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Summary
Summary
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 Notes
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 | p. 1 |
1.1 The First and Second Laws of Thermodynamics | p. 1 |
1.2 Fundamental Equations | p. 2 |
1.3 Ideal Gas | p. 7 |
1.4 Constant Density Solid or Liquid | p. 8 |
1.5 Properties of Mixtures | p. 9 |
1.6 Summary of Thermodynamic Results | p. 9 |
Problems | p. 10 |
Chapter 2 Fundamentals of Transport | p. 12 |
2.1 Physics of Advection and Diffusion | p. 12 |
2.2 Advection Fluxes | p. 14 |
2.3 Diffusion Fluxes | p. 17 |
2.4 Reversible vs. Irreversible Transport | p. 22 |
2.5 Looking Ahead | p. 23 |
Problems | p. 23 |
Chapter 3 Index Notation | p. 25 |
3.1 Indices | p. 25 |
3.2 Representation of Cartesian Differential Equations | p. 26 |
3.3 Special Operators | p. 27 |
3.4 Operators in Non-Cartesian Coordinates | p. 31 |
Problems | p. 34 |
Chapter 4 Transport by Advection and Diffusion | p. 36 |
4.1 Continuity Equation | p. 37 |
4.2 Transport of Species | p. 39 |
4.2.1 Transport in a Binary Mixture | p. 40 |
4.3 Transport of Heat | p. 42 |
4.4 Transport of Momentum | p. 43 |
4.5 Summary of Transport Equations without Sources | p. 44 |
4.6 Conservation Statements from a Finite Volume | p. 44 |
4.7 Eulerian and Lagrangian Coordinates and the Substantial Derivative | p. 46 |
Problems | p. 48 |
Chapter 5 Transport with Source Terms | p. 50 |
5.1 Continuity Equation | p. 51 |
5.2 Species Equation | p. 51 |
5.3 Heat Equation (without Viscous Heating) | p. 52 |
5.4 Momentum Equation | p. 54 |
5.5 Kinetic Energy Equation | p. 55 |
5.6 Heat Equation (with Viscous Heating) | p. 57 |
5.7 Entropy Generation in Irreversible Flows | p. 58 |
5.8 Conservation Statements Derived from a Finite Volume | p. 59 |
5.9 Leibniz's Theorem | p. 62 |
5.10 Looking Ahead | p. 63 |
Problems | p. 64 |
Chapter 6 Specification of Transport Problems | p. 66 |
6.1 Classification of equations | p. 66 |
6.2 Boundary Conditions | p. 67 |
6.3 Elementary Linear Examples | p. 69 |
6.4 Nonlinear Example | p. 73 |
6.5 Scaling Estimates | p. 75 |
Problems | p. 78 |
Chapter 7 Transient One-Dimensional Diffusion | p. 82 |
7.1 Separation of Time and Space Variables | p. 83 |
7.2 Silicon Doping | p. 89 |
7.3 Plane Wall With Heat Generation | p. 93 |
7.4 Transient Groundwater Contamination | p. 97 |
Problems | p. 101 |
Chapter 8 Steady Two-Dimensional Diffusion | p. 103 |
8.1 Separation of Two Spatial Variables | p. 103 |
8.2 Nonhomogeneous Conditions on Nonadjoining Boundaries | p. 105 |
8.3 Nonhomogeneous Conditions on Adjoining Boundaries | p. 107 |
8.3.1 Bar Heat Treatment | p. 108 |
8.4 Nonhomogeneous Condition in Governing Equation | p. 111 |
8.5 Looking Ahead | p. 115 |
Problems | p. 115 |
Chapter 9 Eigenfunction Expansion | p. 119 |
9.1 Method of Eigenfunction Expansion | p. 119 |
9.2 Non-Cartesian Coordinate Systems | p. 127 |
9.3 Transport in Non-Cartesian Coordinates | p. 130 |
Problems | p. 139 |
