Textbook
Transport by Advection and DiffusionSeptember 2012, ©2012

Bennett’s Transport by Advection and Diffusion provides a focused foundation for the principles of transport at the senior or graduate level, with illustrations from a wide range of topics. The text uses an integrated approach to teaching transport phenomena, but widens coverage to include topics such as transport in compressible flows and in open channel flows. Transport by Advection and Diffusion helps students develop the requisite math skills as well as the conceptual understanding needed to succeed in research and education. It presents analytical and numerical tools to aid problem solving in each topic area.
The text is designed for senior or graduate level courses for chemical and mechanical engineering, environmental studies, earth science, materials science, and physics, but it will also appeal to practitioners.
Chapter 1 Thermodynamic Preliminaries 1
1.1 The First and Second Laws of Thermodynamics 1
1.2 Fundamental Equations 2
1.3 Ideal Gas 7
1.4 Constant Density Solid or Liquid 8
1.5 Properties of Mixtures 9
1.6 Summary of Thermodynamic Results 9
1.7 Problems 10
Chapter 2 Fundamentals of Transport 12
2.1 Physics of Advection and Diffusion 12
2.2 Advection Fluxes 14
2.3 Diffusion Fluxes 17
2.4 Reversible vs. Irreversible Transport 22
2.5 Looking Ahead 23
2.6 Problems 23
Chapter 3 Index Notation 25
3.1 Indices 25
3.2 Representation of Cartesian Differential Equations 26
3.3 Special Operators 27
3.4 Operators in NonCartesian Coordinates 31
3.5 Problems 34
Chapter 4 Transport by Advection and Diffusion 36
4.1 Continuity Equation 37
4.2 Transport of Species 39
4.3 Transport of Heat 42
4.4 Transport of Momentum 43
4.5 Summary of Transport Equations without Sources 44
4.6 Conservation Statements from a Finite Volume 44
4.7 Eulerian and Lagrangian Coordinates and the Substantial Derivative 46
4.8 Problems 48
Chapter 5 Transport with Source Terms 50
5.1 Continuity Equation 51
5.2 Species Equation 51
5.3 Heat Equation (without Viscous Heating) 52
5.4 Momentum Equation 54
5.5 Kinetic Energy Equation 55
5.6 Heat Equation (with Viscous Heating) 57
5.7 Entropy Generation in Irreversible Flows 58
5.8 Conservation Statements Derived from a Finite Volume 59
5.9 Leibniz’s Theorem 62
5.10 Looking Ahead 63
5.11 Problems 64
Chapter 6 Specification of Transport Problems 66
6.1 Classification of Equations 66
6.2 Boundary Conditions 67
6.3 Elementary Linear Examples 69
6.4 Nonlinear Example 73
6.5 Scaling Estimates 75
6.6 Problems 78
Chapter 7 Transient OneDimensional Diffusion 82
7.1 Separation of Time and Space Variables 83
7.2 Silicon Doping 89
7.3 Plane Wall With Heat Generation 93
7.4 Transient Groundwater Contamination 97
7.5 Problems 101
Chapter 8 Steady TwoDimensional Diffusion 103
8.1 Separation of Two Spatial Variables 103
8.2 Nonhomogeneous Conditions on Nonadjoining Boundaries 105
8.3 Nonhomogeneous Conditions on Adjoining Boundaries 107
8.4 Nonhomogeneous Condition in Governing Equation 111
8.5 Looking Ahead 115
8.6 Problems 115
Chapter 9 Eigenfunction Expansion 119
9.1 Method of Eigenfunction Expansion 119
9.2 NonCartesian Coordinate Systems 127
9.3 Transport in NonCartesian Coordinates 130
9.4 Problems 139
Chapter 10 Similarity Solution 140
10.1 The Similarity Variable 140
10.2 Laser Heating of a SemiInfinite Solid 142
10.3 Transient Evaporation 146
10.4 Power Series Solution 148
10.5 Mass Transfer with TimeDependent Boundary Condition 152
10.6 Problems 157
Chapter 11 Superposition of Solutions 159
11.1 Superposition in Time 159
11.2 Superposition in Space 164
11.3 Problems 169
Chapter 12 DiffusionDriven Boundaries 172
12.1 Thermal Oxidation 172
12.2 Solidification of an Undercooled Liquid 174
12.3 Solidification of a Binary Alloy from an Undercooled Liquid 178
12.4 Melting of a Solid Initially at the Melting Point 183
12.5 Problems 186
Chapter 13 Lubrication Theory 188
13.1 Lubrication Flows Governed by Diffusion 188
13.2 Scaling Arguments for Squeeze Flow 189
