Preface ........................................................ xv
Frequently Used Notation ..................................... xvii
1 Thermophysical and Transport Fundamentals .................... 1
1.1 Conservation Principles ................................. 1
1.1.1 Lagrangian and Eulerian Frames ................... 1
1.1.2 Mass Conservation ................................ 2
1.1.3 Conservation of Momentum ......................... 3
1.1.4 Conservation of Energy ........................... 6
1.2 Multicomponent Mixtures ................................ 11
1.2.1 Basic Definitions and Relations ................. 11
1.2.2 Thermodynamic Properties ........................ 15
1.3 Fundamentals of Diffusive Mass Transfer ................ 17
1.3.1 Species Mass Conservation ....................... 17
1.3.2 Diffusive Mass Flux and Fick's Law .............. 18
1.3.3 Species Mass Conservation When Fick's Law
Applies ......................................... 19
1.3.4 Other Types of Diffusion ........................ 20
1.3.5 Diffusion in Multicomponent Mixtures ............ 20
1.4 Boundary and Interfacial Conditions .................... 22
1.4.1 General Discussion .............................. 22
1.4.2 Gas-Liquid Interphase ........................... 24
1.4.3 Interfacial Temperature ......................... 24
1.4.4 Sparingly Soluble Gases ......................... 27
1.4.5 Convention for Thermal and Mass Transfer
Boundary Conditions ............................. 30
1.5 Transport Properties ................................... 31
1.5.1 Mixture Rules ................................... 31
1.5.2 Transport Properties of Gases and the Gas-
Kinetic Theory .................................. 32
1.5.3 Diffusion of Mass in Liquids .................... 37
1.6 The Continuum Flow Regime and Size Convention for
Flow Passages .......................................... 38
2 Boundary Layers ............................................. 44
2.1 Boundary Layer on a Flat Plate ......................... 44
2.2 Laminar Boundary-Layer Conservation Equations .......... 48
2.3 Laminar Boundary-Layer Thicknesses ..................... 51
2.4 Boundary-Layer Separation .............................. 53
2.5 Nondimensionalization of Conservation Equations and
Similitude ............................................. 54
Problems .................................................... 58
3 External Laminar Flow: Similarity Solutions for Forced
Laminar Boundary Layers ..................................... 61
3.1 Hydrodynamics of Flow Parallel to a Flat Plate ......... 61
3.2 Heat and Mass Transfer During Low-Velocity Laminar
Flow Parallel to a Flat Plate .......................... 65
3.3 Heat Transfer During Laminar Parallel Flow Over
a Flat Plate With Viscous Dissipation .................. 71
3.4 Hydrodynamics of Laminar Flow Past a Wedge ............. 73
3.5 Heat Transfer During Laminar Flow Past a Wedge ......... 78
3.6 Effects of Compressibility and Property Variations ..... 80
Problems .................................................... 85
4 Internal Laminar Flow ....................................... 90
4.1 Couette and Poiseuille Flows ........................... 90
4.2 The Development of Velocity, Temperature, and
Concentration Profiles ................................. 94
4.2.1 The Development of Boundary Layers .............. 94
4.2.2 Hydrodynamic Parameters of Developing Flow ...... 97
4.2.3 The Development of Temperature and
Concentration Profiles ......................... 100
4.3 Hydrodynamics of Fully Developed Flow ................. 103
4.4 Fully Developed Hydrodynamics and Developed
Temperature or Concentration Distributions ............ 107
4.4.1 Circular Tube .................................. 107
4.4.2 Flat Channel ................................... 110
4.4.3 Rectangular Channel ............................ 113
4.4.4 Triangular Channel ............................. 113
4.4.5 Concentric Annular Duct ........................ 114
4.5 Fully Developed Hydrodynamics, Thermal or
Concentration Entrance Regions ........................ 117
4.5.1 Circular Duct With Uniform Wall Temperature
Boundary Conditions ............................ 117
