Preface ........................................................ xv
Nomenclature .................................................. xxi
Chapter 1 Introduction to Transport Phenomena ................... 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 .............................. 15
1.3.4 Cohesion and Adhesion .............................. 19
1.3.5 Enthalpy and Energy ................................ 19
1.4 Review of Fundamentals of Transport Phenomena ............. 21
1.4.1 Continuum Flow Limitations ......................... 21
1.4.2 Transport Phenomena ................................ 23
1.4.3 Microscale and Nanoscale Transport Phenomena ....... 44
1.4.4 Dimensional Analysis ............................... 48
1.4.5 Scaling ............................................ 58
1.5 Multiphase Systems and Phase Changes ...................... 62
1.5.1 Overview and Classifications ....................... 62
1.5.2 Solid-Liquid Phase Change Including Melting
and Solidification ................................. 66
1.5.3 Solid-Vapor Phase Change Including Sublimation
and Vapor Deposition ............................... 67
1.5.4 Interfacial Phenomena .............................. 68
1.5.5 Condensation ....................................... 69
1.5.6 Evaporation and Boiling ............................ 71
1.5.7 Two-Phase Flow ..................................... 72
1.6 Applications of Transport Phenomena in Multiphase
Systems ................................................... 73
1.6.1 Energy Systems, Including Fuel Cells and
Combustors ......................................... 73
1.6.2 Food and Biological Material Processing ............ 83
1.6.3 Laser-Assisted Manufacturing ....................... 84
1.6.4 Heat Pipes ......................................... 88
1.6.5 Electronics Cooling ................................ 92
1.6.6 Microscale Phase Change Heat Transfer .............. 96
References ................................................ 98
Problems ................................................. 103
Chapter 2 Thermodynamics of Multiphase Systems ............... 107
2.1 Introduction ............................................. 107
2.2 Fundamentals of Thermodynamics ........................... 108
2.2.1 Thermodynamic Laws ................................ 108
2.2.2 Thermodynamic Relations ........................... 109
2.2.3 Gibbs Phase Rule .................................. 111
2.3 Equilibrium and Stability of Single-Phase Systems ........ 111
2.3.1 Equilibrium Criteria for Pure Substances .......... 112
2.3.2 Maxwell Relations ................................. 114
2.3.3 Closed Systems with Compositional Change .......... 115
2.3.4 Stability Criteria ................................ 117
2.3.5 System with Chemical Reactions .................... 123
2.4 Thermodynamic Surfaces and Equations of State ............ 128
2.4.1 Thermodynamic Surfaces of a Single-Component
Substance ......................................... 128
2.4.2 p-T, p-v and T-s Phase Diagrams for a Pure
Substance ......................................... 129
2.4.3 Equations of State for Pure Substances ............ 131
2.4.4 Phase Diagrams for Multicomponent Systems ......... 136
2.5 Equilibrium and Stability of Multiphase Systems .......... 141
2.5.1 Two-Phase Single-Component Systems ................ 141
2.5.2 Clapeyron Equation ................................ 142
2.5.3 Multiphase Multicomponent Systems ................. 146
2.5.4 Metastable Equilibrium and Nucleation ............. 147
2.6 Thermodynamics at the Interfaces ......................... 150
2.6.1 Equilibrium at the Interface ...................... 150
2.6.2 Surface Tension: Thermodynamic Definitions ........ 152
2.6.3 Microscale Vapor Bubbles and Liquid Droplets ...... 156
2.6.4 Disjoining Pressure: Thermodynamic and
Hydrodynamic Definitions .......................... 162
2.6.5 Superheat-Thermodynamic and Kinetic Limit
Definitions ....................................... 167
References ............................................... 172
Problems ................................................. 173
Chapter 3 Generalized Governing Equations: Local Instance
Formulations ........................................ 177
3.1 Introduction .............................................. 177
3.2 Macroscopic (Integral) Formulation ........................ 179
3.2.1 Conservation of Mass .............................. 183
3.2.2 Momentum Equation ................................. 183
3.2.3 Energy Equation ................................... 185
3.2.4 The Second Law of Thermodynamics .................. 186
3.2.5 Species ........................................... 187
3.3 Microscopic (Differential) Formulation .................... 189
3.3.1 Conservation of Mass .............................. 190
3.3.2 Momentum Equation ................................. 191
3.3.3 Energy Equation ................................... 193
3.3.4 The Second Law of Thermodynamics .................. 198
3.3.5 Species ........................................... 199
3.3.6 Jump Conditions at the Interfaces ................. 206
3.3.7 Classification of PDEs and Boundary Conditions .... 219