13.3 Squeeze Flow Damping in an Accelerometer Design 191
13.4 Coating Extrusion 194
13.5 Coating Extrusion on a Porous Surface 198
13.6 Reynolds Equation for Lubrication Theory 202
13.7 Problems 203
Chapter 14 Inviscid Flow 206
14.1 The Reynolds Number 207
14.2 Inviscid Momentum Equation 208
14.3 Ideal Plane Flow 209
14.4 Steady Potential Flow through a Box with Staggered Inlet and Exit 210
14.5 Advection of Species through a Box with Staggered Inlet and Exit 215
14.6 Spherical Bubble Dynamics 217
14.7 Problems 221
Chapter 15 Catalog of Ideal Plane Flows 224
15.1 Superposition of Simple Plane Flows 224
15.2 Potential Flow over an Aircraft Fuselage 225
15.3 Force on a Line Vortex in a Uniform Stream 227
15.4 Flow Circulation 229
15.5 Potential Flow over Wedges 231
15.6 Problems 233
Chapter 16 Complex Variable Methods 234
16.1 Brief Review of Complex Numbers 234
16.2 Complex Representation of Potential Flows 235
16.3 The Joukowski Transform 236
16.4 Joukowski Symmetric Airfoils 238
16.5 Joukowski Cambered Airfoils 240
16.6 Heat Transfer between Nonconcentric Cylinders 242
16.7 Transport with Temporally Periodic Conditions 244
16.8 Problems 246
Chapter 17 MacCormack Integration 249
17.1 FluxConservative Equations 249
17.2 MacCormack Integration 250
17.3 Transient Convection 255
17.4 SteadyState Solution of Coupled Equations 259
17.5 Problems 262
Chapter 18 Open Channel Flow 265
18.1 Analysis of Open Channel Flows 265
18.2 Simple Surface Waves 267
18.3 Depression and Elevation Waves 268
18.4 The Hydraulic Jump 269
18.5 Energy Conservation 271
18.6 DamBreak Example 273
18.7 Tracer Transport in the DamBreak Problem 280
18.8 Problems 280
Chapter 19 Open Channel Flow with Friction 284
19.1 The SaintVenant Equations 284
19.2 The Friction Slope 286
19.3 Flow through a Sluice Gate 287
19.4 Problems 293
Chapter 20 Compressible Flow 296
20.1 General Equations of Momentum and Energy Transport 296
20.2 Reversible Flows 298
20.3 Sound Waves 299
20.4 Propagation of Expansion and Compression Waves 300
20.5 Shock Wave (Normal to Flow) 302
20.6 Shock Tube Analytic Description 304
20.7 Shock Tube Numerical Description 307
20.8 Shock Tube Problem with Dissimilar Gases 311
20.9 Problems 312
Chapter 21 QuasiOneDimensional Compressible Flows 315
21.1 QuasiOneDimensional Flow Equations 315
21.2 QuasiOneDimensional Steady Flow Equations without Friction 318
21.3 Numerical Solution to QuasiOneDimensional Steady Flow 323
21.4 Problems 330
Chapter 22 TwoDimensional Compressible Flows 333
22.1 Flow through a Diverging Nozzle 333
22.2 Problems 342
Chapter 23 RungeKutta Integration 344
23.1 FourthOrder RungeKutta Integration of FirstOrder Equations 344
23.2 RungeKutta Integration of Higher Order Equations 347
23.3 Numerical Integration of Bubble Dynamics 349
23.4 Numerical Integration with Shooting 351
23.5 Problems 355
Chapter 24 Boundary Layer Convection 359
24.1 Scanning Laser Heat Treatment 359
24.2 Convection to an Inviscid Flow 363
24.3 Species Transfer to a Vertically Conveyed Liquid Film 369
24.4 Problems 374
Chapter 25 Convection into Developing Laminar Flows 376
25.1 Boundary Layer Flow over a Flat Plate (Blasius Flow) 376
25.2 Species Transfer across the Boundary Layer 383
25.3 Heat Transfer across the Boundary Layer 387
25.4 A Correlation for Forced Heat Convection from a Flat Plate 389
25.5 Transport Analogies 390
25.6 Boundary Layers Developing on a Wedge (FalknerSkan Flow) 392
25.7 Viscous Heating in the Boundary Layer 394
25.8 Problems 396
Chapter 26 Natural Convection 399
26.1 Buoyancy 399
26.2 Natural Convection from a Vertical Plate 400
26.3 Scaling Natural Convection from a Vertical Plate 401
26.4 Exact Solution to Natural Convection Boundary Layer Equations 404
26.5 Problems 411
Chapter 27 Internal Flow 412
27.1 Entrance Region 412
27.2 Heat Transport in an Internal Flow 414
27.3 Entrance Region of Plug Flow between Plates of Constant Heat Flux 415
27.4 Plug Flow between Plates of Constant Temperature 417