Chapter 10 Similarity Solution | p. 140 |
10.1 The Similarity Variable | p. 140 |
10.2 Laser Heating of a Semi-infinite Solid | p. 142 |
10.3 Transient Evaporation | p. 146 |
10.4 Power Series Solution | p. 148 |
10.5 Mass Transfer with Time-Dependent Boundary Condition | p. 152 |
Problems | p. 157 |
Chapter 11 Superposition of Solutions | p. 159 |
11.1 Superposition in Time | p. 159 |
Set in Motion | p. 162 |
11.2 Superposition in Space | p. 164 |
Problems | p. 169 |
Chapter 12 Diffusion-Driven Boundaries | p. 172 |
12.1 Thermal Oxidation | p. 172 |
12.2 Solidification of an Undercooled Liquid | p. 174 |
12.3 Solidification of a Binary Alloy from an Undercooled Liquid | p. 178 |
12.4 Melting of a Solid Initially at the Melting Point | p. 183 |
Problems | p. 186 |
Chapter 13 Lubrication Theory | p. 188 |
13.1 Lubrication Flows Governed by Diffusion | p. 188 |
13.2 Scaling Arguments for Squeeze Flow | p. 189 |
13.4 Coating Extrusion | p. 194 |
13.5 Coating Extrusion on a Porous Surface | p. 198 |
13.6 Reynolds Equation for Lubrication Theory | p. 202 |
Problems | p. 203 |
Chapter 14 Inviscid Flow | p. 206 |
14.1 The Reynolds Number | p. 207 |
14.2 Inviscid Momentum Equation | p. 208 |
14.3 Ideal Plane Flow | p. 209 |
14.4 Steady Potential Flow through a Box with Staggered Inlet and Exit | p. 210 |
14.5 Advection of Species through a Box with Staggered Inlet and Exit | p. 215 |
14.6 Spherical Bubble Dynamics | p. 217 |
Tension | p. 219 |
Problems | p. 221 |
Chapter 15 Catalog of Ideal Plane Flows | p. 224 |
15.1 Superposition of Simple Plane Flows | p. 224 |
15.2 Potential Flow over an Aircraft Fuselage | p. 225 |
15.3 Force on a Line Vortex in a Uniform Stream | p. 227 |
15.4 Flow Circulation | p. 229 |
15.5 Potential Flow over Wedges | p. 231 |
Problems | p. 233 |
Chapter 16 Complex Variable Methods | p. 234 |
16.1 Brief Review of Complex Numbers | p. 234 |
16.2 Complex Representation of Potential Flows | p. 235 |
16.3 The Joukowski Transform | p. 236 |
16.4 Joukowski Symmetric Airfoils | p. 238 |
16.5 Joukowski Cambered Airfoils | p. 240 |
16.6 Heat Transfer between Nonconcentric Cylinders | p. 242 |
16.7 Transport with Temporally Periodic Conditions | p. 244 |
Problems | p. 246 |
Chapter 17 MacCormack Integration | p. 249 |
17.1 Flux-Conservative Equations | p. 249 |
17.2 MacCormack Integration | p. 250 |
17.3 Transient Convection | p. 255 |
17.4 Steady-State Solution of Coupled Equations | p. 259 |
Problems | p. 262 |
Chapter 18 Open Channel Flow | p. 265 |
18.1 Analysis of Open Channel Flows | p. 265 |
18.2 Simple Surface Waves | p. 267 |
18.3 Depression and Elevation Waves | p. 268 |
18.4 The Hydraulic Jump | p. 269 |
18.5 Energy Conservation | p. 271 |
18.6 Dam-Break Example | p. 273 |
18.7 Tracer Transport in the Dam-Break Problem | p. 280 |
Problems | p. 280 |
Chapter 19 Open Channel Flow with Friction | p. 284 |
19.1 The Saint-Venant Equations | p. 284 |
19.2 The Friction Slope | p. 286 |
19.3 Flow through a Sluice Gate | p. 287 |
Problems | p. 293 |