4.5.2 Circular Duct With Arbitrary Wall Temperature
Distribution in the Axial Direction ............ 124
4.5.3 Circular Duct With Uniform Wall Heat Flux ...... 126
4.5.4 Circular Duct With Arbitrary Wall Heat Flux
Distribution in the Axial Coordinate ........... 129
4.5.5 Flat Channel With Uniform Heat Flux Boundary
Conditions ..................................... 130
4.5.6 Flat Channel With Uniform Wall Temperature
Boundary Conditions ............................ 132
4.5.7 Rectangular Channel ............................ 135
4.6 Combined Entrance Region .............................. 135
4.7 Effect of Fluid Property Variations ................... 137
Appendix 4A: The Sturm-Liouville Boundary-Value Problems ... 141
Problems ................................................... 141
5 Integral Methods ........................................... 151
5.1 Integral Momentum Equations ........................... 151
5.2 Solutions to the Integral Momentum Equation ........... 153
5.2.1 Laminar Flow of an Incompressible Fluid
Parallel to a Flat Plate Without Wall
Injection ...................................... 153
5.2.2 Turbulent Flow of an Incompressible Fluid
Parallel to a Flat Plate Without Wall
Injection ...................................... 156
5.2.3 Turbulent Flow of an Incompressible Fluid
Over a Body of Revolution ...................... 158
5.3 Energy Integral Equation .............................. 159
5.4 Solutions to the Energy Integral Equation ............. 161
5.4.1 Parallel Flow Past a Flat Surface .............. 161
5.4.2 Parallel Flow Past a Flat Surface With an
Adiabatic Segment .............................. 163
5.4.3 Parallel Flow Past a Flat Surface With
Arbitrary Wall Surface Temperature or Heat
Flux ........................................... 165
5.5 Approximate Solutions for Flow Over Axisymmetric
Bodies ................................................ 167
Problems ................................................... 173
6 Fundamentals of Turbulence and External Turbulent Flow ..... 177
6.1 Laminar-Turbulent Transition and the Phenomenology
of Turbulence ......................................... 177
6.2 Fluctuations and Time (Ensemble) Averaging ............ 180
6.3 Reynolds Averaging of Conservation Equations .......... 181
6.4 Eddy Viscosity and Eddy Diffusivity ................... 183
6.5 Universal Velocity Profiles ........................... 185
6.6 The Mixing-Length Hypothesis and Eddy Diffusivity
Models ................................................ 188
6.7 Temperature and Concentration Laws of the Wall ........ 192
6.8 Kolmogorov Theory of the Small Turbulence Scales ...... 196
6.9 Flow Past Blunt Bodies ................................ 200
Problems ................................................... 205
7 Internal Turbulent Flow .................................... 208
7.1 General Remarks ....................................... 208
7.2 Hydrodynamics of Turbulent Duct Flow .................. 211
7.2.1 Circular Duct .................................. 211
7.2.2 Noncircular Ducts .............................. 217
7.3 Heat Transfer: Fully Developed Flow ................... 218
7.3.1 Universal Temperature Profile in a Circular
Duct ........................................... 218
7.3.2 Application of Eddy Diffusivity Models for
Circular Ducts ................................. 221
7.3.3 Noncircular Ducts .............................. 224
7.4 Heat Transfer: Fully Developed Hydrodynamics,
Thermal Entrance Region ............................... 224
7.4.1 Circular Duct With Uniform Wall Temperature
or Concentration ............................... 224
7.4.2 Circular Duct With Uniform Wall Heat Flux ...... 226
7.4.3 Some Useful Correlations for Circular Ducts .... 229
7.4.4 Noncircular Ducts .............................. 231
7.5 Combined Entrance Region .............................. 231
Problems ................................................... 238
8 Effect of Transpiration on Friction, Heat, and Mass
Transfer ................................................... 243
8.1 Couette Flow Film Model ............................... 243
8.2 Gas-Liquid Interphase ................................. 248
Problems ................................................... 256
