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Integral Transforms in Computational Heat and Fluid Flow

Renato Machado Cotta

Covers the Generalized Integral Transform Technique for computational fluid flow and heat transfer.

Bookcover

Format: Hardcover, English, 340 pages
ISBN: 0849386659
Publisher: CRC Press
Pub. Date: 1994

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Publisher Comments

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 increasing practical interest. The book begins with an overview of the generalized integral transform technique that contrasts this approach with classical analytical ideas. The classical integral transform technique is then briefly reviewed. The remainder of the book is devoted to G.I.T.T. and considers diffusion-convection problems with variable equation coefficients in general functional form, situations of variable coefficients in boundary conditions, problems with variable boundaries, classes of problems with difficult auxiliary eigen value-type problems, and analysis of nonlinear diffusion-convection problems through this hybrid approach. Many applications are presented, including transient fin analysis with time-dependent surface dissipation, laminar-forced convection inside externally finned tubes, heat conduction with ablation in finite media, transient analysis of radiating fins, and boundary layer equations. Integral Transforms in Computational Heat and Fluid Flow will interest mechanical engineers in heat transfer and fluid dynamics, as well as researchers and librarians in this area.


Table of Contents

I Introduction 1
II The Classical Integral Transform Technique 7
II.1 General Solution for a Base Problem - Parabolic System 7
II.2 Steady Multidimensional Problem - Elliptic System 18
II.3 Eigenvalue Problem 20
III Systems of Ordinary Differential Equations 33
III.1 Linear Systems 33
III.2 Numerical Methods and Stiff Systems 36
III.3 Infinite Systems and Approximate Solutions 37
IV Problems With Variable Equation Coefficients 41
IV.1 Transient Problem (Parabolic System) 41
IV.2 Steady-State Problem (Elliptic System) 55
IV.3 Applications 60
V Problems With Variable Boundary Condition Coefficients 79
V.1 Time-dependent Boundary Condition Coefficients 79
V.2 An Alternative Approach 83
V.3 Space-dependent Boundary Condition Coefficients 87
V.4 Applications 91
VI Problems With Variable Boundaries 109
VI.1 Moving Boundary Problems 109
VI.2 Diffusion within Irregular Domains - Elliptic Problem 114
VI.3 Diffusion within Irregular Domains - Parabolic Problem 119
VI.4 Applications 124
VII Problems That Involve Difficult Auxiliary Problems 157
VII.1 Sturm-Liouville Problem with a Laplace Transform Variable 158
VII.2 Sturm-Liouville Problem with Complex Variables 165
VII.3 Non-separable Sturm-Liouville Systems 180
VII.4 Non-classical Eigenvalue Problems 189
VIII An Introduction to the Solution of Nonlinear Diffusion-Convection Problems 233
VIII.1 Nonlinear Source Terms 234
VIII.2 Nonlinear Convective Terms 236
VIII.3 Nonlinear Diffusion Coefficients 241
VIII.4 Computational Procedure 244
VIII.5 Applications 248
IX References 303
X Appendices 315
Appendix A Notes 315
Appendix B Alternative Solution of Nonhomogeneous Problems 319

Related Book Categories

Numerical Methods


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