Preface ....................................................... xii
Nomenclature ................................................... xv
Chapter 1 Introduction ......................................... 1
1.1 Introduction ............................................... 1
1.2 Physical Concepts .......................................... 3
1.2.1 Sensible Heat ....................................... 3
1.2.2 Latent Heat ......................................... 5
1.2.3 Phase Change ........................................ 7
1.3 Molecular Level Presentation ............................... 9
1.3.1 Introduction ........................................ 9
1.3.2 Kinetic Theory ..................................... 10
1.3.3 Intermolecular Forces and Boltzmann Transport
Equation ........................................... 16
1.3.4 Cohesion and Adhesion .............................. 20
1.3.5 Enthalpy and Energy ................................ 21
1.4 Fundamentals of Momentum, Heat and Mass Transfer .......... 23
1.4.1 Continuum Flow Limitations ......................... 23
1.4.2 Momentum, Heat and Mass Transfer ................... 25
1.4.3 Microscale and Nanoscale Transport Phenomena ....... 43
1.4.4 Dimensional Analysis ............................... 48
1.4.5 Scaling ............................................ 59
1.5 Modern Applications of Heat and Mass Transfer ............. 61
1.5.1 Energy Systems ..................................... 62
1.5.2 Biological and Biomedical Systems .................. 66
1.5.3 Security ........................................... 69
1.5.4 Information Technology ............................. 71
1.5.5 Nanotechnology ..................................... 74
References ................................................ 78
Problems .................................................. 83
Chapter 2 Generalized Governing Equations ..................... 89
2.1 Introduction .............................................. 89
2.2 Macroscopic (Integral) Local Instance Formulation ......... 91
2.2.1 Conservation of Mass ............................... 93
2.2.2 Momentum Equation .................................. 94
2.2.3 Energy Equation .................................... 95
2.2.4 The Second Law of Thermodynamics ................... 99
2.2.5 Species ............................................ 99
2.3 Microscopic (Differential) Local Instance Formulation .... 101
2.3.1 Conservation of Mass .............................. 102
2.3.2 Momentum Equation ................................. 103
2.3.3 Energy Equation ................................... 105
2.3.4 The Second Law of Thermodynamics .................. 110
2.3.5 Species ........................................... 111
2.3.6 Classification of PDEs and Boundary Conditions .... 121
2.3.7 Jump and Boundary Conditions at the Interfaces .... 124
2.3.8 Rarefied Vapor Self-Diffusion Model ............... 137
2.3.9 An Extension: Combustion .......................... 138
2.4 Volume Averaged Models ................................... 145
2.4.1 Overview of Averaging Approaches .................. 145
2.4.2 Volume-Averaged Multi-Fluid Models ................ 150
2.4.3 Volume-Averaged Homogeneous Model ................. 161
2.4.4 An Extension: Porous Media ........................ 167
2.5 Fundamentals of Turbulence ............................... 181
2.5.1 Description of Turbulence ......................... 181
2.5.2 Time-Averaged Governing Equations ................. 184
References ............................................... 190
Problems ................................................. 192
Chapter 3 Heat Conduction .................................... 209
3.1 Introduction ............................................. 209
3.2 Steady State Heat Conduction ............................. 212
3.2.1 One Dimensional Heat Conduction ................... 212
3.2.2 Multidimensional Heat Conduction .................. 227
3.3 Unsteady State Heat Conduction ........................... 238
3.3.1 Lumped Analysis ................................... 238
3.3.2 One Dimensional Transient Heat Conduction ......... 240
3.3.3 Multidimensional Transient Heat Conduction ........ 261
3.4 Numerical Simulation of Heat Conduction Problems ......... 264
3.4.1 One-Dimensional Steady-State Conduction ........... 265
3.4.2 One-Dimensional Transient Conduction .............. 270
3.4.3 Multidimensional Transient Conduction ............. 273
3.5 Melting and Solidification ............................... 276
3.5.1 Introduction ...................................... 276
3.5.2 Exact Solution .................................... 281
3.5.3 Integral Approximate Solution ..................... 289
3.5.4 Numerical Simulation .............................. 304
3.6 Microscale Heat Conduction ............................... 314
3.6.1 Extensions of Classic Model ....................... 314
3.6.2 Two-Step Model .................................... 316
3.6.3 Microscale Phase Change ........................... 319
References ............................................... 323
Problems ................................................. 325
Chapter 4 External Convective Heat and Mass Transfer .......... 339
4.1 Introduction ............................................. 339
4.2 Concepts of the Boundary Layer Theory .................... 341
4.3 Boundary Layer Approximation ............................. 343
4.4 Governing Equations for Boundary Layer Approximation ..... 344
4.5 Laminar Boundary Layer Solutions for Momentum, Heat,
and Mass Transfer ........................................ 350
4.6 Similarity Solutions ..................................... 351
4.6.1 Uncoupled Mass, Momentum, and Heat Transfer
Problems .......................................... 352
4.6.2 Coupled Mass, Momentum, and Heat Transfer
Problems .......................................... 362
4.7 Integral Methods ......................................... 369
4.8 Computational Methodologies for Forced Convection ........ 375
