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method of weighted residuals and variational principles
with application in fluid mechanics, heat and mass transfer
1 online resource (xiv, 412 pages) : illustrations
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 Transfer3.1 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 Collocation5.2 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 PRINCIPLESChapter 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 Particles8.6 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
Includes bibliographical references and indexes.
Mathematics in science and engineering ; v. 87