Heat Transfer: Thermal Management of Electronics
By Younes Shabany
By Younes Shabany
Contents
Preface…………………………………………………………………………. xiii
About the Author…………………………………………………………………..xv
Chapter 1. Introduction……………………………………………………………..1
1.1 Semiconductor Technology Trends……………………………………….3
1.2 Temperature-Dependent Failures………………………………………….6
1.2.1 Temperature-Dependent Mechanical Failures…………….8
1.2.2 Temperature-Dependent Corrosion Failures…………….. 12
1.2.3 Temperature-Dependent Electrical Failures……………… 12
1.3 Importance of Heat Transfer in Electronics…………………………. 13
1.4 Thermal Design Process…………………………………………………… 14
References………………………………………………………………………………. 18
Chapter 2. Energy, Energy Transfer, and Heat Transfer………………………………… 19
2.1 Energy and Work…………………………………………………………….. 19
2.2 Macroscopic and Microscopic Energies………………………………20
2.3 Energy Transfer and Heat Transfer……………………………………..24
2.4 Equation of State………………………………………………………………25
Problems………………………………………………………………………………….28
References……………………………………………………………………………….28
Chapter 3. Principle of Conservation of Energy……………………………………………29
3.1 First Law of Thermodynamics……………………………………………29
3.2 Energy Balance for a Control Mass……………………………………. 31
3.3 Energy Balance for a Control Volume…………………………………36
Problems………………………………………………………………………………….44
References………………………………………………………………………………. 51
Chapter 4. Heat Transfer Mechanisms………………………………………………………… 53
4.1 Conduction Heat Transfer…………………………………………………. 53
4.2 Convection Heat Transfer………………………………………………….. 57
4.2.1 Simplified Correlations for Convection Heat
Transfer in Air………………………………………………………58
4.3 Radiation Heat Transfer……………………………………………………. 61
Problems………………………………………………………………………………….64
References……………………………………………………………………………….65
Chapter 5. Thermal Resistance Network…………………………………………………….. 67
5.1 Thermal Resistance Concept…………………………………………….. 67
5.2 Series Thermal Layers………………………………………………………72
5.3 Parallel Thermal Layers……………………………………………………. 75
5.4 General Resistance Network………………………………………………79
5.5 Thermal Contact Resistance………………………………………………82
5.6 Thermal Interface Materials………………………………………………85
5.7 Spreading Thermal Resistance…………………………………………..88
5.8 Thermal Resistance of Printed Circuit Boards (PCBs)…………. 91
Problems………………………………………………………………………………….97
References…………………………………………………………………………….. 101
Chapter 6. Thermal Specification of Microelectronic Packages…………………… 103
6.1 Importance of Packaging………………………………………………… 103
6.2 Packaging Types……………………………………………………………. 103
6.3 Thermal Specifications of Microelectronic Packages………….. 110
6.3.1 Junction-to-Air Thermal Resistance………………………. 110
6.3.2 Junction-to-Case and Junction-to-Board
Thermal Resistances……………………………………………. 112
6.3.3 Package Thermal Characterization Parameters………. 114
6.4 Package Thermal Resistance Network………………………………. 115
6.5 Parameters Affecting Thermal Characteristics
of a Package………………………………………………………………….. 119
6.5.1 Package Size………………………………………………………. 119
6.5.2 Packaging Material……………………………………………… 119
6.5.3 Die Size……………………………………………………………… 119
6.5.4 Device Power Dissipation…………………………………….. 121
6.5.5 Air Velocity……………………………………………………….. 121
6.5.6 Board Size and Thermal Conductivity…………………… 122
Problems……………………………………………………………………………….. 123
References…………………………………………………………………………….. 125
Chapter 7. Fins and Heat Sinks………………………………………………………………… 127
7.1 Fin Equation………………………………………………………………….. 127
7.1.1 Infinitely Long Fin………………………………………………. 130
7.1.2 Adiabatic Fin Tip………………………………………………… 132
7.1.3 Convection and Radiation from Fin Tip…………………. 133
7.1.4 Constant Temperature Fin Tip………………………………. 135
7.2 Fin Thermal Resistance, Effectiveness, and Efficiency……….. 140
7.3 Fins with Variable Cross Sections……………………………………. 146
7.4 Heat Sink Thermal Resistance, Effectiveness,
and Efficiency……………………………………………………………….. 150
7.5 Heat Sink Manufacturing Processes…………………………………. 160
Problems……………………………………………………………………………….. 164
