ 211

1

1. INTRODUCTION New technology of electronic component using innovative materials is getting smaller,

faster and more energy efficient. As a result, the heat generated in electronic devices and

systems is critically high. Heat is an inevitable by-product of every electronic component.

It is usually unfavourable to the performance and reliability of an electric component. The

reduced size high-performance electric components lead to higher heat generation density,

therefore causing the component temperature to increase, resulting in the shortened

lifetime, and higher probabilities of malfunction and failure. Therefore, thermal

management should be taken seriously.

One of the examples is modern microprocessor core. It is found on general-purpose

computing platform and accelerated graphic cards which produce a high amount of heat

during its operation. This heat must be dissipated to keep these components within the

required safe operating temperature. Intel co-founder Gordon Moore (1965) stated that

“the number of transistors on a chip will double about every two years”. This law has

become known as Moore’s law (Moore, 1965). Today, microprocessor technology

continues to evolve, microprocessor with 4.3 billion transistors is launched by Intel in the

first quarter of the year 2014. The International Business Machines Corporation (IBM)

launched its neuromorphic TrueNorth chip with 5.4 billion transistors dated 7 August

2014 (Modha). Three years later, IBM researchers introduced the world's first 5-

nanometre chip with 30 billion transistors packed in it (Nield, 2017). Intel not to lag

behind, surprised the market with new technology named Intel’s hyper-scaling process.

With this new technology, Intel can fit 100 million transistors per square millimetre of

chip “for the first time in our industry’s history,” said Kaizad Mistry, a vice president and

co-director of logic technology at the company (Courtland, 2017). On the other side,

Advanced Micro Devices, Inc. (AMD) claimed that they are preparing to launch a new

AMD 32-core 64-thread CPU end of the year 2018 (Hruska, 2018).

Furthermore, the clock speed of processors are measured in Gigahertz and not in

Megahertz anymore, lead to a heat dissipation approaching 100 W (Tadayon, 2000). The

higher the amount of transistor, the smaller the transistor size and higher the clock speed,

this causes the heat flux to be critically high. Therefore, cooling of the microprocessor is

to be taken seriously. NEC Corporation developed a silent liquid cooling system for use

2 Chapter 1. Introduction

in the desktop personal computer in the year 2007. The prominent feature of the system

is the "multiple-heat-source cooling capability," which cools the microprocessor with the

liquid (Uno, 2007). IBM Corporation uses a network of copper pipes that sit just above

the new Power6 processor and carry cold water to them and warm water away. According

to IBM, Water cooling is 4,000 times more efficient than air cooling (Nicoolai, 2008).

The conventional cooling method uses the fan cooling or the combination with the heat

sink. However, these conventional cooling methods generate acoustic noise and have

limitations in confined space. Thus, the well-known alternative way is the use of heat

pipe. Heat pipe is a highly effective thermal conductance device. It has an ability to

transport large quantities of heat against gravity through a small cross-sectional area over

a relatively long length with a comparatively small temperature difference by an

evaporation-condensation cycle with no additional power input to the system.

Heat pipe is widely used in heat-generating components such as computer central

processing unit (CPU) for heat withdrawal. As electronic devices are shifting towards a

more compact form factor (i.e. a design that is smaller than other similar designs in its

field), heat pipe has attracted increasing interest in the research community. Heat pipe has

an advantage, as it can vary its geometrical properties. Hence, heat pipe can be easily

constructed in the available space around the electronics needed to be cooled.

Other than computer industry, heat pipe has numerous applications in automotive industry

such as vehicle brake system cooling, aeronautical industry such as airplane anti-icing

system, aerospace industry such as iso-thermalization of large surfaces, manufacturing

industry such as die casting and injection molding, nuclear power plants, road and bridge

de-icing, and human body temperature control.