3.3.8 Rarefied Vapor Self-Diffusion Model ............... 222
3.3.9 An Extension: Combustion .......................... 223
References ............................................... 230
Problems ................................................. 231
Chapter 4 Generalized Governing Equations: Averaging
Formulations ........................................ 238
4.1 Introduction ............................................. 238
4.2 Overview of Averaging Approaches ......................... 239
4.2.1 Eulerian Averaging ................................ 239
4.2.2 Lagrangian Averaging .............................. 243
4.2.3 Molecular Statistical Averaging ................... 243
4.3 Volume-Averaged Multi-Fluid Models ....................... 244
4.3.1 Continuity Equation ............................... 244
4.3.2 Momentum Equation ................................. 245
4.3.3 Energy Equation ................................... 248
4.3.4 The Second Law of Thermodynamics .................. 251
4.3.5 Species ........................................... 252
4.4 Volume-Averaged Homogeneous Model ........................ 258
4.4.1 Continuity Equation ............................... 258
4.4.2 Momentum Equation ................................. 258
4.4.3 Energy Equation ................................... 259
4.4.4 The Second Law of Thermodynamics .................. 260
4.4.5 Species ........................................... 260
4.5 Area-Averaged Models for Channel Flows ................... 264
4.5.1 Homogeneous Model ................................. 266
4.5.2 Separated Flow Model .............................. 270
4.6 An Extension: Porous Media ............................... 273
4.6.1 Conservation of Mass .............................. 275
4.6.2 Conservation of Momentum .......................... 276
4.6.3 Energy Equation ................................... 285
4.6.4 The Second Law of Thermodynamics .................. 287
4.6.5 Species ........................................... 288
4.6.6 Multiphase Transport in Porous Media .............. 289
4.7 Boltzmann Statistical Averaging ........................... 303
4.7.1 Boltzmann Equation ................................ 303
4.7.2 Lattice Boltzmann Model (LBM) ..................... 311
4.7.3 LBM for Multiphase Flows .......................... 314
References ............................................... 318
Problems ................................................. 320
Chapter 5 Solid-Liquid-Vapor Phenomena and Interfacial Heat
and Mass Transfer ................................... 331
5.1 Introduction ............................................. 331
5.2 Surface Tension .......................................... 332
5.2.1 Capillary Pressure: The Young-Laplace Equation .... 332
5.2.2 Interface Shapes at Equilibrium ................... 334
5.2.3 Effects of Interfacial Tension Gradients .......... 337
5.3 Wetting Phenomena and Contact Angles ..................... 342
5.3.1 Equilibrium and Apparent Contact Angles ........... 342
5.3.2 Wettability and Adsorption ........................ 344
5.4 Phase Equilibrium in Microscale Interfacial Systems ...... 347
5.4.1 Ultra-Thin Liquid Films, Disjoining Pressure ...... 347
5.4.2 Change in Saturated Vapor Pressure over a Curved
Interface ......................................... 350
5.5 Transport Effects at the Interface ....................... 351
5.5.1 Interfacial Mass, Momentum, Energy, and Species
Balances .......................................... 351
5.5.2 Interfacial Resistance in Vaporization and
Condensation ...................................... 366
5.5.3 Formation of and Heat Transfer through Thin
Liquid Films ...................................... 368
5.5.4 Heat Transfer in the Thin-Film Region of an
Axially-Grooved Structure ......................... 373
5.6 Dynamic Behaviors of Interfaces .......................... 382
5.6.1 Rayleigh-Taylor and Kelvin-Helmholtz
Instabilities ..................................... 382
5.6.2 Surface Waves on Liquid Film Flow ................. 386
5.7 Numerical Simulation of Interfaces and Free Surfaces ..... 392
5.7.1 Continuum Approach: Interface Tracking
Techniques ........................................ 393
5.7.2 Noncontinuum Approach: Molecular Dynamic
Simulation ........................................ 402
References ............................................... 406
Problems ................................................. 410
Chapter 6 Melting and Solidification .......................... 421
6.1 Introduction ............................................. 421
6.2 Boundary Conditions at the Solid-Liquid Interface ........ 424
6.3 Exact Solution ........................................... 427
6.3.1 Governing Equations of the Solidification
Problem ........................................... 427
6.3.2 Dimensionless Form of the Governing Equations ..... 429
6.3.3 Exact Solution of the One-Region Problem .......... 430
6.3.4 Exact Solution of the Two-Region Problem .......... 435
6.4 Integral Approximate Solution ............................ 436
6.4.1 Heat Conduction in a Semi-Infinite Body ........... 436
6.4.2 One-Region Problem ................................ 439