References…………………………………………………………………………….. 168
Chapter 8. Heat Conduction Equation………………………………………………………. 169
8.1 One-Dimensional Heat Conduction Equation
for a Plane Wall……………………………………………………………… 171
8.2 General Heat Conduction Equation………………………………….. 175
8.3 Boundary and Initial Conditions………………………………………. 177
8.3.1 Temperature Boundary Condition…………………………. 178
8.3.2 Heat Flux Boundary Condition…………………………….. 179
8.3.3 Convection Boundary Condition…………………………… 181
8.3.4 Radiation Boundary Condition……………………………… 183
8.3.5 General Boundary Condition………………………………… 185
8.3.6 Interface Boundary Condition………………………………. 185
8.4 Steady-State Heat Conduction…………………………………………. 187
8.4.1 One-Dimensional, Steady-State Heat Conduction…… 187
8.4.2 Two-Dimensional, Steady-State Heat Conduction…… 191
8.5 Transient Heat Conduction………………………………………………. 194
8.6 Lumped Systems……………………………………………………………. 196
8.6.1 Simple Lumped System Analysis………………………….. 196
8.6.2 General Lumped System Analysis………………………… 198
8.6.3 Validity of Lumped System Analysis……………………..202
Problems………………………………………………………………………………..204
References……………………………………………………………………………..208
Chapter 9. Fundamentals of Convection Heat Transfer………………………………..209
9.1 Type of Flows…………………………………………………………………209
9.1.1 External and Internal Flows………………………………….209
9.1.2 Forced and Natural Convection Flows…………………… 210
9.1.3 Laminar and Turbulent Flows………………………………. 210
9.1.4 Steady-State and Transient Flows………………………….. 212
9.2 Viscous Force, Velocity Boundary Layer, and
Friction Coefficient………………………………………………………… 212
9.3 Temperature Boundary Layer and Convection Heat
Transfer Coefficient………………………………………………………… 214
9.4 Conservation Equations………………………………………………….. 215
9.5 Boundary Layer Equations……………………………………………… 217
References…………………………………………………………………………….. 218
Chapter 10. Forced Convection Heat Transfer: External Flows……………………. 219
10.1 Normalized Boundary Layer Equations…………………………. 219
10.2 Reynolds Number, Prandtl Number, Eckert Number,
and Nusselt Number……………………………………………………. 221
10.3 Functional Forms of Friction Coefficient and
Convection Heat Transfer Coefficient…………………………….223
10.4 Flow over Flat Plates……………………………………………………227
10.4.1 Laminar Flow over a Flat Plate with
Constant Temperature……………………………………..227
10.4.2 Turbulent Flow over a Flat Plate with
Uniform Temperature………………………………………234
10.4.3 Flow over a Flat Plate with Uniform Surface
Heat Flux………………………………………………………. 237
10.5 Flow Across Cylinders………………………………………………… 239
10.6 Cylindrical Pin-Fin Heat Sink……………………………………….244
10.7 Procedure for Solving External Forced
Convection Problems……………………………………………………246
Problems………………………………………………………………………………248
References…………………………………………………………………………… 253
Chapter 11. Forced Convection Heat Transfer: Internal Flows……………………… 255
11.1 Mean Velocity and Mean Temperature………………………….. 255
11.2 Laminar and Turbulent Pipe Flows……………………………….. 257
11.3 Entry Length and Fully Developed Flow……………………….. 257
11.4 Pumping Power and Convection Heat Transfer in
Internal Flows……………………………………………………………..259
11.5 Velocity Profiles and Friction Factor Correlations……………263
11.6 Temperature Profiles and Convection Heat Transfer
Correlations……………………………………………………………….. 267
11.7 Fans and Pumps………………………………………………………….. 271
11.7.1 Types of Fans………………………………………………… 271
11.7.2 Fan Curve and System Impedance Curve………….. 274
11.7.3 Fan Selection…………………………………………………. 276
11.7.4 Types of Pumps……………………………………………… 279
11.8 Plate-Fin Heat Sinks……………………………………………………. 281
Problems………………………………………………………………………………283
References……………………………………………………………………………285
Chapter 12. Natural Convection Heat Transfer……………………………………………287
12.1 Buoyancy Force and Natural Convection Flows………………287
12.2 Natural Convection Velocity and Temperature
Boundary Layers…………………………………………………………290
12.3 Normalized Natural Convection Boundary Layer
Equations…………………………………………………………………… 291
