• Wiley

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Bennett's Transport by Advection and Diffusion provides analytical and numerical tools to aid problem solving in every topic area of the text. These tools foster use of generalized methods in the exercises, and enrich understanding. The book helps to develop the math skills necessary to combine with the conceptual understanding needed to succeed in research and education. The text also improves upon an 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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Ted Bennett is Associate Professor of Mechanical and Environmental Engineering at the University of California – Santa Barbara. He received his PhD from UC Berkeley in 1996. He has taught the transport phenomena course for the last 9 years, and in 2000 was awarded the Distinguished Teaching Award.

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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

2.3 Diffusion Fluxes 17

2.4 Reversible vs. Irreversible Transport 22

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 Non-Cartesian 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

5.11 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 One-Dimensional 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 Two-Dimensional 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

8.6 Problems 115

Chapter 9 Eigenfunction Expansion 119

9.1 Method of Eigenfunction Expansion 119

9.2 Non-Cartesian Coordinate Systems 127

9.3 Transport in Non-Cartesian Coordinates 130

9.4 Problems 139

Chapter 10 Similarity Solution 140

10.1 The Similarity Variable 140

10.2 Laser Heating of a Semi-Infinite Solid 142

10.3 Transient Evaporation 146

10.4 Power Series Solution 148

10.5 Mass Transfer with Time-Dependent 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 Diffusion-Driven 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 Flux-Conservative Equations 249

17.2 MacCormack Integration 250

17.3 Transient Convection 255

17.4 Steady-State 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 Dam-Break Example 273

18.7 Tracer Transport in the Dam-Break Problem 280

18.8 Problems 280

Chapter 19 Open Channel Flow with Friction 284

19.1 The Saint-Venant 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 Quasi-One-Dimensional Compressible Flows 315

21.1 Quasi-One-Dimensional Flow Equations 315

21.2 Quasi-One-Dimensional Steady Flow Equations without Friction 318

21.3 Numerical Solution to Quasi-One-Dimensional Steady Flow 323

21.4 Problems 330

Chapter 22 Two-Dimensional Compressible Flows 333

22.1 Flow through a Diverging Nozzle 333

22.2 Problems 342

Chapter 23 Runge-Kutta Integration 344

23.1 Fourth-Order Runge-Kutta Integration of First-Order Equations 344

23.2 Runge-Kutta 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 (Falkner-Skan 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 Temperature-Dependent Properties 447

29.1 Temperature-Dependent Conductivity in a Solid 447

29.2 Temperature-Dependent Diffusivity in Internal Convection 451

29.3 Temperature-Dependent 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 Smooth-Wall 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 K-Epsilon Model of Turbulence 581

36.1 Turbulent Kinetic Energy Equation 581

36.2 Dissipation Equation for Turbulent Kinetic Energy 585

36.3 The Standard K-Epsilon Model 586

36.4 Problems 587

Chapter 37 The K-Epsilon Model Applied to Fully Developed Flows 589

37.1 K-Epsilon Model for Poiseuille Flow between Smooth Parallel Plates 589

37.2 Transition Point between Mixing Length and K-Epsilon Models 591

37.3 Solving the K and E Equations 593

37.4 Solution of the Momentum Equation with the K-Epsilon 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