6.4.3 Two-Region Problem ................................ 443
6.4.5 Solidification/Melting in Cylindrical Coordinate
Systems ........................................... 450
6.5 Numerical Simulation ..................................... 454
6.5.1 Overview .......................................... 454
6.5.2 Enthalpy Method ................................... 455
6.5.3 Equivalent Heat Capacity Method ................... 460
6.5.4 Temperature-Transforming Model .................... 462
6.6 Solidification of a Binary Solution System ............... 465
6.6.1 Overview .......................................... 465
6.6.2 Integral Approximate Method ....................... 466
6.6.3 Mixture Model ..................................... 471
6.6.4 Volume-A veraging Model ........................... 475
6.7 Contact Melting in a Rectangular Cavity .................. 479
6.7.1 Fixed Melting and Contact Melting ................. 479
6.7.2 Contact Melting in a Rectangular Cavity ........... 480
6.8 Melting and Solidification in Porous Media ............... 484
6.8.1 Convection-Controlled One-Region Melting
Problem ........................................... 484
6.8.2 An Enthalpy Model for Two-Region Melting/
Solidification .................................... 488
6.9 Applications of Solid-Liquid Phase Change ................ 492
6.9.1 Latent Heat Thermal Energy Storage ................ 492
6.9.2 Heat Pipe Startup from Frozen State ............... 495
6.9.3 Thermal Protection from Intense Localized
Heating Using PCM ................................. 499
6.9.4 Microwave Thawing of Food and Biological
Materials ......................................... 501
6.9.5 Laser Drilling .................................... 505
6.9.6 Selective Laser Sintering (SLS) of Metal
Powders ........................................... 508
6.10 Microscale Phase Change .................................. 512
6.10.1 Overview .......................................... 512
6.10.2 Two-Step Model .................................... 513
References ............................................... 517
Problems ................................................. 522
Chapter 7 Sublimation and Vapor Deposition .................... 531
7.1 Introduction ............................................. 531
7.2 Sublimation .............................................. 534
7.2.1 Sublimation over a Flat Plate ..................... 534
7.2.2 Sublimation inside an Adiabatic Tube .............. 538
7.2.3 Sublimation inside a Tube Subjected to External
Heating ........................................... 543
7.2.4 Sublimation with Chemical Reaction ................ 550
7.3 Chemical Vapor Deposition (CVD) .......................... 554
7.3.1 Introduction ....................................... 554
7.3.2 Governing Equations of CVD ........................ 557
7.3.3 Transport Properties .............................. 559
7.3.4 Typical Selected Applications ..................... 563
References ............................................... 574
Problems ................................................. 577
Chapter 8 Condensation ........................................ 581
8.1 Introduction ............................................. 581
8.2 Dropwise Condensation .................................... 587
8.2.1 Dropwise Condensation Formation Theories .......... 587
8.2.2 Critical Droplet Radius for Spontaneous Growth
and Destruction ................................... 588
8.2.3 Thermal Resistances in the Condensation
Processes ......................................... 594
8.2.4 Heat Transfer Coefficient for Dropwise
Condensation ...................................... 597
8.3 Filmwise Condensation .................................... 599
8.3.1 Regimes of Filmwise Condensation .................. 599
8.3.2 Modeling of Laminar Film Condensation of a
Binary Vapor Mixture .............................. 600
8.3.3 Filmwise Condensation in a Stagnant Pure Vapor
Reservoir ......................................... 605
8.3.4 Effects of Vapor Motion ........................... 614
8.3.5 Turbulent Film Condensation ....................... 619
8.3.6 Other Filmwise Condensation Configurations ........ 625
8.3.7 Effects of Noncondensable Gas ..................... 627
8.3.8 Flooding or Entrainment Limit ..................... 633
8.4 Nongravitational Condensate Removal ...................... 638
8.4.1 Condensation in a Tube with Suction at the
Porous Wall ....................................... 638
8.4.2 Annular Condensation Heat Transfer in a
Microgravity Environment .......................... 643
8.4.3 Condensation Removal by a Centrifugal Field
via a Rotating Disk ............................... 649
8.4.4 Condensation by Capillary Action in a Heat Pipe ... 652
8.5 Film Condensation in Porous Media ........................ 658
8.5.1 Overview .......................................... 658
8.5.2 Gravity-Dominated Film Condensation on an
Inclined Wall ..................................... 660
8.5.3 Effect of Surface Tension on Condensation in
Porous Media ...................................... 663
References ............................................... 667