12.3.1 Grashof and Rayleigh Numbers………………………..293
12.3.2 Functional Form of the Convection Heat
Transfer Coefficient………………………………………… 295
12.4 Laminar and Turbulent Natural Convection over a
Vertical Flat Plate………………………………………………………..296
12.5 Natural Convection around Inclined and
Horizontal Plates…………………………………………………………300
12.6 Natural Convection around Vertical and
Horizontal Cylinders……………………………………………………303
12.7 Natural Convection in Enclosures………………………………….304
12.8 Natural Convection from Array of Vertical Plates…………… 310
12.9 Mixed Convection………………………………………………………. 313
Problems……………………………………………………………………………… 314
References…………………………………………………………………………… 318
Chapter 13. Radiation Heat Transfer…………………………………………………………. 319
13.1 Radiation Intensity and Emissive Power………………………… 320
13.2 Blackbody Radiation……………………………………………………324
13.3 Radiation Properties of Surfaces…………………………………… 326
13.3.1 Surface Emissivity…………………………………………. 326
13.3.2 Surface Absorptivity………………………………………. 328
13.3.3 Surface Reflectivity………………………………………… 329
13.3.4 Surface Transmissivity……………………………………. 330
13.3.5 Kirchhoff’s Law…………………………………………….. 331
13.4 Solar and Atmospheric Radiations………………………………… 332
13.5 Radiosity……………………………………………………………………. 336
13.6 View Factors………………………………………………………………. 337
13.7 Radiation Heat Transfer between Black Bodies……………….340
13.8 Radiation Heat Transfer between Nonblack Bodies…………. 341
13.9 Radiation Heat Transfer from a Plate-Fin Heat Sinks………. 343
Problems………………………………………………………………………………349
References…………………………………………………………………………… 350
Chapter 14. Computer Simulations and Thermal Design…………………………….. 351
14.1 Heat Transfer and Fluid Flow Equations: A Summary…….. 352
14.2 Fundamentals of Computer Simulation………………………….. 353
14.2.1 Steady-State, One-Dimensional
Heat Conduction…………………………………………….. 353
14.2.2 Steady-State, Two-Dimensional
Heat Conduction…………………………………………….. 356
14.2.3 Transient Heat Conduction………………………………. 359
14.2.4 Fluid Flow and Energy Equations…………………….. 362
14.3 Turbulent Flows………………………………………………………….. 373
14.4 Solution of Finite-Difference Equations…………………………380
14.5 Commercial Thermal Simulation Tools…………………………. 381
14.5.1 Creating the Thermal Model……………………………. 382
14.5.2 Creating the Mesh………………………………………….. 391
14.5.3 Solving Flow and Temperature Equations…………. 393
14.5.4 Review the Results…………………………………………. 396
14.5.5 Presenting the Results……………………………………..397
14.6 Importance of Modeling and Simulation in
Thermal Design………………………………………………………….. 398
References……………………………………………………………………………399
Chapter 15. Experimental Techniques and Thermal Design………………………… 401
15.1 Flow Rate Measurement Techniques……………………………… 401
15.2 System Impedance Measurement…………………………………..407
15.3 Fan and Pump Curve Measurements……………………………..409
15.4 Velocity Measurement Methods……………………………………. 410
15.5 Temperature Measurement Techniques………………………….. 414
15.6 Acoustic Noise Measurements……………………………………… 417
15.7 Importance of Experimental Measurements in
Thermal Design………………………………………………………….. 419
References…………………………………………………………………………… 420
Chapter 16. Advanced Cooling Technologies…………………………………………….. 421
16.1 Heat Pipes………………………………………………………………….. 421
16.1.1 Capillary Limit……………………………………………… 423
16.1.2 Boiling Limit………………………………………………….424
16.1.3 Sonic Limit……………………………………………………. 426
16.1.4 Entrainment Limit………………………………………….. 426
16.1.5 Other Heat Pipe Performance Limits………………… 427
16.1.6 Heat Pipe Applications in Electronic Cooling……. 428
16.1.7 Heat Pipe Selection and Modeling……………………. 430
16.1.8 Thermosyphons, Loop Heat Pipes, and
Vapor Chambers…………………………………………….. 435
16.2 Liquid Cooling……………………………………………………………. 439
16.3 Thermoelectric Coolers………………………………………………..445
16.4 Electrohydrodynamic Flow…………………………………………..449
16.5 Synthetic Jet……………………………………………………………….. 450
References…………………………………………………………………………… 452
Appendix: Tables of Material Properties……………………….. 455
