4 Time-Dependent Conduction 121 4.1 Immersion Cooling or Heating 121 4.2 Lumped Capacitance Model (The “Late” Regime) 124 4.3 Semi-infinite Solid Model (The “Early” 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 .4.3 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 Effectiveness–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 Kirchhoff’s 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
Heat Transfer presents the fundamentals of the generation, use, conversion, and exchange of heat between physical systems. A pioneer in establishing heat transfer as a pillar of the modern thermal sciences, Professor Adrian Bejan presents the fundamental concepts and problem-solving methods of the discipline, predicts the evolution of heat transfer configurations, the principles of thermodynamics, and more.
Building upon his classic 1993 book Heat Transfer, the author maintains his straightforward scientific approach to teaching essential developments such as Fourier conduction, fins, boundary layer theory, duct flow, scale analysis, and the structure of turbulence. In this new volume, Bejan explores topics and research developments that have emerged during the past decade, including the designing of convective flow and heat and mass transfer, the crucial relationship between configuration and performance, and new populations of configurations such as tapered ducts, plates with multi-scale features, and dendritic fins.