دانلود کتاب Finite Difference Methods in Heat Transfer

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Cover
Title Page
Copyright Page
Contents
Preface
Preface—First Edition
Chapter 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
Chapter 2: Discrete Approximation of Derivatives
2.1. 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
2.3.2. Discretization of Boundary Conditions with Control Volumes
2.3.2.1. 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
Chapter 3: Methods of Solving Systems of Algebraic Equations
3.1. Reduction to Algebraic Equations
3.2. Direct Methods
3.2.1. Gauss Elimination Method
3.2.2. 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
Chapter 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
4.2.1. Stability for Steady-State Systems
4.2.2. Finite Volume Method
4.2.2.1. Interpolation Functions
Problems
Chapter 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
5.1.3.1. Prescribed Heat Flux Boundary Condition
5.1.4. Combined Method
5.1.4.1. Stability of Combined Method
5.1.5. Cylindrical and Spherical Symmetry
5.1.6. Application of Simple Explicit Method
5.1.6.1. Solid Cylinder and Sphere
5.1.6.2. Stability of Solution
5.1.6.3. Hollow Cylinder and Sphere
5.1.7. Application of Simple Implicit Scheme
5.1.7.1. Solid Cylinder and Sphere
5.1.7.2. Hollow Cylinder and Sphere
5.1.8. Application of Crank–Nicolson Method
5.2. Advective–Diffusive Systems
5.2.1. Purely Advective (Wave) Equation
5.2.1.1. Upwind Method
5.2.1.2. MacCormack’s Method
5.2.1.3. Warming and Beam’s Method
5.2.2. Advection–Diffusion Equation
5.2.2.1. Simple Explicit Scheme
5.2.2.2. Implicit Finite Volume Method
5.3. Hyperbolic Heat Conduction Equation
5.3.1. Finite Difference Representation of Hyperbolic Heat Conduction Equation
Problems
Chapter 6: Transient Multidimensional Systems
6.1. Simple Explicit Method
6.1.1. Two-Dimensional Diffusion
6.1.2. Two-Dimensional Transient Convection–Diffusion
6.1.2.1. FTCS Differencing
6.1.2.2. Upwind Differencing
6.1.2.3. Control Volume Approach
6.2. Combined Method
6.3. ADI Method
6.4. ADE Method
6.5. An Application Related to the Hyperthermia Treatment of Cancer
Problems
Chapter 7: Nonlinear Diffusion
7.1. Lagging Properties by One Time Step
7.2. Use of Three-Time-Level Implicit Scheme
7.2.1. Internal Nodes
7.2.2. Limiting Case R = 0 for Cylinder and Sphere
7.2.3. Boundary Nodes
7.3. Linearization
7.3.1. Stability Criterion
7.4. False Transient
7.4.1. Simple Explicit Scheme
7.4.2. Simple Implicit Scheme
7.4.3. A Set of Diffusion Equations
7.5. Applications in Coupled Conduction and Radiation in Participating Media
7.5.1. One-Dimensional Problem with Diffusion Approximation
7.5.2. Solution of the Three-Dimensional Equation of Radiative Transfer
Problems
Chapter 8: Multidimensional Incompressible Laminar Flow
8.1. Vorticity-Stream Function Formulation
8.1.1. Vorticity and Stream Function
8.1.2. Finite Difference Representation of Vorticity-Stream Function Formulation
8.1.2.1. Vorticity Transport Equation
8.1.2.2. Poisson’s Equation for Stream Function
8.1.2.3. Poisson’s Equation for Pressure
8.1.3. Method of Solution for Omega and Psi
8.1.3.1. Solution for a Transient Problem
8.1.3.2. Solution for a Steady-State Problem
8.1.4. Method of Solution for Pressure
8.1.5. Treatment of Boundary Conditions
8.1.5.1. Boundary Conditions on Velocity
8.1.5.2. Boundary Conditions on Psi
8.1.5.3. Boundary Condition on Omega
8.1.5.4. Boundary Conditions on Pressure
8.1.5.5. Initial Condition
8.1.6. Energy Equation
8.2. Primitive Variables Formulation