Index……………………………………………………………………………….. 471
About the Author…………………………………………………………………..xv
Chapter 1. Introduction……………………………………………………………..1
1.1 Semiconductor Technology Trends……………………………………….3
1.2 Temperature-Dependent Failures………………………………………….6
1.2.1 Temperature-Dependent Mechanical Failures…………….8
1.2.2 Temperature-Dependent Corrosion Failures…………….. 12
1.2.3 Temperature-Dependent Electrical Failures……………… 12
1.3 Importance of Heat Transfer in Electronics…………………………. 13
1.4 Thermal Design Process…………………………………………………… 14
References………………………………………………………………………………. 18
Chapter 2. Energy, Energy Transfer, and Heat Transfer………………………………… 19
2.1 Energy and Work…………………………………………………………….. 19
2.2 Macroscopic and Microscopic Energies………………………………20
2.3 Energy Transfer and Heat Transfer……………………………………..24
2.4 Equation of State………………………………………………………………25
Problems………………………………………………………………………………….28
References……………………………………………………………………………….28
Chapter 3. Principle of Conservation of Energy……………………………………………29
3.1 First Law of Thermodynamics……………………………………………29
3.2 Energy Balance for a Control Mass……………………………………. 31
3.3 Energy Balance for a Control Volume…………………………………36
Problems………………………………………………………………………………….44
References………………………………………………………………………………. 51
Chapter 4. Heat Transfer Mechanisms………………………………………………………… 53
4.1 Conduction Heat Transfer…………………………………………………. 53
4.2 Convection Heat Transfer………………………………………………….. 57
4.2.1 Simplified Correlations for Convection Heat
Transfer in Air………………………………………………………58
4.3 Radiation Heat Transfer……………………………………………………. 61
Problems………………………………………………………………………………….64
References……………………………………………………………………………….65
Chapter 5. Thermal Resistance Network…………………………………………………….. 67
5.1 Thermal Resistance Concept…………………………………………….. 67
5.2 Series Thermal Layers………………………………………………………72
5.3 Parallel Thermal Layers……………………………………………………. 75
5.4 General Resistance Network………………………………………………79
5.5 Thermal Contact Resistance………………………………………………82
5.6 Thermal Interface Materials………………………………………………85
5.7 Spreading Thermal Resistance…………………………………………..88
5.8 Thermal Resistance of Printed Circuit Boards (PCBs)…………. 91
Problems………………………………………………………………………………….97
References…………………………………………………………………………….. 101
Chapter 6. Thermal Specification of Microelectronic Packages…………………… 103
6.1 Importance of Packaging………………………………………………… 103
6.2 Packaging Types……………………………………………………………. 103
6.3 Thermal Specifications of Microelectronic Packages………….. 110
6.3.1 Junction-to-Air Thermal Resistance………………………. 110
6.3.2 Junction-to-Case and Junction-to-Board
Thermal Resistances……………………………………………. 112
6.3.3 Package Thermal Characterization Parameters………. 114
6.4 Package Thermal Resistance Network………………………………. 115
6.5 Parameters Affecting Thermal Characteristics
of a Package………………………………………………………………….. 119
6.5.1 Package Size………………………………………………………. 119
6.5.2 Packaging Material……………………………………………… 119
6.5.3 Die Size……………………………………………………………… 119
6.5.4 Device Power Dissipation…………………………………….. 121
6.5.5 Air Velocity……………………………………………………….. 121
6.5.6 Board Size and Thermal Conductivity…………………… 122
Problems……………………………………………………………………………….. 123
References…………………………………………………………………………….. 125
Chapter 7. Fins and Heat Sinks………………………………………………………………… 127
7.1 Fin Equation………………………………………………………………….. 127
7.1.1 Infinitely Long Fin………………………………………………. 130
7.1.2 Adiabatic Fin Tip………………………………………………… 132
7.1.3 Convection and Radiation from Fin Tip…………………. 133
7.1.4 Constant Temperature Fin Tip………………………………. 135
7.2 Fin Thermal Resistance, Effectiveness, and Efficiency……….. 140
7.3 Fins with Variable Cross Sections……………………………………. 146
7.4 Heat Sink Thermal Resistance, Effectiveness,
and Efficiency……………………………………………………………….. 150
7.5 Heat Sink Manufacturing Processes…………………………………. 160
Problems……………………………………………………………………………….. 164
References…………………………………………………………………………….. 168