27.5 Fully Developed Transport Profiles 419
27.6 Fully Developed Heat Transport in Plug Flow between Plates of Constant Heat Flux 421
27.7 Fully Developed Species Transport in Plug Flow Between Surfaces of Constant Concentration 424
27.8 Problems 426
Chapter 28 Fully Developed Transport in Internal Flows 429
28.1 Momentum Transport in a Fully Developed Flow 429
28.2 Heat Transport in a Fully Developed Flow 430
28.3 Species Transport in a Fully Developed Flow 441
28.4 Problems 444
Chapter 29 Influence of TemperatureDependent Properties 447
29.1 TemperatureDependent Conductivity in a Solid 447
29.2 TemperatureDependent Diffusivity in Internal Convection 451
29.3 TemperatureDependent Gas Properties in Boundary Layer Flow 457
29.4 Problems 462
Chapter 30 Turbulence 465
30.1 The Transition to Turbulence 466
30.2 Reynolds Decomposition 468
30.3 Decomposition of the Continuity Equation 469
30.4 Decomposition of the Momentum Equation 470
30.5 The Mixing Length Model of Prandtl 471
30.6 Regions in a Wall Boundary Layer 473
30.7 Parameters of the Mixing Length Model 476
30.8 Problems 477
Chapter 31 Fully Developed Turbulent Flow 479
31.1 Turbulent Poiseuille Flow Between Smooth Parallel Plates 480
31.2 Turbulent Couette Flow between Smooth Parallel Plates 485
31.3 Turbulent Poiseuille Flow in a SmoothWall Pipe 488
31.4 Utility of the Hydraulic Diameter 490
31.5 Turbulent Poiseuille Flow in a Smooth Annular Pipe 490
31.6 Reichardt’s Formula for Turbulent Diffusivity 495
31.7 Poiseuille Flow with Blowing between Walls 497
31.8 Problems 504
Chapter 32 Turbulent Heat and Species Transfer 507
32.1 Reynolds Decomposition of the Heat Equation 507
32.2 The Reynolds Analogy 508
32.3 Thermal Profile Near the Wall 510
32.4 Mixing Length Model for Heat Transfer 513
32.5 Mixing Length Model for Species Transfer 514
32.6 Problems 515
Chapter 33 Fully Developed Transport in Turbulent Flows 517
33.1 Chemical Vapor Deposition in Turbulent Tube Flow with Generation 517
33.2 Heat Transfer in a Fully Developed Internal Turbulent Flow 522
33.3 Heat Transfer in a Turbulent Poiseuille Flow between Smooth Parallel Plates 523
33.4 Fully Developed Transport in a Turbulent Flow of a Binary Mixture 532
33.5 Problems 543
Chapter 34 Turbulence over Rough Surfaces 545
34.1 Turbulence over a Fully Rough Surface 546
34.2 Turbulent Heat and Species Transfer from a Fully Rough Surface 547
34.3 Application of the Rough Surface Mixing Length Model 549
34.4 Application of Reichardt’s Formula to Rough Surfaces 553
34.5 Problems 563
Chapter 35 Turbulent Boundary Layer 565
35.1 Formulation of Transport in Turbulent Boundary Layer 565
35.2 Formulation of Heat Transport in the Turbulent Boundary Layer 575
35.3 Problems 580
Chapter 36 The KEpsilon Model of Turbulence 581
36.1 Turbulent Kinetic Energy Equation 581
36.2 Dissipation Equation for Turbulent Kinetic Energy 585
36.3 The Standard KEpsilon Model 586
36.4 Problems 587
Chapter 37 The KEpsilon Model Applied to Fully Developed Flows 589
37.1 KEpsilon Model for Poiseuille Flow between Smooth Parallel Plates 589
37.2 Transition Point between Mixing Length and KEpsilon Models 591
37.3 Solving the K and E Equations 593
37.4 Solution of the Momentum Equation with the KEpsilon Model 597
37.5 Turbulent Diffusivity Approaching the Centerline of the Flow 598
37.6 Turbulent Heat Transfer with Constant Temperature Boundary 601
37.7 Problems 604
Appendix A 606
Index 611
 Provides a focused foundation for the principles of transport at the senior or graduate level, with illustrations from a wide range of topics.
 Develops analytical and numerical tools to aid problem solving in every topic area of the text.
 Helps students develop the math skills necessary to combine with conceptual understanding needed to succeed in research and education.
 Uses integrated approach to teaching transport phenomena, but widens this to include topics such as transport in compressible flows and in open channel flows.
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