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Integral Transforms in Computational Heat and Fluid Flow
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INTRODUCTION
THE CLASSICAL INTEGRAL TRANSFORM TECHNIQUE
General Solution for a Base Problem - Parabolic System
Steady Multidimensional Problem - Elliptic System
Eigenvalue Problem
SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS
Linear Systems
Numerical Methods and Stiff Systems
Infinite Systems and Approximate Solutions
PROBLEMS WITH VARIABLE EQUATION COEFFICIENTS
Transient Problem (Parabolic System)
Steady-State Problem (Elliptic System)
Applications
PROBLEMS WITH VARIABLE BOUNDARY CONDITION COEFFICIENTS
Time-dependent Boundary Condition Coefficients
An Alternative Approach
Space-dependent Boundary Condition Coefficients
Applications
PROBLEMS WITH VARIABLE BOUNDARIES
Moving Boundary Problems
Diffusion within Irregular Domains - Elliptic Problem
Diffusion within Irregular Domains - Parabolic Problem
Applications
PROBLEMS THAT INVOLVE DIFFICULT AUXILIARY PROBLEMS
Sturm-Liouville Problem with a Laplace Transform Variable
Sturm-Liouville Problem with Complex Variables
Non-separable Sturm-Liouville Systems
Non-classical Eigenvalue Problems
AN INTRODUCTION TO THE SOLUTION OF NONLINEAR DIFFUSION-CONVECTION PROBLEMS
Nonlinear Source Terms
Nonlinear Convective Terms
Nonlinear Diffusion Coefficients
Computational Procedure
Applications
REFERENCES
APPENDICES
A - Notes
B - Alternative Solution of Nonhomogeneous Problems
C - Integral Transform Method for Eigenvalue Problems
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Integral Transforms in Computational Heat and Fluid Flow is a comprehensive volume that emphasizes the generalized integral transform technique (G.I.T.T.) and the developments that have made the technique a powerful computational tool of practical interest. The book progressively demonstrates the approach through increasingly difficult extensions and test problems. It begins with an overview of the generalized integral transform technique in contrast with classical analytical ideas. Various applications are presented throughout the book, including transient fin analysis with time-dependent surface dissipation, laminar forced convection inside externally finned tubes, metals oxidation at high temperatures, forced convection in liquid metals, and Navier-Stokes equations.
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