| Description |
1 online resource (511 pages) |
| Series |
Heat Transfer Ser |
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Heat Transfer Ser
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| Contents |
Intro; Title Page; Copyright Page; Dedication; Table of Contents; Preface; Preface-First Edition; 1. Basic Relations; 1.1 Classification of Second-Order Partial Differential Equations; 1.1.1 Physical Significance of Parabolic, Elliptic, and Hyperbolic Systems; 1.2 Parabolic Systems; 1.3 Elliptic Systems; 1.3.1 Steady-State Diffusion; 1.3.2 Steady-State Advection-Diffusion; 1.3.3 Fluid Flow; 1.4 Hyperbolic Systems; 1.5 Systems of Equations; 1.5.1 Characterization of System of Equations; 1.5.2 Wave Equation; 1.6 Boundary Conditions; 1.7 Uniqueness of the Solution; Problems |
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2. Discrete Approximation of Derivatives2.1 Taylor Series Formulation; 2.1.1 Finite Difference Approximation of First Derivative; 2.1.2 Finite Difference Approximation of Second Derivative; 2.1.3 Differencing via Polynomial Fitting; 2.1.4 Finite Difference Approximation of Mixed Partial Derivatives; 2.1.5 Changing the Mesh Size; 2.1.6 Finite Difference Operators; 2.2 Control Volume Approach; 2.3 Boundary and Initial Conditions; 2.3.1 Discretization of Boundary Conditions with Taylor Series; 2.3.1.1 Boundary Condition of the First Kind; 2.3.1.2 Boundary Conditions of the Second and Third Kinds |
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2.3.2 Discretization of Boundary Conditions with Control Volumes2.3.2.1 Boundary Condition of the First Kind; 2.3.2.2 Boundary Condition of the Second Kind; 2.3.2.3 Boundary Condition of the Third Kind; 2.4 Errors Involved in Numerical Solutions; 2.4.1 Round-Off Errors; 2.4.2 Truncation Error; 2.4.3 Discretization Error; 2.4.4 Total Error; 2.4.5 Stability; 2.4.6 Consistency; 2.5 Verification and Validation; 2.5.1 Code Verification; 2.5.2 Solution Verification; Problems; Notes; 3. Methods of Solving Systems of Algebraic Equations; 3.1 Reduction to Algebraic Equations; 3.2 Direct Methods |
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3.2.1 Gauss Elimination Method3.2.2 Thomas Algorithm; 3.3 Iterative Methods; 3.3.1 Gauss-Seidel Iteration; 3.3.2 Successive Overrelaxation; 3.3.3 Red-Black Ordering Scheme; 3.3.4 LU Decomposition with Iterative Improvement; 3.3.5 Biconjugate Gradient Method; 3.4 Nonlinear Systems; Problems; 4. One-Dimensional Steady-State Systems; 4.1 Diffusive Systems; 4.1.1 Slab; 4.1.2 Solid Cylinder and Sphere; 4.1.3 Hollow Cylinder and Sphere; 4.1.4 Heat Conduction through Fins; 4.1.4.1 Fin of Uniform Cross Section; 4.1.4.2 Finite Difference Solution; 4.2 Diffusive-Advective Systems |
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4.2.1 Stability for Steady-State Systems4.2.2 Finite Volume Method; 4.2.2.1 Interpolation Functions; Problems; 5. One-Dimensional Transient Systems; 5.1 Diffusive Systems; 5.1.1 Simple Explicit Method; 5.1.1.1 Prescribed Potential at the Boundaries; 5.1.1.2 Convection Boundary Conditions; 5.1.1.3 Prescribed Flux Boundary Condition; 5.1.1.4 Stability Considerations; 5.1.1.5 Effects of Boundary Conditions on Stability; 5.1.1.6 Effects of r on Truncation Error; 5.1.1.7 Fourier Method of Stability Analysis; 5.1.2 Simple Implicit Method; 5.1.2.1 Stability Analysis; 5.1.3 Crank-Nicolson Method |
| Notes |
5.1.3.1 Prescribed Heat Flux Boundary Condition |
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Print version record |
| Form |
Electronic book
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| Author |
Orlande, Helcio R. B
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Colaço, Marcelo J
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Cotta, Renato M
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| ISBN |
9781351349918 |
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1351349910 |
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