4.8.1 One-Dimensional Steady-State Convection and
Diffusion ......................................... 376
4.8.2 Multidimensional Convection and Diffusion
Problems .......................................... 385
4.8.3 Numerical Solution of Flow Field .................. 388
4.8.4 Numerical Simulation of Interfaces and Free
Surfaces .......................................... 395
4.9 Application of Computational Methods ..................... 400
4.10 Analogies and Differences in Different Transport
Phenomena ................................................ 406
4.11 Turbulence ............................................... 412
4.11.1 Turbulent Boundary Layer Equations ................ 412
4.11.2 Algebraic Models for Eddy Diffusivity ............. 414
4.11.3 K-ε Model ......................................... 422
4.11.4 Momentum and Heat Transfer for Turbulent Flow
over a Flat Plate ................................. 424
References ............................................... 430
Problems ................................................. 433
Chapter 5 Internal Convective Heat Transfer .................. 438
5.1 Introduction ............................................. 438
5.2 Basic Definitions, Terminology and Governing Equations ... 439
5.3 Hydrodynamically and Thermally Fully Developed Laminar
Flow ..................................................... 447
5.4 Hydrodynamically Fully Developed and Thermally
Developing Laminar Flow .................................. 453
5.4.1 Constant Wall Temperature ......................... 454
5.4.2 Constant Heat Flux at the Wall .................... 456
5.5 Hydrodynamically Fully Developed Flow with Coupled
Thermal and Concentration Entry Effects .................. 458
5.5.1 Sublimation inside an Adiabatic Tube .............. 458
5.5.2 Sublimation inside a Tube Subjected to External
Heating ........................................... 463
5.6 Developing Flow, Thermal and Concentration Effects ....... 470
5.7 Full Numerical Solutions ................................. 475
5.8 Forced Convection in Microchannels ....................... 482
5.8.1 Introduction ...................................... 482
5.8.2 Fully Developed Laminar Flow and Temperature
Profile ........................................... 485
5.8.3 Fully Developed Flow with Developing Temperature
Profile ........................................... 493
5.9 Turbulence ............................................... 499
5.9.1 Time-Averaged Governing Equations ................. 499
5.9.2 Velocity Profile and Friction Coefficient for
Fully Developed Flow .............................. 500
5.9.3 Heat Transfer in Fully Developed Turbulent Flow ... 503
References ............................................... 509
Problems ................................................. 511
Chapter 6 Natural Convection ................................. 515
6.1 Introduction ............................................. 515
6.2 Governing Equations for Natural Convection ............... 517
6.2.1 Generalized Governing Equations ................... 517
6.2.2 External Natural Convection from Heated Vertical
Plate ............................................. 519
6.2.3 Dimensionless Parameters .......................... 520
6.3 Scale Analysis ........................................... 521
6.3.1 High Prandtl Number Fluids (Pr >> 1) .............. 523
6.3.2 Low Prandtl Number Fluids (Pr << 1) ............... 525
6.4 External Natural Convection .............................. 526
6.4.1 Similarity Solution for Natural Convection on
a Vertical Surface ................................ 526
6.4.2 Integral Solution for Laminar and Turbulent
Natural Convection ................................ 533
6.4.3 Natural Convection over Inclined and Horizontal
Surfaces .......................................... 540
6.4.4 Natural Convection over Cylinders and Spheres ..... 543
6.4.5 Free Boundary Flow ................................ 551
6.5 Natural Convection in Enclosures ......................... 555
6.5.1 Scale Analysis .................................... 556
6.5.2 Rectangular Enclosures ............................ 560
6.5.3 Annular Space between Concentric Cylinders and
Spheres ........................................... 569
6.6 Natural Convection in Melting and Solidification ......... 572
6.6.1 Solidification around Horizontal Cylinder ......... 572
6.6.2 Melting in a Rectangular Enclosure Heated from
the Side .......................................... 575
6.7 Instability Analysis of Natural Convection ............... 580
References ............................................... 583
Problems ................................................. 587
Chapter 7 Condensation and Evaporation ....................... 590
7.1 Introduction ............................................. 590
7.2 Dropwise Condensation .................................... 599
7.2.1 Surface Tension and Capillary Pressure ............ 599
7.2.2 Thermal Resistances in the Condensation
Processes ......................................... 603
7.2.3 Heat Transfer Coefficient for Dropwise
Condensation ...................................... 607
7.3 Filmwise Condensation .................................... 609
7.3.1 Regimes of Filmwise Condensation .................. 609
7.3.2 Modeling for Laminar Film Condensation of
a Binary Vapor Mixture ............................ 610
7.3.3 Filmwise Condensation in a Stagnant Pure Vapor
Reservoir ......................................... 615
7.3.4 Effects of Vapor Motion ........................... 623
7.3.5 Turbulent Film Condensation ....................... 629
7.3.6 Other Filmwise Condensation Configurations ........ 634
7.3.7 Effects of Noncondensable Gas ..................... 636
7.4 Falling Film Evaporation on a Heated Wall and Spray
Cooling .................................................. 642
7.4.1 Classical Nusselt Evaporation ..................... 642
