Publisher Description

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.

Author Biography

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.

Table of Contents

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 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 5.10 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 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 8.5 Looking Ahead 115 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

Feature

Chapter 1: Thermodynamic Preliminaries Chapter 2: Fundamentals of Transport Chapter 3: Index Notation Chapter 4: Transport by Advection and Diffusion Chapter 5: Transport with Source Terms Chapter 6: Specification of Transport Problems Chapter 7: Transient One-Dimensional Diffusion Chapter 8: Steady Two-Dimensional Diffusion Chapter 9: Eigenfunction Expansion Chapter 10: Similarity Solution Chapter 11: Superposition of Solutions Chapter 12: Diffusion-Driven Boundaries Chapter 13: Lubrication Theory Chapter 14: Inviscid Flow Chapter 15: Catalog of Ideal Plane Flows Chapter 16: Complex Variable Methods Chapter 17: MacCormack Integration Chapter 18: Open Channel Flow Chapter 19: Open Channel Flow with Friction Chapter 20: Compressible Flow Chapter 21: Quasi-One-Dimensional Compressible Flows Chapter 22: Two-Dimensional Compressible Flows Chapter 23: Runge-Kutta Integration Chapter 24: Boundary Layer Convection Chapter 25: Convection into Developing Laminar Flows Chapter 26: Natural Convection Chapter 27: Internal Flow Chapter 28: Fully Developed Transport in Internal Flows Chapter 29: Influence of Temperature-Dependent Properties Chapter 30: Turbulence Chapter 31: Fully Developed Turbulent Flow Chapter 32: Turbulent Heat and Species Transfer Chapter 33: Fully Developed Transport in Turbulent Flows Chapter 34: Turbulence over Rough Surfaces Chapter 35: Turbulent Boundary Layer Chapter 36: The K-Epsilon Model of Turbulence Chapter 37: The K-Epsilon Model Applied to Fully Developed Flows

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