9 Analogy Among Momentum, Heat, and Mass Transfer ............ 258
9.1 General Remarks ....................................... 258
9.2 Reynolds Analogy ...................................... 259
9.3 Prandtl-Taylor Analogy ................................ 261
9.4 Von Kaiman Analogy .................................... 263
9.5 The Martinelli Analogy ................................ 265
9.6 The Analogy of Yu et al ............................... 265
9.7 Chilton-Colburn Analogy ............................... 267
Problems ................................................... 272
10 Natural Convection ......................................... 275
10.1 Natural-Convection Boundary Layers on Flat Surfaces ... 275
10.2 Phenomenology ......................................... 278
10.3 Scaling Analysis of Laminar Boundary Layers ........... 280
10.4 Similarity Solutions for a Semi-Infinite Vertical
Surface ............................................... 285
10.5 Integral Analysis ..................................... 289
10.6 Some Widely Used Empirical Correlations for Flat
Vertical Surfaces ..................................... 294
10.7 Natural Convection on Horizontal Flat Surfaces ........ 295
10.8 Natural Convection on Inclined Surfaces ............... 297
10.9 Natural Convection on Submerged Bodies ................ 298
10.10 Natural Convection in Vertical Flow Passages ......... 300
10.11 Natural Convection in Enclosures ..................... 304
10.12 Natural Convection in a Two-Dimensional Rectangle
With Heated Vertical Sides ........................... 305
10.13 Natural Convection in Horizontal Rectangles .......... 307
10.14 Natural Convection in Inclined Rectangular
Enclosures ........................................... 309
10.15 Natural Convection Caused by the Combined Thermal
and Mass Diffusion Effects ........................... 311
10.15.1 Conservation Equations and Scaling
Analysis ..................................... 311
10.15.2 Heat and Mass Transfer Analogy ............... 316
10.16 Solutions for Natural Convection Caused by Combined
Thermal and Mass Diffusion Effects ................... 317
Problems ................................................... 327
11 Mixed Convection ........................................... 332
11.1 Laminar Boundary-Layer Equations and Scaling
Analysis .............................................. 332
11.2 Solutions for Laminar Flow ............................ 337
11.3 Stability of Laminar Flow and Laminar-Turbulent
Transition ............................................ 341
11.4 Correlations for Laminar External Flow ................ 343
11.5 Correlations for Turbulent External Flow .............. 348
11.6 Internal Flow ......................................... 349
11.6.1 General Remarks ................................ 349
11.6.2 Flow Regime Maps ............................... 351
11.7 Some Empirical Correlations for Internal Flow ......... 351
Problems ................................................... 358
12 Turbulence Models .......................................... 362
12.1 Reynolds-Averaged Conservation Equations and the
Eddy Diffusivity Concept .............................. 362
12.2 One-Equation Turbulence Models ........................ 364
12.3 Near-Wall Turbulence Modeling and Wall Functions ...... 367
12.4 The K-ε Model ......................................... 371
12.4.1 General Formulation ............................ 371
12.4.2 Near-Wall Treatment ............................ 374
12.4.3 Turbulent Heat and Mass Fluxes ................. 376
12.5 Other Two-Equation Turbulence Models .................. 376
12.6 The Reynolds Stress Transport Models .................. 377
12.6.1 General Formulation ............................ 377
12.6.2 Simplification for Heat and Mass Transfer ...... 380
12.6.3 Near-Wall Treatment of Turbulence .............. 380
12.6.4 Summary of Equations and Unknowns .............. 381
12.7 Algebraic Stress Models ............................... 381
12.8 Turbulent Models for Buoyant Flows .................... 382
12.9 Direct Numerical Simulation ........................... 385
12.10 Large Eddy Simulation ................................ 390
