Preface xi
About the Author xv
Acknowledgments xvi
List of Symbols xvii
About the Companion Website xxvi
1 Introduction 1
1.1 Fundamental Concepts 1
1.1.1 Heat Transfer 1
1.1.2 Temperature 2
1.1.3 Specific Heats 4
1.2 The Objective of Heat Transfer 5
1.3 Conduction 6
1.3.1 The Fourier Law 6
1.3.2 Thermal Conductivity 8
1.3.3 Cartesian Coordinates 12
1.3.4 Cylindrical Coordinates 14
1.3.5 Spherical Coordinates 15
1.3.6 Initial and Boundary Conditions 16
1.4 Convection 18
1.5 Radiation 23
1.6 Evolutionary Design 24
1.6.1 Irreversible Heating 25
1.6.2 Reversible Heating 27
References 29
Problems 30
2 Unidirectional Steady Conduction 37
2.1 Thin Walls 37
2.1.1 Thermal Resistance 37
2.1.2 Composite Walls 39
2.1.3 Overall Heat Transfer Coefficient 40
2.2 Cylindrical Shells 42
2.3 Spherical Shells 44
2.4 Critical Insulation Radius 45
2.5 Variable Thermal Conductivity 48
2.6 Internal Heat Generation 49
2.7 Evolutionary Design: Extended Surfaces (Fins) 51
2.7.1 The Enhancement of Heat Transfer 51
2.7.2 Constant Cross-Sectional Area 53
2.7.2.1 The Longitudinal Conduction Model 53
2.7.2.2 Long Fin 54
2.7.2.3 Fin with Insulated Tip 55
2.7.2.4 Heat Transfer Through the Tip 57
2.7.2.5 Fin Efficiency 58
2.7.2.6 Fin Effectiveness 59
2.7.3 Variable Cross-Sectional Area 60
2.7.4 Scale Analysis: When the Unidirectional Conduction Model Is Valid 61
2.7.5 Fin Shape Subject to Volume Constraint 63
2.7.6 Heat Tube Shape 64
2.7.7 Rewards from Freedom 66
References 70
Problems 71
3 Multidirectional Steady Conduction 85
3.1 Analytical Solutions 85
3.1.1 Two-Dimensional Conduction in Cartesian Coordinates 85
3.1.1.1 Homogeneous Boundary Conditions 85
3.1.1.2 Separation of Variables 87
3.1.1.3 Orthogonality 88
3.1.2 Heat Flux Boundary Conditions 92
3.1.3 Superposition of Solutions 95
3.1.4 Cylindrical Coordinates 98
3.1.5 Three-Dimensional Conduction 100
3.2 Integral Method 101
3.3 Scale Analysis 103
3.4 Evolutionary Design 104
3.4.1 Shape Factors 104
3.4.2 Trees: Volumeâ"Point Flow 108
3.4.3 Rewards from Freedom 111
References 113
Problems 114
4 Time-Dependent Conduction 121
4.1 Immersion Cooling or Heating 121
4.2 Lumped Capacitance Model (The âLateâ Regime) 124
4.3 Semi-infinite Solid Model (The âEarlyâ Regime) 125
4.3.1 Constant Surface Temperature 125
4.3.2 Constant Heat Flux Surface 128
4.3.3 Surface in Contact with Fluid Flow 129
4.4 Unidirectional Conduction 133
4.4.1 Plate 133
4.4.2 Cylinder 138
4.4.3 Sphere 141
4.4.4 Plate, Cylinder, and Sphere with Fixed Surface Temperature 142
4.5 Multidirectional Conduction 148
4.6 Concentrated Sources and Sinks 152
4.6.1 Instantaneous (One-Shot) Sources and Sinks 152
4.6.2 Persistent (Continuous) Sources and Sinks 154
4.6.3 Moving Heat Sources 156
4.7 Melting and Solidification 158
4.8 Evolutionary Design 162
4.8.1 Spacings Between Buried Heat Sources 162
4.8.2 The S-Curve Growth of Spreading and Collecting 164
References 166
Problems 167
5 External Forced Convection 177
5.1 Classification of Convection Configurations 177
5.2 Basic Principles of Convection 179
5.2.1 Mass Conservation Equation 179
5.2.2 Momentum Equations 180
5.2.3 Energy Equation 185
5.3 Laminar Boundary Layer 189
5.3.1 Velocity Boundary Layer 189
5.3.2 Thermal Boundary Layer 195
5.3.2.1 Thick Thermal Boundary Layer 195
5.3.2.2 Thermal Boundary Layer 196
5.3.3 Nonisothermal Wall 198
5.3.4 Film Temperature 200
5.4 Turbulent Boundary Layer 202
5.4.1 Transition from Laminar to Turbulent Flow 202
5.4.2 Time-Averaged Equations 203
5.4.3 Eddy Diffusivities 206
5.4.4 Wall Friction 208
5.4.5 Heat Transfer 211
5.5 Other External Flows 215
5.5.1 Single Cylinder 215
5.5.2 Sphere 218
5.5.3 Other Body Shapes 218
5.5.4 Arrays of Cylinders 219
5.5.5 Turbulent Jets 221
5.6 Evolutionary Design 223
5.6.1 Size of Object with Heat Transfer 223
5.6.2 Evolution of Size 225
5.6.3 Visualization: Heatlines 226
References 227
Problems 230
6 Internal Forced Convection 245
6.1 Laminar Flow Through a Duct 245
6.1.1 Entrance Region 245
6.1.2 Fully Developed Flow Region 247
6.1.3 Friction Factor and Pressure Drop 249
6.2 Heat Transfer in Laminar Flow 252
6.2.1 Thermal Entrance Region 252
