Finite Difference Methods in Heat Transfer

Description

Finite Difference Methods in Heat Transfer, Second Edition focuses on finite difference methods and their application to the solution of heat transfer problems. Such methods are based on the discretization of governing equations, initial and boundary conditions, which then replace a continuous partial differential problem by a system of algebraic equations. Finite difference methods are a versatile tool for scientists and for engineers. This updated book serves university students taking graduate-level coursework in heat transfer, as well as being an important reference for researchers and engineering.

Key Features

• Provides a self-contained approach in finite difference methods for students and professionals
• Covers the use of finite difference methods in convective, conductive, and radiative heat transfer
• Presents numerical solution techniques to elliptic, parabolic, and hyperbolic problems
• Includes hybrid analytical–numerical approaches

Table of Contents

1. Basic Relations
2. Classification of Second-Order Partial Differential Equations
3. Parabolic Systems
4. Elliptic Systems
5. Hyperbolic Systems
6. Systems of Equations
7. Boundary Conditions
8. Uniqueness of the Solution Problems
9. Discrete Approximation of Derivatives
10. Taylor Series Formulation
11. Finite Difference Operators
12. Control-Volume Approach
13. Application of Control-Volume Approach
14. Boundary Conditions
15. Errors Involved in Numerical Solutions Problems
16. Methods of Solving Sets of Algebraic Equations
17. Reduction to Algebraic Equations
18. Direct Methods
19. Iterative Methods
20. Nonlinear Systems Problems
21. One-Dimensional Steady-State Systems
22. Diffusive Systems
23. Diffusive-Convective System
24. Diffusive-Convective System with Flow Problems
25. One-Dimensional Parabolic Systems
26. Simple Explicit Method
27. Simple Implicit Method
28. Crank-Nicolson Method
29. Combined Method
30. Cylindrical and Spherical Symmetry
31. A Summary of Finite-Difference Schemes Problems
32. Multidimensional Parabolic Systems
33. Simple Explicit Method
    1. Two-Dimensional Diffusion
    2. Two-Dimensional Steady Laminar Boundary Layer Flow
    3. Two-Dimensional Transient Convection-Diffusion
34. Combined Method
    1. Three-Dimensional Diffusion
35. Alternating Direction Implicit (ADI) Method
36. Alternating Direction Explicit (ADE) Method
    1. One-Dimensional Diffusion
    2. Two-Dimensional Diffusion
37. Modified Upwind Method
    1. Transient Forced Convection Inside Ducts for Step Change in Fluid Inlet
38. Temperature
39. Pressure-Velocity Coupling Problems
40. Elliptic Systems
41. Steady-State Diffusion
42. Velocity Field for Incompressible, Constant Property, Two-Dimensional Flow
43. Vorticity – Stream Function Formulation
44. Problems
45. Hyperbolic Systems
46. Hyperbolic Convection (Wave) Equation
47. Hyperbolic Heat Conduction Equation
48. System of Vector Equations Problems
49. Nonlinear Diffusion
50. Lagging Properties by One Time Step
51. Use of Three-Time Level Implicit Scheme
52. Linearization
53. Method of False Transients for Solving Steady-State Diffusion
54. Simultaneous Conduction and Radiation in Participating Media – Diffusion
55. Approximation
56. Three-Dimensional Simultaneous Conduction and Radiation in Participating Media
57. Problems
58. Phase Change Problems
59. Mathematical Formulation of Phase Change Problems
60. Variable Time Step Approach for Single-Phase Solidification
61. Variable Time Step Approach for Two-Phase Solidification
62. Enthalpy Method
63. Phase Change Problems with Natural Convection
64. Problems
65. Numerical Grid Generation
66. Coordinate Transformation Relations
67. Basic Ideas in Simple Transformations
68. Basic Ideas in Numerical Grid Generation and Mapping
69. Boundary Value Problem of Numerical Grid Generation
70. Finite Difference Representation of Boundary Value Problem of Numerical Grid Generation
71. Steady State Heat Conduction in Irregular Geometry
72. Laminar Forced Convection in Irregular Channels
73. Laminar Free Convection in Irregular Enclosures
74. Problems
75. Hybrid Numerical-Analytic Solutions
76. The Classical (CITT) and the Generalized Integral Transform (GITT) Techniques
77. GITT with Partial Transformation
78. Unified Integral Transforms (UNIT) Algorithm
79. Applications in Heat Conduction
80. Applications in Heat Convection
81. Problems
82. References
83. Appendices
84. Appendix I Discretization Formulae
85. Index

Author(s) Description

Helcio Rangel Barreto Orlande was born in Rio de Janeiro on March 9, 1965. He obtained his B.S. in Mechanical Engineering from the Federal University of Rio de Janeiro (UFRJ) in 1987 and his M.S. in Mechanical Engineering from the same University in 1989. After obtaining his Ph.D. in Mechanical Engineering in 1993 from North Carolina State University, he joined the Department of Mechanical Engineering of UFRJ, where he was the department head during 2006 and 2007. His research areas of interest include the solution of inverse heat and mass transfer problems, as well as the use of numerical, analytical and hybrid numerical-analytical methods of solution of direct heat and mass transfer problems. He is the co-author of 4 books and more than 280 papers in major journals and conferences. He is a member of the Scientific Council of the International Centre for Heat and Mass Transfer and a Delegate in the Assembly for International Heat Transfer Conferences.

Marcelo J. Colaço is an Associate Professor in the Department of Mechanical Engineering at the Federal University of Rio de Janeiro – UFRJ, Brazil. He received his Ph.D. from UFRJ in 2001. He then spent 15 months as a postdoctoral fellow at the University of Texas at Arlington working on optimization algorithms, inverse problems in heat transfer, and electro-magneto-hydrodynamics including solidification.