The method of weighted residuals and variational principles with application in fluid mechanics, heat and mass transfer
The method of weighted residuals and variational principles, with application in fluid mechanics, heat and mass transfer
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| Format: | eBook |
| Language: | English |
| Published: |
New York
Academic Press
1972, 1972
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| Series: | Mathematics in science and engineering
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| Subjects: | |
| Online Access: | |
| Collection: | Elsevier eBook collection Mathematics - Collection details see MPG.ReNa |
Table of Contents:
- 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
- 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
- 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
- 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
- Includes bibliographical references and indexes
- 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