1.1 Historical Development of Heat Pipes

The development of the heat pipe began in 1831 when Jacob Perkins and Angier March

Perkins patented their hermetic tube boiler (UK Patent No. 6146) which applied in central

heating system. The hermetic tube boiler works on the principle of single-phase working

fluid circulating in tubes between the furnace and the steam drum at high pressure

(Skempton, 2002). The hermetic tube boiler was produced commercially for over 100

years under A.M. Perkins & Sons Ltd (Reay et al., 2013). In 1839, Angier March Perkins

patented his hot water hermetic heating tubes in UK Patent No. 8311.

Chapter 1. Introduction 3

In the nineteenth century, Perkins family invented Perkins tube through a series of patents

in the United Kingdom. The Perkins tube was the first use and described as a device that

contains only a small quantity of water and operating like a two-phase thermosyphon in

UK Patent No. 7059, dated April 1936. Perkins tube predates the heat pipe for several

decades and plays an essential part in the history of heat pipe (Perkins, 1836).

Thermosyphon is a passive refrigeration device also known as wickless gravity-assisted

heat pipes. It is helpful to understand the operation of thermosyphon before discussing

the heat pipe as heat pipe is similar to thermosyphon in some respects. Thermosyphon

consists of a small quantity of working fluid and a majority the vapour phase, placed in a

closed, sealed tubular vessel. The working principle of the thermosyphon system is that

the working fluid is heated and vaporized at the lower end of the tube called evaporator.

The vaporized working fluid which has lower density travels up to the cold end of the

tube called condenser and condensed back to the liquid. The condensate which has a

higher density drains back down the sides of the vessels interior wall to the hot end by

gravity. The circulation of the working fluid is due to the density difference between cold

temperature fluid (liquid) and hot temperature fluid (vapour).

Gaugler (1944) of the General Motors Corporation who was working on the refrigeration

problems in the mid of the twentieth century invented a heat transfer device. This heat

transfer device would evaporate the liquid to a point above the place where condensation

would take place with no additional work required to raise the liquid. This heat transfer

device introduced the concept of heat pipe and applied for a patent on 21 December 1942.

The patent was then published as US Patent No. 2350348, dated 6 June 1944. The concept

of heat pipe was re-evaluated by Trefethen (1962). However, the heat pipe concept

received relatively little attention until Grover (1966) at Los Alamos National Laboratory

in New Mexico filed his evaporation-condensation heat transfer device patent on behalf

of the US Atomic Energy Commission on 2 December 1963. Grover referred his device

to a heat pipe and described the device as a “synergistic engineering structure which is

equivalent to a material having thermal conductivity greatly exceeding that of any known

metal.

The heat pipe was then recognized as a reliable thermal device based largely on the work

of Cotter (1965) who works at Los Alamos as well. Research on heat pipe began

worldwide after Cotter publication. Many laboratories initiated efforts in this regard. The

United Kingdom Atomic Energy Laboratory at Harwell investigated the use of sodium


heat pipes as thermionic diode converters (Bainton, 1965). A similar research was started

at the Joint Nuclear Research Centre in Ispra, Italy (Grover et al., 1965). Others country

such as Germany and France are also actively involved in heat pipe research.

Initially, an emphasis for the use of heat pipe in space application is due to its lighter

weight, higher heat flux, and has capillary driven wicks on its inner pipe wall, which can

operate in zero gravity environment without any external force field. The first flight of

heat pipes which were used for satellite thermal control on Geodetic Earth Orbiting

Satellite (GEOS-B) was launched from Vandenburg Air Force Base in 1968. Heat pipes

were considerable growth in the terrestrial application by early 1970. Feldman and

Whiting (1967, 1968), Eastman (1968), and Katzoff (1966) discussed the terrestrial

applications of heat pipes in air conditioning, engine cooling, and electronics cooling.

A large number of research and development works had been published over the last four

decades. Today, the number of publication in the areas of heat pipe continue to grow.

