Thermal Spreading and Contact Resistance: Fundamentals and Applications

by Yuri S. Muzychka, M. Michael Yovanovich

Overview

Thermal Spreading and Contact Resistance: Fundamentals and Applications

Single source reference on how applying thermal spreading and contact resistance can solve problems across a variety of engineering fields

Thermal Spreading and Contact Resistance: Fundamentals and Applications offers comprehensive coverage of the key information that engineers need to know to understand thermal spreading and contact resistance, including numerous predictive models for determining thermal spreading resistance and contact conductance of mechanical joints and interfaces, plus detailed examples throughout the book.

Written by two of the leading experts in the field, Thermal Spreading and Contact Resistance: Fundamentals and Applications includes information on:

• Contact conductance, mass transfer, transport from super-hydrophobic surfaces, droplet/surface phase change problems, and tribology applications such as sliding surfaces and roller bearings
• Heat transfer in micro-devices and thermal spreaders, orthotropic systems, and multi-source applications for electronics thermal management applications
• Fundamental principles, thermal spreading in isotropic half-space regions, circular flux tubes and disc spreaders, and rectangular flux channels and compound spreaders
• Systems with non-uniform sink plane conductance, transient spreading resistance, and contact resistance between both non-conforming and conforming rough surfaces

Providing comprehensive coverage of the subject, Thermal Spreading and Contact Resistance: Fundamentals and Applications is an essential resource for mechanical, aerospace, and chemical engineers working on research in the fields of heat transfer, thermal management of electronics, and tribology, as well as thermal engineers and researchers in the field of thermal physics.

Product Details

ISBN-13:	9781394187522
Publisher:	Wiley
Publication date:	08/29/2023
Series:	Wiley-ASME Press Series
Pages:	464
Product dimensions:	7.00(w) x 10.00(h) x 1.00(d)

About the Author

Yuri S. Muzychka is a Professor of Mechanical Engineering at Memorial University of Newfoundland, Canada. He is a Fellow of ASME, CSME, and the Engineering Institute of Canada (EIC) and has published over 250 journal and conference proceedings papers, in addition to three handbook chapters.

M. Michael Yovanovich is a Distinguished Professor Emeritus at the University of Waterloo, Canada. He is a fellow of ASME, CSME, AIAA, AAAS, and RSC. He has published seven handbook chapters and over 350 journal and conference proceedings papers, and has given over 150 keynote lectures.