Chapter 8. Heat Conduction Equation………………………………………………………. 169
8.1 One-Dimensional Heat Conduction Equation
for a Plane Wall……………………………………………………………… 171
8.2 General Heat Conduction Equation………………………………….. 175
8.3 Boundary and Initial Conditions………………………………………. 177
8.3.1 Temperature Boundary Condition…………………………. 178
8.3.2 Heat Flux Boundary Condition…………………………….. 179
8.3.3 Convection Boundary Condition…………………………… 181
8.3.4 Radiation Boundary Condition……………………………… 183
8.3.5 General Boundary Condition………………………………… 185
8.3.6 Interface Boundary Condition………………………………. 185
8.4 Steady-State Heat Conduction…………………………………………. 187
8.4.1 One-Dimensional, Steady-State Heat Conduction…… 187
8.4.2 Two-Dimensional, Steady-State Heat Conduction…… 191
8.5 Transient Heat Conduction………………………………………………. 194
8.6 Lumped Systems……………………………………………………………. 196
8.6.1 Simple Lumped System Analysis………………………….. 196
8.6.2 General Lumped System Analysis………………………… 198
8.6.3 Validity of Lumped System Analysis……………………..202
Problems………………………………………………………………………………..204
References……………………………………………………………………………..208
Chapter 9. Fundamentals of Convection Heat Transfer………………………………..209
9.1 Type of Flows…………………………………………………………………209
9.1.1 External and Internal Flows………………………………….209
9.1.2 Forced and Natural Convection Flows…………………… 210
9.1.3 Laminar and Turbulent Flows………………………………. 210
9.1.4 Steady-State and Transient Flows………………………….. 212
9.2 Viscous Force, Velocity Boundary Layer, and
Friction Coefficient………………………………………………………… 212
9.3 Temperature Boundary Layer and Convection Heat
Transfer Coefficient………………………………………………………… 214
9.4 Conservation Equations………………………………………………….. 215
9.5 Boundary Layer Equations……………………………………………… 217
References…………………………………………………………………………….. 218
Chapter 10. Forced Convection Heat Transfer: External Flows……………………. 219
10.1 Normalized Boundary Layer Equations…………………………. 219
10.2 Reynolds Number, Prandtl Number, Eckert Number,
and Nusselt Number……………………………………………………. 221
10.3 Functional Forms of Friction Coefficient and
Convection Heat Transfer Coefficient…………………………….223
10.4 Flow over Flat Plates……………………………………………………227
10.4.1 Laminar Flow over a Flat Plate with
Constant Temperature……………………………………..227
10.4.2 Turbulent Flow over a Flat Plate with
Uniform Temperature………………………………………234
10.4.3 Flow over a Flat Plate with Uniform Surface
Heat Flux………………………………………………………. 237
10.5 Flow Across Cylinders………………………………………………… 239
10.6 Cylindrical Pin-Fin Heat Sink……………………………………….244
10.7 Procedure for Solving External Forced
Convection Problems……………………………………………………246
Problems………………………………………………………………………………248
References…………………………………………………………………………… 253
Chapter 11. Forced Convection Heat Transfer: Internal Flows……………………… 255
11.1 Mean Velocity and Mean Temperature………………………….. 255
11.2 Laminar and Turbulent Pipe Flows……………………………….. 257
11.3 Entry Length and Fully Developed Flow……………………….. 257
11.4 Pumping Power and Convection Heat Transfer in
Internal Flows……………………………………………………………..259
11.5 Velocity Profiles and Friction Factor Correlations……………263
11.6 Temperature Profiles and Convection Heat Transfer
Correlations……………………………………………………………….. 267
11.7 Fans and Pumps………………………………………………………….. 271
11.7.1 Types of Fans………………………………………………… 271
11.7.2 Fan Curve and System Impedance Curve………….. 274
11.7.3 Fan Selection…………………………………………………. 276
11.7.4 Types of Pumps……………………………………………… 279
11.8 Plate-Fin Heat Sinks……………………………………………………. 281
Problems………………………………………………………………………………283
References……………………………………………………………………………285
Chapter 12. Natural Convection Heat Transfer……………………………………………287
12.1 Buoyancy Force and Natural Convection Flows………………287
12.2 Natural Convection Velocity and Temperature
Boundary Layers…………………………………………………………290
12.3 Normalized Natural Convection Boundary Layer
Equations…………………………………………………………………… 291
12.3.1 Grashof and Rayleigh Numbers………………………..293