6.2.2 Thermally Fully Developed Region 253
6.2.3 Uniform Wall Heat Flux 255
6.2.4 Isothermal Wall 258
6.3 Turbulent Flow 261
6.3.1 Transition, Entrance Region, and Fully Developed Flow 261
6.3.2 Friction Factor and Pressure Drop 263
6.3.3 Heat Transfer Coefficient 265
6.4 Total Heat Transfer Rate 269
6.4.1 Isothermal Wall 269
6.4.2 Uniform Wall Heating 271
6.5 Evolutionary Design 271
6.5.1 Size of Duct with Fluid Flow 271
6.5.2 Tree-Shaped Ducts 272
6.5.3 Spacings 274
6.5.4 Packaging for Maximum Heat Transfer Density 276
References 277
Problems 278
7 Natural Convection 291
7.1 What Drives Natural Convection? 291
7.2 Boundary Layer Flow on Vertical Wall 292
7.2.1 Boundary Layer Equations 292
7.2.2 Scale Analysis of the Laminar Regime 295
7.2.3 Isothermal Wall 299
7.2.4 Transition and the Effect of Turbulence 302
7.2.5 Uniform Heat Flux 304
7.3 Other External Flows 305
7.3.1 Thermally Stratified Reservoir 305
7.3.2 Inclined Walls 306
7.3.3 Horizontal Walls 308
7.3.4 Horizontal Cylinder 310
7.3.5 Sphere 310
7.3.6 Vertical Cylinder 310
7.3.7 Other Immersed Bodies 311
7.4 Internal Flows 314
7.4.1 Vertical Channels 314
7.4.2 Enclosures Heated from the Side 317
7.4.3 Enclosures Heated from Below 320
7.4.4 Inclined Enclosures 323
7.4.5 Annular Space Between Horizontal Cylinders 325
7.4.6 Annular Space Between Concentric Spheres 326
7.5 Evolutionary Design 327
7.5.1 Spacings 327
7.5.2 Miniaturization 329
References 331
Problems 333
8 Convection with Change of Phase 343
8.1 Condensation 343
8.1.1 Laminar Film on Vertical Surface 343
8.1.2 Turbulent Film on Vertical Surface 350
8.1.3 Film Condensation in Other Configurations 353
8.1.4 Dropwise and Direct-Contact Condensation 359
8.2 Boiling 361
8.2.1 Pool Boiling 361
8.2.2 Nucleate Boiling and Peak Heat Flux 365
8.2.3 Film Boiling and Minimum Heat Flux 369
8.2.4 Flow Boiling 373
8.3 Evolutionary Design 373
8.3.1 Latent Heat Storage 374
8.3.2 Shaping Inserts for Faster Melting 375
8.3.3 Rhythmic Surface Renewal 376
References 376
Problems 378
9 Heat Exchangers 387
9.1 Classification of Heat Exchangers 387
9.2 Overall Heat Transfer Coefficient 391
9.3 Log-Mean Temperature Difference Method 397
9.3.1 Parallel Flow 397
9.3.2 Counterflow 399
9.3.3 Other Flow Arrangements 400
9.4 Effectivenessâ"NTU Method 408
9.4.1 Effectiveness and Limitations Posed by the Second Law 408
9.4.2 Parallel Flow 409
9.4.3 Counterflow 410
9.4.4 Other Flow Arrangements 411
9.5 Pressure Drop 417
9.5.1 Pumping Power 417
9.5.2 Abrupt Contraction and Enlargement 418
9.5.3 Acceleration and Deceleration 422
9.5.4 Tube Bundles in Cross-Flow 423
9.5.5 Compact Heat Exchanger Surfaces 423
9.6 Evolutionary Design 428
9.6.1 Entrance-Length Heat Exchangers 428
9.6.2 Dendritic Heat Exchangers 428
9.6.3 Heat Exchanger Size 430
9.6.4 Heat Tubes with Convection 432
References 435
Problems 437
10 Radiation 447
10.1 Introduction 447
10.2 Blackbody Radiation 448
10.2.1 Definitions 448
10.2.2 Temperature and Energy 450
10.2.3 Intensity 452
10.2.4 Emissive Power 453
10.3 Heat Transfer Between Black Surfaces 460
10.3.1 Geometric View Factor 460
10.3.2 Relations Between View Factors 463
10.3.2.1 Reciprocity 463
10.3.2.2 Additivity 464
10.3.2.3 Enclosure 466
10.3.3 Two-Surface Enclosures 467
10.4 Diffuse-Gray Surfaces 471
10.4.1 Emissivity 471
10.4.2 Absorptivity and Reflectivity 475
10.4.3 Kirchhoffâs Law 482
10.4.4 Two-Surface Enclosures 485
10.4.5 Enclosures with More than Two Surfaces 489
10.5 Participating Media 493
10.5.1 Volumetric Absorption 493
10.5.2 Gas Emissivities and Absorptivities 494
10.5.3 Gas Surrounded by Black Surface 500
10.5.4 Gray Medium Surrounded by Diffuse-Gray Surfaces 501
10.6 Evolutionary Design 502
10.6.1 Terrestrial Solar Power 502
10.6.2 Extraterrestrial Solar Power 503
10.6.3 Climate 505
References 506
Problems 507
Appendix A Constants and Conversion Factors 521
Appendix B Properties of Solids 527
Appendix C Properties of Liquids 541
Appendix D Properties of Gases 551
Appendix E Mathematical Formulas 557
Appendix F Turbulence Transition 565
Appendix G Extremum Subject to Constraint 571
Author Index 573
Subject Index 579