Table of Contents

About the Authors xv

Preface xvi

Acknowledgments xix

Nomenclature xx

1 Fundamental Principles of Thermal Spreading Resistance 1

1.1 Applications 2

1.2 Semi-Infinite Regions, Flux Tubes, Flux Channels, and Finite Spreaders 4

1.3 Governing Equations and Boundary Conditions 6

1.4 Thermal Spreading Resistance 8

1.5 Solution Methods 11

1.6 Summary 12

2 Thermal Spreading in Isotropic Half-Space Regions 15

2.1 Circular Area on a Half-Space 15

2.2 Elliptical Area on a Half-Space 20

2.3 Method of Superposition of Point Sources 25

2.4 Rectangular Area on a Half-Space 29

2.5 Spreading Resistance of Symmetric Singly Connected Areas: The Hyperellipse 33

2.6 Regular Polygonal Isoflux Sources 34

2.7 Additional Results for Other Source Shapes 36

2.8 Model for an Arbitrary Singly Connected Heat Source on a Half-Space 38

2.9 Circular Annular Area on a Half-Space 40

2.10 Other Doubly Connected Areas on a Half-Space 41

2.11 Problems with Source Plane Conductance 42

2.12 Circular Area on Single Layer (Coating) on Half-Space 45

2.13 Thermal Spreading Resistance Zone: Elliptical Heat Source 48

2.14 Temperature Rise of Multiple Isoflux Sources 52

2.15 Temperature Rise in an Arbitrary Area 56

2.16 Superposition of Isoflux Circular Heat Sources 58

2.17 Superposition of Micro- and Macro-Spreading Resistances 64

3 Circular Flux Tubes and Disks 71

3.1 Semi-Infinite Flux Tube 71

3.2 Finite Disk with Sink Plane Conductance 77

3.3 Compound Disk 82

3.4 Multilayered Disks 85

3.5 Flux Tube with Circular Annular Heat Source 88

3.6 Flux Tubes and Disks with Edge Conductance 90

3.7 Spreading Resistance for an Eccentric Source on a Flux Tube 93

3.8 Thermal Spreading with Variable Conductivity Near the Contact Surface 94

3.9 Effect of Surface Curvature on Thermal Spreading Resistance in a Flux Tube 97

4 Rectangular Flux Channels 103

4.1 Two-Dimensional Semi-Infinite Flux Channel 104

4.2 Three-Dimensional Semi-Infinite Flux Channel 108

4.3 Finite Two- and Three-Dimensional Flux Channels 111

4.4 Compound Two- and Three-Dimensional Flux Channels 115

4.5 Finite Two- and Three-Dimensional Flux Channels with Eccentric Heat Sources 120

4.6 Rectangular Flux Channels with Edge Conductance 124

4.7 Multilayered Rectangular Flux Channels 126

4.8 Rectangular Flux Channel with an Elliptic Heat Source 128

4.9 Spreading in a Curved Flux Channel (Annular Sector) 130

4.10 Effect of Surface Curvature on Thermal Spreading Resistance in a Two-Dimensional Flux Channel 134

5 Orthotropic Media 137

5.1 Heat Conduction in Orthotropic Media 137

5.2 Circular Source on a Half-Space 141

5.3 Single-Layer Flux Tubes 143

5.4 Single-Layer Rectangular Flux Channel 144

5.5 Multilayered Orthotropic Spreaders 147

5.6 General Multilayered Rectangular Orthotropic Spreaders 153

5.7 Measurement of Orthotropic Thermal Conductivity 160

6 Multisource Analysis for Microelectronic Devices 167

6.1 Multiple Heat Sources on Finite Isotropic Spreaders 168

6.2 Influence Coefficient Method 172

6.3 Extension to Compound, Orthotropic, and Multilayer Spreaders 175

6.4 Non-Fourier Conduction Effects in Microscale Devices 181

6.5 Application to Irregular-Shaped Heat Sources 185

7 Transient Thermal Spreading Resistance 189

7.1 Transient Spreading Resistance of an Isoflux Source on an Isotropic Half-Space 189

7.2 Transient Spreading Resistance of an Isothermal Source on a Half-Space 195

7.3 Models for Transient Thermal Spreading in a Half-Space 199

7.4 Transient Spreading Resistance Between Two Half-Spaces in Contact Through a Circular Area 201

7.5 Transient Spreading in a Two-Dimensional Flux Channel 202

7.6 Transient Spreading in a Circular Flux Tube from an Isoflux Source 203

7.7 Transient Spreading in a Circular Flux Tube from an Isothermal Source 205

7.8 Models for Transient Thermal Spreading in Circular Flux Tubes 207

8 Applications with Nonuniform Conductance in the Sink Plane 213

8.1 Applications with Nonuniform Conductance 213

8.2 Finite Flux Channels with Variable Conductance 218

8.3 Finite Flux Tube with Variable Conductance 225

9 Further Applications of Spreading Resistance 231

9.1 Moving Heat Sources 231

9.2 Problems Involving Mass Diffusion 243

9.3 Mass Diffusion with Chemical Reaction 246

9.4 Diffusion Limited Slip Behavior: Super-Hydrophobic Surfaces 254

9.5 Problems with Phase Change in the Source Region (Solidification) 261

9.6 Thermal Spreading with Temperature-Dependent Thermal Conductivity 263

9.7 Thermal Spreading in Spherical Domains 268

10 Introduction to Thermal Contact Resistance 275

10.1 Thermal Contact Resistance 275

10.2 Types of Joints or Interfaces 278

10.3 Parameters Influencing Contact Resistance or Conductance 282

10.4 Assumptions for Resistance and Conductance Model Development 283

10.5 Measurement of Joint Conductance and Thermal Interface Material Resistance 283

11 Conforming Rough Surface Models 287

11.1 Conforming Rough Surface Models 288

11.2 Plastic Contact Model for Asperities 290

11.3 Elastic Contact Model for Asperities 294

11.4 Conforming Rough Surface Model: Elastic–Plastic Asperity Deformation 296

11.5 Radiation Resistance and Conductance for Conforming Rough Surfaces 300

11.6 Gap Conductance for Large Parallel Isothermal Plates 302

11.7 Gap Conductance for Joint Between Conforming Rough Surfaces 303

11.8 Joint Conductance for Conforming Rough Surfaces 306

11.9 Joint Conductance for Conforming Rough Surfaces: Scale Analysis Approach 310

11.10 Joint Conductance Enhancement Methods 317

11.11 Thermal Resistance at Bolted Joints 332

12 Contact of Nonconforming Smooth Solids 337

12.1 Joint Resistances of Nonconforming Smooth Solids 338

12.2 Point Contact Model 338

12.3 Local Gap Thickness 341

12.4 Contact Resistance of Isothermal Elliptical Contact Area 341

12.5 Elastogap Resistance Model 342

12.6 Joint Radiative Resistance 344

12.7 Joint Resistance of Sphere-Flat Contact 345

12.8 Joint Resistance for Contact of a Sphere and Layered Substrate 349

12.9 Joint Resistance for Elastic–Plastic Contact of Hemisphere and Flat in Vacuum 352

12.10 Ball Bearing Resistance 356

12.11 Line Contact Models 356

12.12 Joint Resistance of Nonconforming Rough Surfaces 359

12.13 System for Nonconforming Rough Surface Contact 360

12.14 Joint Resistance of Nonconforming Rough Surface and Smooth Flat Contact 370

Appendix A Special Functions 379

A. 1 Gamma and Beta Function 379

A. 2 Error Function 382

A. 3 Bessel Functions 384

A. 4 Elliptic Integrals 389

A. 5 Legendre Functions 391

A. 6 Hypergeometric Function 392

Appendix B Hardness 395

B. 1 Micro- and Macro-hardness Indenters 395

B. 2 Micro- and Macro-hardness Tests and Correlations 400

B. 3 Correlation Equations for Vickers Coefficients 406

B. 4 Temperature Effects on Vickers and Brinell Hardness 407

B. 5 Nanoindentation Tests 411

Appendix C Thermal Properties 419

C.1 Thermal Properties of Solids 420

C.2 Thermal Conductivity of Gases 420

C.3 Resistance of Thermal Interface Materials (TIMs) 423

References 423

Index 425