8.2.1. Determination of the Velocity Field: The SIMPLEC Method
8.2.2. Treatment of Boundary Conditions
8.2.2.1. Pressure
8.2.2.2. Momentum and Energy Equations
8.3. Two-Dimensional Steady Laminar Boundary Layer Flow
Problems
Chapter 9: Compressible Flow
9.1. Quasi-One-Dimensional Compressible Flow
9.1.1. Solution with MacCormack’s Method
9.1.2. Solution with WAF-TVD Method
9.2. Two-Dimensional Compressible Flow
Problems
Chapter 10: Phase Change Problems
10.1. Mathematical Formulation of Phase Change Problems
10.1.1. Interface Condition
10.1.2. Generalization to Multidimensions
10.1.3. Dimensionless Variables
10.1.4. Mathematical Formulation
10.2. Variable Time Step Approach for Single-Phase Solidification
10.2.1. Finite Difference Approximation
10.2.1.1. Differential Equation
10.2.1.2. Boundary Condition at x = 0
10.2.1.3. Interface Conditions
10.2.2. Determination of Time Steps
10.2.2.1. Starting Time Step Δt0
10.2.2.2. Time Step Δt1
10.2.2.3. Time Step Δtn
10.3. Variable Time Step Approach for Two-Phase Solidification
10.3.1. Finite Difference Approximation
10.3.1.1. Equation for the Solid Phase
10.3.1.2. Boundary Condition at x = 0
10.3.1.3. Equation for the Liquid Phase
10.3.1.4. Interface Conditions
10.3.2. Determination of Time Steps
10.3.2.1. Starting Time Step Δt0
10.3.2.2. Time Step Δt1
10.3.2.3. Time Steps Δtn, (2 ≤ n ≤ N – 4)
10.3.2.4. Time Step ΔtN-3
10.3.2.5. Time Step ΔtN–2
10.3.2.6. Time Step ΔtN–1
10.4. Enthalpy Method
10.4.1. Explicit Enthalpy Method: Phase Change with Single Melting Temperature
10.4.1.1. Algorithm for Explicit Method
10.4.1.2. Interpretation of Enthalpy Results
10.4.1.3. Improved Algorithm for Explicit Method
10.4.2. Implicit Enthalpy Method: Phase Change with Single Melting Temperature
10.4.2.1. Algorithm for Implicit Method
10.4.3. Explicit Enthalpy Method: Phase Change over a Temperature Range
10.5. Phase Change Model for Convective–Diffusive Problems
10.5.1. Model for the Passive Scalar Transport Equation
10.5.2. Model for the Energy Equation
Problems
Chapter 11: Numerical Grid Generation
11.1. Coordinate Transformation Relations
11.1.1. Gradient
11.1.2. Divergence
11.1.3. Laplacian
11.1.4. Normal Derivatives
11.1.5. Tangential Derivatives
11.2. Basic Ideas in Simple Transformations
11.3. Basic Ideas in Numerical Grid Generation and Mapping
11.4. Boundary Value Problem of Numerical Grid Generation
11.5. Finite Difference Representation of Boundary Value Problem of Numerical Grid Generation
11.6. Steady-State Heat Conduction in Irregular Geometry
11.7. Steady-State Laminar Free Convection in Irregular Enclosures—Vorticity-Stream Function Formulation
11.7.1. The Nusselt Number
11.7.2. Results
11.8. Transient Laminar Free Convection in Irregular Enclosures—Primitive Variables Formulation
11.9. Computational Aspects for the Evaluation of Metrics
11.9.1. One-Dimensional Advection–Diffusion Equation
11.9.2. Two-Dimensional Heat Conduction in a Hollow Sphere
Problems
Notes
Chapter 12: Hybrid Numerical–Analytical Solutions
12.1. Combining Finite Differences and Integral Transforms
12.1.1. The Hybrid Approach
12.1.2. Hybrid Approach Application: Transient Forced Convection in Channels
12.2. Unified Integral Transforms
12.2.1. Total Transformation
12.2.2. Partial Transformation
12.2.3. Computational Algorithm
12.2.4. Test Case
12.3. Convective Eigenvalue Problem
Problems
Appendix A. Subroutine Gauss
Appendix B. Subroutine Trisol
Appendix C. Subroutine SOR
Appendix D. Subroutine BICGM2
Appendix E. Program to Solve Example 10.1
Bibliography
Index
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