12.3.2 Functional Form of the Convection Heat
Transfer Coefficient………………………………………… 295
12.4 Laminar and Turbulent Natural Convection over a
Vertical Flat Plate………………………………………………………..296
12.5 Natural Convection around Inclined and
Horizontal Plates…………………………………………………………300
12.6 Natural Convection around Vertical and
Horizontal Cylinders……………………………………………………303
12.7 Natural Convection in Enclosures………………………………….304
12.8 Natural Convection from Array of Vertical Plates…………… 310
12.9 Mixed Convection………………………………………………………. 313
Problems……………………………………………………………………………… 314
References…………………………………………………………………………… 318
Chapter 13. Radiation Heat Transfer…………………………………………………………. 319
13.1 Radiation Intensity and Emissive Power………………………… 320
13.2 Blackbody Radiation……………………………………………………324
13.3 Radiation Properties of Surfaces…………………………………… 326
13.3.1 Surface Emissivity…………………………………………. 326
13.3.2 Surface Absorptivity………………………………………. 328
13.3.3 Surface Reflectivity………………………………………… 329
13.3.4 Surface Transmissivity……………………………………. 330
13.3.5 Kirchhoff’s Law…………………………………………….. 331
13.4 Solar and Atmospheric Radiations………………………………… 332
13.5 Radiosity……………………………………………………………………. 336
13.6 View Factors………………………………………………………………. 337
13.7 Radiation Heat Transfer between Black Bodies……………….340
13.8 Radiation Heat Transfer between Nonblack Bodies…………. 341
13.9 Radiation Heat Transfer from a Plate-Fin Heat Sinks………. 343
Problems………………………………………………………………………………349
References…………………………………………………………………………… 350
Chapter 14. Computer Simulations and Thermal Design…………………………….. 351
14.1 Heat Transfer and Fluid Flow Equations: A Summary…….. 352
14.2 Fundamentals of Computer Simulation………………………….. 353
14.2.1 Steady-State, One-Dimensional
Heat Conduction…………………………………………….. 353
14.2.2 Steady-State, Two-Dimensional
Heat Conduction…………………………………………….. 356
14.2.3 Transient Heat Conduction………………………………. 359
14.2.4 Fluid Flow and Energy Equations…………………….. 362
14.3 Turbulent Flows………………………………………………………….. 373
14.4 Solution of Finite-Difference Equations…………………………380
14.5 Commercial Thermal Simulation Tools…………………………. 381
14.5.1 Creating the Thermal Model……………………………. 382
14.5.2 Creating the Mesh………………………………………….. 391
14.5.3 Solving Flow and Temperature Equations…………. 393
14.5.4 Review the Results…………………………………………. 396
14.5.5 Presenting the Results……………………………………..397
14.6 Importance of Modeling and Simulation in
Thermal Design………………………………………………………….. 398
References……………………………………………………………………………399
Chapter 15. Experimental Techniques and Thermal Design………………………… 401
15.1 Flow Rate Measurement Techniques……………………………… 401
15.2 System Impedance Measurement…………………………………..407
15.3 Fan and Pump Curve Measurements……………………………..409
15.4 Velocity Measurement Methods……………………………………. 410
15.5 Temperature Measurement Techniques………………………….. 414
15.6 Acoustic Noise Measurements……………………………………… 417
15.7 Importance of Experimental Measurements in
Thermal Design………………………………………………………….. 419
References…………………………………………………………………………… 420
Chapter 16. Advanced Cooling Technologies…………………………………………….. 421
16.1 Heat Pipes………………………………………………………………….. 421
16.1.1 Capillary Limit……………………………………………… 423
16.1.2 Boiling Limit………………………………………………….424
16.1.3 Sonic Limit……………………………………………………. 426
16.1.4 Entrainment Limit………………………………………….. 426
16.1.5 Other Heat Pipe Performance Limits………………… 427
16.1.6 Heat Pipe Applications in Electronic Cooling……. 428
16.1.7 Heat Pipe Selection and Modeling……………………. 430
16.1.8 Thermosyphons, Loop Heat Pipes, and
Vapor Chambers…………………………………………….. 435
16.2 Liquid Cooling……………………………………………………………. 439
16.3 Thermoelectric Coolers………………………………………………..445
16.4 Electrohydrodynamic Flow…………………………………………..449
16.5 Synthetic Jet……………………………………………………………….. 450
References…………………………………………………………………………… 452
Appendix: Tables of Material Properties……………………….. 455
Index……………………………………………………………………………….. 471