7.4.2 Laminar Falling Film with Surface Waves ........... 646
7.4.3 Turbulent Falling Film ............................ 649
7.4.4 Surface Spray Cooling ............................. 649
References ............................................... 652
Problems ................................................. 655
Chapter 8 Boiling ............................................ 665
8.1 Introduction ............................................. 665
8.2 Pool Boiling Regimes ..................................... 666
8.3 Nucleate Boiling ......................................... 669
8.3.1 Nucleation and Inception .......................... 670
8.3.2 Bubble Dynamics ................................... 675
8.3.3 Bubble Detachment ................................. 685
8.3.4 Nucleate Site Density ............................. 690
8.3.5 Bubble Growth and Merger .......................... 691
8.3.6 Heat Transfer in Nucleate Boiling ................. 695
8.4 Critical Heat Flux ....................................... 701
8.5 Transition Boiling and Minimum Heat Flux ................. 705
8.5.1 Transition Boiling ................................ 705
8.5.2 Minimum Heat Flux ................................. 707
8.6 Film Boiling ............................................. 709
8.6.1 Film Boiling Analysis ............................. 709
8.6.2 Direct Numerical Simulation of Film Boiling ....... 719
8.6.3 Leidenfrost Phenomena ............................. 722
References ............................................... 730
Problems ................................................. 735
Chapter 9 Fundamentals of Thermal Radiation .................. 739
9.1 Electromagnetic Waves and Thermal Radiation .............. 739
9.2 The Blackbody as the Ideal Radiator ...................... 741
9.2.1 The Planck Distribution and its Consequences ...... 742
9.2.2 The Blackbody Fraction ............................ 748
9.3 Properties of Real Surfaces: Definitions, Measurements
and Prediction ........................................... 750
9.3.1 Opaque Surface Property Definitions ............... 750
9.3.2 EM Theory Predictions of Properties ............... 759
9.4 Application and Exploitation of Radiative Properties ..... 766
9.4.1 Spacecraft Thermal Design ......................... 766
9.4.2 Solar Thermal Energy Collectors ................... 771
9.4.3 Other Property Choices for Radiation/Surface
Interactions ...................................... 777
9.5 High-energy Radiation-Surface Interactions ............... 778
9.5.1 Nanoscale Surface Modification for Tailoring
Properties ........................................ 780
9.5.2 Macroscale Laser-Surface Interactions ............. 781
9.6 Light Pipes and Fiber Optics ............................. 783
9.7 Infrared Sensing, Cameras and Photography ................ 785
9.8 Other Contemporary Applications and Research ............. 786
References ............................................... 787
Problems ................................................. 788
CHAPTER 10 Heat Transfer by Radiation ......................... 794
10.1 Radiative Transfer through Transparent Media ............. 794
10.1.1 Transfer between Two Areas ........................ 794
10.1.2 Diffuse Surfaces: The Configuration Factor ........ 796
10.1.3 Configuration Factor Algebra ...................... 800
10.2 The Enclosure; The Net Radiation Method for Diffuse
Surfaces ................................................. 804
10.2.1 Radiosity, Irradiation, and Net Energy Transfer ... 805
10.2.2 Gray Surfaces ..................................... 807
10.2.3 Nongray Surfaces .................................. 814
10.2.4 Surfaces with Varying Temperature, Radiative
Flux, or Properties ............................... 817
10.3 Multimode Heat Transfer with Radiation ................... 821
10.3.1 Numerical Methods ................................. 824
10.3.2 Conduction Dominated Problems ..................... 826
10.3.3 Radiation Dominated Problems ...................... 826
10.3.4 Problems with Both Modes Significant .............. 827
10.4 Inverse Problems ......................................... 828
10.4.1 An Inverse Design Problem ......................... 830
10.4.2 Regularization .................................... 835
10.4.3 Unresolved Problems in Inverse Cases .............. 837
10.5 The Effect of Participating Media ........................ 838
10.5.1 Absorption, Emission and Scattering from
a Medium .......................................... 838
10.5.2 Properties of Participating Media ................. 839
10.5.3 The Radiative Transfer Equation ................... 844
10.5.4 Some Limiting Solutions for Radiative Transfer .... 848
10.6 Applications of Radiative Transfer ....................... 862
10.6.1 Radiation Measurement and Sensing: IR Cameras,
Optical Pyrometers and Remote Sensing ............. 862
10.6.2 Atmospheric Phenomena Caused by Scattering ........ 863
10.6.3 Pollution, Greenhouse Gases and the Greenhouse
Effect, Atmospheric Radiation and the Global
Energy Balance ................................... 865
References ............................................... 866
Problems ................................................. 868
List of Appendices ............................................ 875
Appendix A Constants, Units and Conversion Factors ......... 876
Appendix В Transport Properties of Solids .................. 880
Appendix С Transport Properties of Gases and Liquids
at Atmospheric Pressure ......................... 888
Appendix D Transport Properties for Phase Change ........... 895
Appendix E Mass Transfer Properties ........................ 899
Appendix F Configuration Factors and Surface Properties
for Radiation ................................... 911
Appendix G Mathematical Relations .......................... 916
Index ......................................................... 925
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