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Preface | p. xiii |
List of Symbols | p. xix |
Diffusive Fluxes and Material Properties | p. 1 |
Introduction | p. 1 |
Basic Constitutive Equations | p. 2 |
Diffusivities for Energy, Species, and Momentum | p. 7 |
Magnitudes of Transport Coefficients | p. 8 |
Molecular Interpretation of Transport Coefficients | p. 13 |
Limitations on Length and Time Scales | p. 19 |
References | p. 22 |
Problems | p. 23 |
Fundamentals of Heat and Mass Transfer | p. 26 |
Introduction | p. 26 |
General Forms of Conservation Equations | p. 27 |
Conservation of Mass | p. 34 |
Conservation of Energy: Thermal Effects | p. 36 |
Heat Transfer at Interfaces | p. 38 |
Conservation of Chemical Species | p. 41 |
Mass Transfer at Interfaces | p. 43 |
Molecular View of Species Conservation | p. 44 |
References | p. 48 |
Problems | p. 48 |
Formulation and Approximation | p. 53 |
Introduction | p. 53 |
One-Dimensional Examples | p. 54 |
Order-of-Magnitude Estimation and Scaling | p. 69 |
"Dimensionality" in Modeling | p. 77 |
Time Scales in Modeling | p. 87 |
References | p. 97 |
Problems | p. 98 |
Solution Methods Based on Scaling Concepts | p. 113 |
Introduction | p. 113 |
Similarity Method | p. 114 |
Regular Perturbation Analysis | p. 120 |
Singular Perturbation Analysis | p. 127 |
References | p. 141 |
Problems | p. 141 |
Solution Methods for Linear Problems | p. 151 |
Introduction | p. 151 |
Properties of Linear Boundary-Value Problems | p. 152 |
Finite Fourier Transform Method | p. 157 |
Basis Functions | p. 162 |
Fourier Series | p. 170 |
FFT Solutions for Rectangular Geometries | p. 174 |
FFT Solutions for Cylindrical Geometries | p. 184 |
FFT Solutions for Spherical Geometries | p. 190 |
Point-Source Solutions | p. 200 |
More on Self-Adjoint Eigenvalue Problems and FFT Solutions | p. 204 |
References | p. 209 |
Problems | p. 210 |
Fundamentals of Fluid Mechanics | p. 220 |
Introduction | p. 220 |
Conservation of Momentum | p. 220 |
Total Stress, Pressure, and Viscous Stress | p. 226 |
Fluid Kinematics | p. 230 |
Constitutive Equations for Viscous Stress | p. 236 |
Fluid Mechanics at Interfaces | p. 243 |
Force Calculations | p. 250 |
Stream Function | p. 255 |
Dimensionless Groups and Flow Regimes | p. 261 |
References | p. 265 |
Problems | p. 265 |
Unidirectional and Nearly Unidirectional Flow | p. 270 |
Introduction | p. 270 |
Steady Flow with a Pressure Gradient | p. 271 |
Steady Flow with a Moving Surface | p. 277 |
Time-Dependent Flow | p. 279 |
Limitations of Exact Solutions | p. 282 |
Nearly Unidirectional Flow | p. 288 |
References | p. 300 |
Problems | p. 300 |
Creeping Flow | p. 315 |
Introduction | p. 315 |
General Features of Low Reynolds Number Flow | p. 315 |
Unidirectional and Nearly Unidirectional Solutions | p. 319 |
Stream-Function Solutions | p. 324 |
Point-Force Solutions | p. 331 |
Particles and Suspensions | p. 334 |
Corrections to Stokes' Law | p. 343 |
References | p. 350 |
Problems | p. 351 |
Laminar Flow at High Reynolds Number | p. 361 |
Introduction | p. 361 |
General Features of High Reynolds Number Flow | p. 362 |
Irrotational Flow | p. 371 |
Boundary Layers at Solid Surfaces | p. 378 |
Internal Boundary Layers | p. 387 |
References | p. 393 |
Problems | p. 394 |
Forced-Convection Heat and Mass Transfer in Confined Laminar Flows | p. 401 |
Introduction | p. 401 |
Péclet Number | p. 402 |
Nusselt and Sherwood Numbers | p. 406 |
Entrance Region | p. 411 |
Fully Developed Region | p. 415 |
Conservation of Energy: Mechanical Effects | p. 423 |
Taylor Dispersion | p. 427 |
References | p. 433 |
Problems | p. 434 |
Forced-Convection Heat and Mass Transfer in Unconfined Laminar Flows | p. 440 |
Introduction | p. 440 |
Heat and Mass Transfer in Creeping Flow | p. 441 |
Heat and Mass Transfer in Laminar Boundary Layers | p. 446 |
Scaling Laws for Nusselt and Sherwood Numbers | p. 451 |
References | p. 457 |
Problems | p. 458 |
Transport in Buoyancy-Driven Flow | p. 463 |
Introduction | p. 463 |
Buoyancy and the Boussinesq Approximation | p. 464 |
Confined Flows | p. 466 |
Dimensional Analysis and Boundary-Layer Equations | p. 474 |
Unconfined Flows | p. 478 |
References | p. 485 |
Problems | p. 486 |
Transport in Turbulent Flow | p. 491 |
Introduction | p. 491 |
Basic Features of Turbulence | p. 491 |
Time-Smoothed Equations | p. 499 |
Eddy Diffusivity Models | p. 505 |
Other Approaches for Turbulent-Flow Calculations | p. 518 |
References | p. 524 |
Problems | p. 525 |
Simultaneous Energy and Mass Transfer and Multicomponent Systems | p. 529 |
Introduction | p. 529 |
Conservation of Energy: Multicomponent Systems | p. 530 |
Simultaneous Heat and Mass Transfer | p. 532 |
Introduction to Coupled Fluxes | p. 545 |
Stefan-Maxwell Equations | p. 550 |
Generalized Diffusion in Dilute Mixtures | p. 553 |
Generalized Stefan-Maxwell Equations | p. 557 |
References | p. 563 |
Problems | p. 564 |
Transport in Electrolyte Solutions | p. 573 |
Introduction | p. 573 |
Formulation of Macroscopic Problems | p. 574 |
Macroscopic Examples | p. 580 |
Equilibrium Double Layers | p. 585 |
Electrokinetic Phenomena | p. 592 |
References | p. 601 |
Problems | p. 602 |
Vectors and Tensors | p. 609 |
Introduction | p. 609 |
Representation of Vectors and Tensors | p. 609 |
Vector and Tensor Products | p. 612 |
Vector-Differential Operators | p. 617 |
Integral Transformations | p. 620 |
Position Vectors | p. 623 |
Orthogonal Curvilinear Coordinates | p. 625 |
Surface Geometry | p. 634 |
References | p. 638 |
Ordinary Differential Equations and Special Functions | p. 639 |
Introduction | p. 639 |
First-Order Equations | p. 640 |
Equations with Constant Coefficients | p. 641 |
Bessel and Spherical Bessel Equations | p. 642 |
Other Equations with Variable Coefficients | p. 647 |
References | p. 650 |
Index | p. 651 |
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