The first few chapters establish the tools needed for later analyses while also covering heat and mass transfer in stationary media. The similarities among the molecular or diffusive transport mechanisms--heat conduction, diffusion of chemical species, and viscous transfer of momentum--are highlighted. Conservation equations for scalar quantites are derived first in general form, and then used to obtain the governing equations for total mass, energy, and chemical species. The scaling and order-of-magnitude concepts which are crucial in modeling are also introduced. Certain key methods for solving the differential equations in transport problems, including similarity, perturbation, and finite Fourier transform techniques, are described using conduction and diffusion problems as examples.

Following chapters are devoted to fluid mechanics, beginning with fundamental equations for momentum transfer and then discussing unidirectional flow, nearly unidirectional (lubrication) flow, creeping flow, and laminar boundary layer flow. Forced-convection heat and mass transfer in laminar flow, multicomponent energy and mass transfer, free convection, and turbulence are also covered. The appendix summarizes vector and tensor operations and relations involving various coordinate systems.

Based on twenty years of teaching and extensive class testing, Analysis of Transport Phenomena offers students both extensive coverage of the topic and inclusion of modern examples from bioengineering, membrane science, and materials processing. It is mathematically self-contained and is also unique in its treatment of scaling and approximation techniques and its presentation of the finite Fourier transform method for solving partial differential equations.

Chapter 1 Diffusive Fluxes and Material Properties

1.1. Introduction

1.2. Basic Constitutive Equations

1.3. Diffusivities for Energy, Species, and Momentum

1.4. Magnitudes of Transport Coefficients

1.5. Molecular Interpretations of Transport Coefficients

1.6. Continuum Approximation

References

Problems

Chapter 2 Conservation Equations and the Fundamentals of Heat and Mass Transfer

2.1. Introduction

2.2. General Forms of Conservation Equations

2.3. Conservation of Mass

2.4. Conservation of Energy

2.5. Heat Transfer at Interfaces

2.6. Conservation of Chemical Species

2.7. Mass Transfer at Interfaces

2.8. One-Dimensional Examples

2.9. Species Conservation from a Molecular Viewpoint

References

Problems

Chapter 3 Scaling and Approximation Techniques

3.1. Introduction

3.2. Scaling

3.3. Reductions in Dimensionality

3.4. Simplifications Based on Time Scales

3.5. Similarity Method

3.6. Regular Perturbation Analysis

3.7. Singular Perturbation Analysis

3.8. Integral Approximation Method

References

Problems

Chapter 4 Solution Methods for Conduction and Diffusion Problems

4.1. Introduction

4.2. Fundamentals of the Finite Fourier Transform (FFT) Method

4.3. Basis Functions as Solutions to Eigenvalue Problems

4.4. Representation of an Arbitrary Function Using Orthonormal Functions

4.5. FFT Method for Problems in Rectangular Coordinates

4.6. Self-Adjoint Eigenvalue Problems and Sturm-Liouville Theory

4.7. FFT Method for Problems in Cylindrical Coordinates

4.8. FFT Method for Poblems in Spherical Coordinates

4.9. Point-Source Solutions

4.10. Integral Representations

References

Problems

Chapter 5 Fundamentals of Fluid Mechanics

5.1. Introduction

5.2. Fluid Kinetics

5.3. Conservation of Momentum

5.4. Total Stress, Pressure, and Viscous Stress

5.5. Fluid Statics

5.6. Constitutive Equations for the Viscous Stress

5.7. Fluid Mechanics at Interfaces

5.8. Dynamic Pressure

5.9. Stream function

5.10. Nondimensionalization and Simplification of the Navier-Stokes Equation

Tables

References

Problems

Chapter 6 Unidirectional and Nearly Unidirectional Flow

6.1. Introduction

6.2. Steady Flow with a Pressure Gradient

6.3. Steady Flow with a Moving Surface

6.4. Time-Dependent Flow

6.5. Limitations of Exact Solutions

6.6. Lubrication Approximation

References

Problems

Chapter 7 Creeping Flow

7.1. Introduction

7.2. General Features of Low Reynolds Number Flow

7.3. Unidirectional and Nearly Unidirectional Solutions

7.4. Stream Function Solutions

7.5. Point-Force Solutions

7.6. Particle Motion and Suspension Viscosity

7.7. Corrections to Stokes' Law

References

Problems

Chapter 8 Laminar Flow at High Reynolds Number

8.1. Introduction

8.2. General Features of High Reynolds Number Flow

8.3. Irrotational Flow

8.4. Boundary Layers Near Solid Surfaces

8.5. Internal Boundary Layers

References

Problems

Chapter 9 Forced-Convection Heat and Mass Transfer in Confined Laminar Flows

9.1. Introduction

9.2. Peclet Number

9.3. Nusselt and Sherwood Numbers

9.4. Entrance Region

9.5. Fully Developed Region

9.6. Conservation of Energy: Mechanical Effects

9.7. Taylor Dispersion

References

Problems

Chapter 10 Forced-Convection Heat and Mass Transfer in Unconfined Laminar Flows

10.1. Introduction

10.2. Heat and Mass Transfer in Creeping Flow

10.3. Heat and Mass Transfer in Laminar Boundary Layers

10.4. Scaling Laws for Nusselt and Sherwood Numbers

References

Problems

Chapter 11 Multicomponent Energy and Mass Transfer

11.1. Introduction

11.2. Conservation of Energy: Multicomponent Systems

11.3. Simultaneous Heat and Mass Transfer

11.4. Introduction to Coupled Fluxes

11.5. Stefan-Maxwell Equations

11.6. Generalized Diffusion in Dilute Mixtures

11.7. Transport in Electrolyte Solutions

11.8. Generalized Stefan-Maxwell Equations

References

Problems

Chapter 12 Transport in Buoyancy-Driven Flow

12.1. Introduction

12.2. Buoyancy and the Boussinesq Approximation

12.3. Confined Flows

12.4. Dimensional Analysis and Boundary Layer Equations

12.5. Unconfined Flows

References

Problems

Chapter 13 Transport in Turbulent Flow

13.1. Introduction

13.2. Basic Features of Turbulence

13.3. Time-Smoothed Equations

13.4. Eddy Diffusivity Models

13.5. Other Approaches for Turbulent Flow Calculations

References

Problems.

Appendix: Vectors and Tensors

Introduction

A.1. Representation of Vectors and Tensors

A.2. Vector and Tensor Products

A.3. Vector Differential Operators

A.4. Integral Transformations

A.5. Position Vectors

A.6. Orthogonal Curvilinear Coordinates

A.7. Surface Geometry

References

Index