Problems ................................................. 670
Chapter 9 Evaporation ......................................... 678
9.1 Introduction ............................................. 678
9.2 Classification and Criteria of Evaporation ............... 681
9.3 Evaporation from an Adiabatic Wall ....................... 685
9.3.1 Evaporation from Horizontal Films ................. 685
9.3.2 Evaporation from a Vertical Falling Film .......... 691
9.4 Falling Film Evaporation on a Heated Wall ................ 701
9.4.1 Classical Nusselt Evaporation ..................... 702
9.4.2 Laminar Falling Film with Surface Waves ........... 706
9.4.3 Turbulent Falling Film ............................ 714
9.4.4 Surface Spray Cooling ............................. 716
9.4.5 Evaporation from a Wedge or Cone Embedded in a
Porous Medium ..................................... 718
9.5 Direct Contact Evaporation ............................... 724
9.5.1 Evaporation of a Liquid Droplet in a Hot Gas ...... 724
9.5.2 Evaporation of a Liquid Jet in a Pure Vapor ....... 727
9.6 Evaporation inside Pores and Slots/Microchannels ......... 729
9.6.1 Evaporation from Cylindrical Pore under
Low/Moderate Heat Flux ............................ 730
9.6.2 Fluid Flow Effect in Pore/Slots during
Evaporation ....................................... 734
9.6.3 Evaporation under High Heat Flux .................. 738
9.6.4 Evaporation in an Inclined MicroChannel ........... 744
9.7 Evaporation from Inverted Meniscus in Porous Media ....... 747
References ............................................... 755
Problems ................................................. 758
Chapter 10 Boiling ............................................ 765
10.1 Introduction ............................................. 765
10.2 Pool Boiling Regimes ..................................... 767
10.3 Nucleate Boiling ......................................... 770
10.3.1 Nucleation and Inception .......................... 770
10.3.2 Bubble Dynamics ................................... 775
10.3.3 Bubble Detachment ................................. 786
10.3.4 Nucleate Site Density ............................. 791
10.3.5 Bubble Growth and Merger .......................... 792
10.3.6 Heat Transfer in Nucleate Boiling ................. 796
10.4 Critical Heat Flux ....................................... 803
10.5 Transition Boiling and Minimum Heat Flux ................. 806
10.5.1 Transition Boiling ................................ 806
10.5.2 Minimum Heat Flux ................................. 809
10.6 Film Boiling ............................................. 811
10.6.1 Film Boiling Analysis ............................. 811
10.6.2 Direct Numerical Simulation of Film Boiling ....... 821
10.6.3 Leidenfrost Phenomena ............................. 824
10.7 Boiling in Porous Media .................................. 833
10.7.1 Nucleate Boiling in a Wicked Surface .............. 833
10.7.2 Boiling in Porous Media Heated from Below ......... 837
10.7.3 Film Boiling Analysis in Porous Media ............. 840
References ............................................... 843
Problems ................................................. 849
Chapter 11 Two-Phase Flow and Heat Transfer ................... 853
11.1 Introduction ............................................. 853
11.2 Flow Patterns of Liquid-Vapor (Gas) Two-Phase Flow ....... 854
11.2.1 Concepts and Notations ............................ 854
11.2.2 Flow Patterns in Vertical Tubes ................... 857
11.2.3 Flow Patterns in Horizontal Tubes ................. 861
11.3 Two-Phase Flow Models .................................... 864
11.3.1 Homogeneous Flow Model ............................ 864
11.3.2 Separated Flow Model .............................. 866
11.3.3 Frictional Pressure Drop .......................... 870
11.3.4 Void Fraction ..................................... 878
11.4 Forced Convective Condensation in Tubes .................. 883
11.4.1 Two-Phase Flow Regimes ............................ 883
11.4.2 Heat Transfer Predictions ......................... 885
11.5 Forced Convective Boiling in Tubes ....................... 889
11.5.1 Regimes in Horizontal and Vertical Tubes .......... 889
11.5.2 Bubble Lift-Off Size in Forced Convective
Boiling ........................................... 895
11.5.3 Heat Transfer Predictions ......................... 899
11.6 Two-Phase Flow and Heat Transfer in Micro- and
Minichannels ............................................. 904
11.6.1 Two-Phase Flow Patterns ........................... 904
11.6.2 Flow Condensation ................................. 908
11.6.3 Row Evaporation and Boiling ....................... 920
References ............................................... 937
Problems ................................................. 944
Appendix A: Constants and Conversion Factors .................. 950
Appendix B: Thermophysical Properties ......................... 954
Appendix C: Vectors and Tensors .............................. 1006
Index ........................................................ 1013
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