Chapter 20 Compressible Flow | p. 296 |
20.1 General Equations of Momentum and Energy Transport | p. 296 |
20.2 Reversible Flows | p. 298 |
20.3 Sound Waves | p. 299 |
20.4 Propagation of Expansion and Compression Waves | p. 300 |
20.5 Shock Wave (Normal to Flow) | p. 302 |
20.6 Shock Tube Analytic Description | p. 304 |
20.7 Shock Tube Numerical Description | p. 307 |
20.8 Shock Tube Problem with Dissimilar Gases | p. 312 |
Problems | p. 313 |
Chapter 21 Quasi-One-Dimensional Compressible Flows | p. 316 |
21.1 Quasi-One-Dimensional Flow Equations | p. 316 |
21.2 Quasi-One-Dimensional Steady Flow Equations without Friction | p. 319 |
21.3 Numerical Solution to Quasi-One-Dimensional Steady Flow | p. 324 |
Example | p. 328 |
Problems | p. 332 |
Chapter 22 Two-Dimensional Compressible Flows | p. 335 |
22.1 Flow through a Diverging Nozzle | p. 335 |
Problems | p. 345 |
Chapter 23 Runge-Kutta Integration | p. 347 |
23.1 Fourth Order Runge-Kutta Integration of First Order Equations | p. 347 |
23.2 Runge-Kutta Integration of Higher Order Equations | p. 350 |
23.3 Numerical Integration of Bubble Dynamics | p. 352 |
23.4 Numerical Integration with Shooting | p. 355 |
Problems | p. 359 |
Chapter 24 Boundary Layer Convection | p. 362 |
24.1 Scanning Laser Heat Treatment | p. 362 |
24.2 Convection to an Inviscid Flow | p. 366 |
24.3 Species Transfer to a Vertically Conveyed Liquid Film | p. 372 |
Problems | p. 377 |
Chapter 25 Convection into Developing Laminar Flows | p. 379 |
25.1 Boundary Layer Flow over a Flat Plate (Blasius Flow) | p. 379 |
25.2 Species Transfer across the Boundary Layer | p. 385 |
25.3 Heat Transfer across the Boundary Layer | p. 389 |
25.4 A Correlation for Forced Heat Convection from a Flat Plate | p. 393 |
25.5 Transport Analogies | p. 394 |
25.6 Boundary Layers Developing on a Wedge (Falkner-Skan Flow) | p. 396 |
25.7 Viscous Heating in the Boundary Layer | p. 398 |
Problems | p. 400 |
Chapter 26 Natural Convection | p. 403 |
26.1 Buoyancy | p. 403 |
26.2 Natural Convection from a Vertical plate | p. 404 |
26.3 Scaling Natural Convection from a Vertical Plate | p. 405 |
26.4 Exact Solution to Natural Convection Boundary Layer Equations | p. 408 |
Problems | p. 416 |
Chapter 27 Internal Flow | p. 417 |
27.1 Entrance Region | p. 417 |
27.2 Heat Transport in an Internal Flow | p. 419 |
27.3 Entrance Region of Plug Flow between Plates of Constant Heat Flux | p. 420 |
27.4 Plug Flow between Plates of Constant Temperature | p. 422 |
27.5 Fully Developed Transport Profiles | p. 424 |
27.6 Fully Developed Heat Transport in Plug Flow between Plates of Constant Heat Flux | p. 426 |
27.7 Fully Developed Species Transport in Plug Flow Between Surfaces of Constant Concentration | p. 429 |
Problems | p. 431 |
Chapter 28 Fully Developed Transport in Internal Flows | p. 434 |
28.1 Momentum Transport in a Fully Developed Flow | p. 434 |
28.2 Heat Transport in a Fully Developed Flow | p. 435 |
Boundaries | p. 437 |
Problems | p. 449 |