Many researchers are actively involved in research and development of heat pipes. The

industrial community began to look for a solution in energy savings due to the high cost

of energy. Various types of heat pipes were invented and developed. Among the broad

variety of heat pipes, the commonly found heat pipes are variable conductance heat-pipes,

loop heat pipes, miniature heat pipes, and micro heat pipes. These heat pipes are matured

enough for the use in various applications like power engineering, chemical engineering,

space technology, and many other engineering fields. Heat pipes are also used in many

everyday applications, such as laptops, electronics, games consoles, air conditioner,

refrigeration, television, and much more because of their low weight, high reliability,

operating self-sufficiency, and high effective thermal conductivity which approximately

5,000 W/m⋅K to 200,000 W/m⋅K . Heat pipe has the ability to transfer and dissipate a

large amount of heat with a very small temperature difference between the hot and cold

end. Hence heat pipe will continue to play a crucial role in cooling technology.

1.2 Fundamental Working Principles of Heat Pipes

Heat pipes are characteristically straight and round but not restricted to cylindrical

geometry. It can be bend and flatten into a different form even in other complex shapes.

The schematic diagram of a conventional heat pipe is shown in Figure 1.1 below. Heat

pipe is made up of an evaporator, adiabatic and condenser section. The adiabatic section

separates the evaporator and condenser section. Some of the heat pipes might not have


the adiabatic section, and some heat pipes might have multiple heat sources and heat sinks.

The design of heat pipe depends on specific applications. There are three main

components of a heat pipe: the sealed container, small amount of working fluid, and the

wick or capillary structure.

The working principle of heat pipe is similar to “reverse thermosyphon” due to its ability

to transport heat against gravity by an evaporation-condensation cycle. The difference

between heat pipe and thermosyphon is that heat pipe consists of wick on the inner pipe

wall. A two-phase closed thermosyphon is a gravity-assisted wickless heat pipe (Faghri,

1995).

Wick is a type of porous medium. The porous medium is a solid matrix that consists of

many pores or voids filled by fluid (liquid or gas) and permeate in between the solid.

There are many naturally existing porous media such as rocks, soils, and biological tissue

while materials such as ceramics, foam and metal wick in the heat pipe are considered as

man-made.

Figure 1.1 Schematic diagram of a conventional heat pipe

The wick lined on the inner wall of a heat pipe is functioned to generate capillary pressure

that drives the working fluid from the condenser back to the evaporator. Other than

providing a mechanism for the working fluid return to the evaporator, the wick in the heat

pipe also facilitates the working fluid to distribute evenly over the evaporator surface.

Since the wick exerts capillary force the return of the condensate back to the evaporator,

Evaporator

section Condenser

section Adiabatic

section

Heat Source Heat Sink

Condenser end cap

Evaporator end cap

Wick

Vapour flow Liquid flow

Container


hence the position for evaporator section can be in any orientation and not restricted to be

at the lower end of the heat pipe. In addition, the wick lined in the inner tube of heat pipe

increases the surface area for better evaporative heat transfer and leads to a high effective

thermal conductance of the heat pipe and efficient in heat transfer.

The heat pipe container consists of a pipe wall and the end caps on both ends. The

container is usually made of high thermal conductivity metals like copper and aluminium.

The working fluid is in equilibrium with its vapour. Usually, water, acetone, nitrogen,

methanol, ammonia or sodium is used as working fluid based on the operating

temperature. One of the main incentives for using the heat pipe is the working fluids in

its cooling system has the ability to absorb heat that closes to the heat generating regions

in microscale. Then, it will move arbitrary distances to locations where more convenient

to reject heat to the surrounding environment.