12.11 Computational Fluid Dynamics ......................... 394
Problems ................................................... 395
13 Flow and Heat Transfer in Miniature Flow Passages .......... 397
13.1 Size Classification of Miniature Flow Passages ........ 397
13.2 Regimes in Gas-Carrying Vessels ....................... 399
13.3 The Slip Flow and Temperature-Jump Regime ............. 402
13.4 Slip Couette Flow ..................................... 406
13.5 Slip Flow in a Flat Channel ........................... 408
13.5.1 Hydrodynamics of Fully Developed Flow .......... 408
13.5.2 Thermally Developed Heat Transfer, UHF ......... 410
13.5.3 Thermally Developed Heat Transfer, UWT ......... 413
13.6 Slip Flow in Circular Microtubes ...................... 415
13.6.1 Hydrodynamics of Fully Developed Flow .......... 415
13.6.2 Thermally Developed Flow Heat Transfer, UHF .... 416
13.6.3 Thermally Developed Flow Heat Transfer, UWT .... 418
13.6.4 Thermally Developing Flow ...................... 420
13.7 Slip Flow in Rectangular Channels ..................... 422
13.7.1 Hydrodynamics of Fully Developed Flow .......... 422
13.7.2 Heat Transfer .................................. 424
13.8 Slip Flow in Other Noncircular Channels ............... 426
13.9 Compressible Flow in Microchannels with Negligible
Rarefaction ........................................... 427
13.9.1 General Remarks ................................ 427
13.9.2 One-Dimensional Compressible Flow of an Ideal
Gas in a Constant-Cross-Section Channel ........ 428
13.10 Continuum Flow in Miniature Flow Passages ............ 431
Problems ................................................... 441
APPENDIX A: Constitutive Relations in Polar Cylindrical and
Spherical Coordinates ...................................... 449
APPENDIX B: Mass Continuity and Newtonian Incompressible
Fluid Equations of Motion in Polar Cylindrical and
Spherical Coordinates ...................................... 451
APPENDIX C: Energy Conservation Equations in Polar
Cylindrical and Spherical Coordinates for Incompressible
Fluids With Constant Thermal Conductivity .................. 453
APPENDIX D: Mass-Species Conservation Equations in Polar
Cylindrical and Spherical Coordinates for Incompressible
Fluids ..................................................... 454
APPENDIX E: Thermodynamic Properties of Saturated Water and
Steam ...................................................... 456
APPENDIX F: Transport Properties of Saturated Water and
Steam ...................................................... 458
APPENDIX G: Properties of Selected Ideal Gases at
1 Atmosphere ............................................... 459
APPENDIX H: Binary Diffusion Coefficients of Selected Gases
in Air at 1 Atmosphere ..................................... 465
APPENDIX I: Henry's Constant, in bars, of Dilute Aqueous
Solutions of Selected Substances at Moderate Pressures ..... 466
APPENDIX J: Diffusion Coefficients of Selected Substances in
Water at Infinite Dilution at 25°C ......................... 467
APPENDIX К: Lennard-Jones Potential Model Constants for
Selected Molecules ......................................... 468
APPENDIX L: Collision Integrals for the Lennard-Jones
Potential Model ............................................ 469
APPENDIX M: Some RANS-Type Turbulence Models .................. 470
M.l The Spalart-Allmaras Model ............................ 470
M.2 The K-ω Model.......................................... 472
M.3 The K-ε Nonlinear Reynolds Stress Model ............... 475
M.4 The RNG K-ε Model ..................................... 477
M.5 The Low-Re RSM of Launder and Shima ................... 478
APPENDIX N: Physical Constants ................................ 480
APPENDIX O: Unit Conversions .................................. 482
APPENDIX P: Summary of Important Dimensionless Numbers ........ 485
APPENDIX Q: Summary of Some Useful Heat Transfer and
Friction-Factor Correlations ............................... 487
References .................................................... 501
Index ......................................................... 517
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