Chapter 29 Influence of Temperature-Dependent Properties | p. 452 |
29.1 Temperature-Dependent Conductivity in a Solid | p. 452 |
29.2 Temperature-Dependent Diffusivity in Internal Convection | p. 456 |
29.3 Temperature-Dependent Gas Properties in Boundary Layer Flow | p. 463 |
Problems | p. 469 |
Chapter 30 Turbulence | p. 472 |
30.1 The Transition to Turbulence | p. 473 |
30.2 Reynolds Decomposition | p. 475 |
30.3 Decomposition of the Continuity Equation | p. 476 |
30.4 Decomposition of the Momentum Equation | p. 477 |
30.5 The Mixing Length Model of Prandtl | p. 478 |
30.6 Regions in a Wall Boundary Layer | p. 480 |
30.7 Parameters of the Mixing Length Model | p. 483 |
Problems | p. 484 |
Chapter 31 Fully Developed Turbulent Flow | p. 486 |
31.1 Turbulent Poiseuille Flow Between Smooth Parallel Plates | p. 487 |
31.2 Turbulent Couette Flow between Smooth Parallel Plates | p. 492 |
31.3 Turbulent Poiseuille Flow in a Smooth Wall Pipe | p. 495 |
31.4 Utility of the Hydraulic Diameter | p. 497 |
31.5 Turbulent Poiseuille Flow in a Smooth Annular Pipe | p. 497 |
31.6 Reichardt's Formula for Turbulent Diffusivity | p. 502 |
31.7 Poiseuille Flow with Blowing between Walls | p. 504 |
Problems | p. 512 |
Chapter 32 Turbulent Heat and Species Transfer | p. 515 |
32.1 Reynolds Decomposition of the Heat Equation | p. 515 |
32.2 The Reynolds Analogy | p. 516 |
32.3 Thermal Profile Near the Wall | p. 518 |
32.4 Mixing Length Model for Heat Transfer | p. 521 |
32.5 Mixing Length Model for Species Transfer | p. 522 |
Problems | p. 523 |
Chapter 33 Fully Developed Turbulent Transport in Developed Flows | p. 524 |
33.1 Chemical Vapor Deposition in Turbulent Tube Flow with Generation | p. 524 |
33.2 Heat Transfer in a Fully Developed Internal Turbulent Flow | p. 529 |
33.3 Heat Transfer in a Turbulent Poiseuille Flow between Smooth Parallel Plates | p. 530 |
33.4 Fully Developed Transport in a Turbulent Flow of a Binary Mixture | p. 539 |
Problems | p. 551 |
Chapter 34 Turbulence over Rough Surfaces | p. 553 |
34.1 Turbulence over a Fully Rough Surface | p. 554 |
34.2 Turbulent Heat and Species Transfer from a Fully Rough Surface | p. 555 |
34.3 Application of the Rough Surface Mixing Length Model | p. 557 |
34.4 Application of Reichardt's Formula to Rough Surfaces | p. 561 |
Problems | p. 571 |
Chapter 35 Turbulent Boundary Layer | p. 573 |
35.1 Formulation of Transport in Turbulent Boundary Layer | p. 573 |
35.2 Formulation of Heat Transport in the Turbulent Boundary Layer | p. 584 |
Chapter 36 The K-Epsilon Model of Turbulence | p. 590 |
36.1 Turbulent Kinetic Energy Equation | p. 590 |
36.2 Dissipation Equation for Turbulent Kinetic Energy | p. 594 |
36.3 The Standard K-Epsilon Model | p. 595 |
Problems | p. 596 |
Chapter 37 The K-Epsilon Model Applied to Internal Flows | p. 598 |
37.1 K-Epsilon Model for Poiseuille Flow between Smooth Parallel Plates | p. 598 |
37.2 Transition Point between Mixing Length and K-Epsilon Models | p. 600 |
37.3 Solving the K and E Equations | p. 602 |