Heat pipe employed the evaporative cooling to transfer the energy in the form of heat

from the hot end (or known as the evaporator) through evaporation to the cold end (or

known as the condenser) where condensation happens. The heat is applied to the external

wall of the heat pipe and conduct through the pipe wall and the wick structure at the

evaporator section. The working fluid at the evaporator section absorbs the heat and

vaporizes. The vapour then travels through the adiabatic section to the condenser section,

driven by the resulting vapour pressure. At the condenser section, the vapour condensed,

releasing a large amount of latent heat of vaporization to the heat sink. The condensate

then flows back to the evaporator using capillary action, also known as capillarity,

capillary motion or wicking. Capillary action is the ability of a liquid to flow within the

void spaces of a porous medium due to the adhesion of the liquid to the sides of the tube

and cohesion between particular liquid molecules and surface tension that acts to hold the

liquid surface intact. If the liquid flow in a sufficiently narrow tube and the adhesion of

the liquid to the tube walls is sufficiently strong, the interaction between these two

phenomena causes the liquid to work in opposition to the gravity and to be drawn upward

in the tube.

1.3 Porous Media

Porous media is a material which consists of a solid matrix with an interconnected void.

The interconnectedness of the void, which sometimes called the pores, allows one or more

fluids to flow through the material. The void is saturated by single fluid (liquid or gas)


in single-phase flow. While in multiphase flow, liquid and gases share the void space.

When the fluid filled the voids completely, the porous media is saturated.

The porous media has been used in many applications, especially in the science and

engineering field. One of the examples is the use of wick structure in heat pipe cooling

application. It is attached to the inner linings of the heat pipe’s tube to enhance and aid

the evaporative heat transfer rate. The materials of wick structure are either made of

aluminum, steel, copper or nickel in the various range of pore sizes. Fibrous materials,

like ceramics, have also been used widely. Recently, the interest of wick material has

turned to carbon fiber. Carbon fiber filaments are chemically stable and have many fine

longitudinal grooves on their surface results in higher capillary pressures.

The porous medium with matrices composed of smaller sphere particles has a more solid-

liquid contact surface area and solid-solid contact point compared to plain media as

illustrated in Figure 1.2. One can say the porous medium with matrices composed of

smaller sphere particles has a larger effective area for heat to transfer and hence the rate

of heat transfer will be higher.

(a)

(b)

(c)

Figure 1.2 The variation of the matrices of porous medium with (a) no sphere particles; (b) large sphere particles; and (c) small sphere particles

To improve the heat transfer rate through a porous medium in a heat pipe, many

researchers (Lu et al., 1999, Levkov and Kulkov, 2016, Woodside and Messmer, 1961,

Florez et al., 2013, Ren et al., 2007a, Hanlon and Ma, 2003, Li et al., 2006, Li and

Peterson, 2006b, Li and Peterson, 2006a, Li and Peterson, 2007, Deng et al., 2017)

examined in depth the porous properties and characteristics through experimental and

theoretical investigation.

Porous media is most often characterized by its porosity. The porous structure has a

significant effect on heat conduction in porous media. The higher the porosity, the lower

the thermal conductivity will be. In general, the overall thermal conductivity of porous

media depends on the geometry of the medium and the properties of liquid and solid. So


this overall thermal conductivity is known as effective thermal conductivity. It is in a

function of porosity and thermal conductivity of solid and liquid.

Deng (2017) applied fractal geometry to characterize the pore distribution of porous

material. He stated that the effective thermal conductivity is also affected by the fractal

dimensions of the porous material, even when porosity remains constant.

By examining the porous structure and its properties such as porosity, pore size, particle

size, porous layer thickness, total solid-liquid contact surface area and heat flux, a deeper

understanding of the heat transfer mechanism in a porous media can be achieved to

innovate and improve the heat pipes.

1.4 Evaporation in Porous Media

When a liquid sits in one place, for example, a puddle, its molecules will escape into a

gas. This is the process called evaporation. Evaporation can happen either when liquids

are cold or when they are warm, but the higher rate of evaporation is with warmer liquids.

It is because when the matter has a higher temperature, its molecules have more energy

to move and vibrate quicker, and the space between them also increases. When the energy

in specific molecules reaches a certain level, they would escape into the sur

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