Finite Difference Methods in Heat Transfer | KitaabNow

Finite Difference Methods in Heat Transfer

  • Author: M. Necati Özişik, Helcio R. B. Orlande, Marcelo J. Colaço, Renato M. Cotta
  • ISBN: 9781482243451
  • Publisher: CRC Press
  • Edition: 2nd
  • Publication Date: September 5, 2017
  • Format: Hardback – 600 Pages
  • Language: English


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.

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