The Method of Weighted Residuals and Variational Principles: With Application in Fluid Mechanics, Heat and Mass Transfer

Front Cover
The Method of Weighted Residuals and Variational Principles
Copyright Page
Contents
Preface
Acknowledgments
PART I: THE METHOD OF WEIGHTED RESIDUALS
	Chapter 1. Introduction
		1.1 Basic Equations and Their Classification
		1.2 Method of Weighted Residuals
		References
	Chapter 2. Boundary-Value Problems in Heat and Mass Transfer
		2.1 One-Dimensional Heat Conduction
		2.2 Reduction to Ordinary Differential Equations
		2.3 Boundary Methods
		2.4 General Treatment of Steady-State Heat Conduction
		2.5 Mass Transfer from a Sphere
		2.6 Choice of Trial Functions
		Exercises
		References
	Chapter 3. Eigenvalue and Initial-Value Problems in Heat and Mass Transfer
		3.1 Eigenvalue Problems
		3.2 Transient Heat and Mass Transfer
		3.3 Entry-Length and Initial-Value Problems
		3.4 Mass Transfer to a Moving Fluid
		3.5 Heat Transfer Involving a Phase Change
		Exercises
		References
	Chapter 4. Applications to Fluid Mechanics
		4.1 Laminar Flow in Ducts
		4.2 Boundary Layer Flow past a Flat Plate
		4.3 Laminar Boundary Layers
		4.4 Natural Convection
		4.5 Coupled Entry-Length Problems
		4.6 Steady-State Flow Problems
		Exercises
		References
	Chapter 5. Chemical Reaction Systems
		5.1 Orthogonal Collocation
		5.2 Unsteady Diffusion
		5.3 Reaction and Diffusion in a Catalyst Particle
		5.4 Tubular Reactor with Axial Dispersion
		5.5 Packed Bed Reactor with Radial Dispersion
		5.6 Relation to Other Techniques: Galerkin, Least Squares, Finite Difference, Finite Element Methods
		Exercises
		References
	Chapter 6. Convective Instability Problems
		6.1 Choice of Trial Functions
		6.2 Application of the Galerkin Method
		6.3 Time-Dependent Motion
		6.4 Variational Methods
		6.5 Nonlinear Convective Instability
		6.6 Hydrodynamic Stability
		Exercises
		References
PART II: VARIATIONAL PRINCIPLES
	Chapter 7. Introduction to Variational Principles
		7.1 Calculus of Variations
		7.2 Steady-State Heat Conduction
		7.3 Laminar Flow through Ducts
		7.4 Relation to Galerkin and Finite Element Methods
		7.5 Variational Principles for Eigenvalue Problems
		7.6 Enclosure Theorems
		7.7 Least Squares Interpretation of D. H. Weinstein’s Method
		7.8 Lower Bounds for Eigenvalues
		Exercises
		References
	Chapter 8. Variational Principles in Fluid Mechanics
		8.1 Basic Equations
		8.2 Variational Principles for Perfect Fluids
		8.3 Magnetohydrodynamics
		8.4 Non-Newtonian Fluids
		8.5 Slow Flow past Drops and Particles
		8.6 Variational Principles for Navier-Stokes Equations
		8.7 Energy Methods for Stability of Fluid Motion
		Exercises
		References
	Chapter 9. Variational Principles for Heat and Mass Transfer Problems
		9.1 Fréchet Derivatives
		9.2 Variational Principles for Non-Self-Adjoint Equations
		9.3 Variational Principles for the Transport Equation
		9.4 Applications to Heat Transfer
		9.5 Applications to Mass Transfer
		9.6 Upper Bound for Heat Transport by Turbulent Convection
		Exercises
		References
	Chapter 10. On the Search for Variational Principles
		10.1 Introduction
		10.2 Entropy Production
		10.3 Heat Transfer
		10.4 Fluid Mechanics
		Exercises
		References
	Chapter 11. Convergence and Error Bounds
		11.1 Definitions
		11.2 Boundary-Value Problems
		11.3 Initial-Value Problems
		11.4 Eigenvalue Problems
		11.5 Error Bounds Using the Maximum Principle
		11.6 Error Bounds Using the Mean-Square Residual
		References
Author Index
Subject Index