Finite Difference Methods in Heat Transfer

Helcio R. B. Orlande, Marcelo J. Colaço, Renato M. Cotta, M. Necati Özişik

• Publisher: CRC Press
• Year: 2017
• Print ISBN: 9781482243451
• eBook ISBN: 9781351349918
• Topic: Scienze fisiche
• Subtopic: Energia

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.

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

1

Basic Relations

Numerical methods are useful for solving fluid dynamics, heat and mass transfer problems, and other partial differential equations of mathematical physics when such problems cannot be handled by exact analysis techniques because of nonlinearities, complex geometries, and complicated boundary conditions. The development of high-speed digital computers significantly enhanced the use of numerical methods in various branches of science and engineering. Many complicated problems can now be solved at a very little cost and in a very short time with the available computing power.

Presently, the finite difference method (FDM), the finite volume method (FVM), and the finite-element method (FEM) are widely used for the solution of partial differential equations of heat, mass, and momentum transfer. Extensive amounts of literature exist on the application of these methods for the solution of such problems. Each method has its advantages depending on the nature of the physical problem to be solved, but there is no best method for all problems. For instance, the dimension of the problem is an important factor that deserves some consideration because an efficient method for one-dimensional problems may not be so efficient for two- or three-dimensional problems. FDMs are simple to formulate and can readily be extended to two- or three-dimensional problems. Furthermore, FDM is very easy to learn and apply for the solution of partial differential equations encountered in the modeling of engineering problems for simple geometries. For problems involving irregular geometries in the solution domain, the FEM is known for having more flexibility because the region near the boundary can readily be divided into subregions. A major drawback of FDM used to be its difficulty to handle effectively the solution of problems over arbitrarily-shaped complex geometries because of interpolation between the boundaries and the interior points, in order to develop finite difference expressions for nodes next to the boundaries. More recently, with the advent of numerical grid generation approaches, the FDM has become comparable to FEM in dealing with irregular geometries, while still maintaining the simplicity of the standard FDM.

In this book, we ...

Table of contents

• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• Preface—First Edition
• 1. Basic Relations
• 2. Discrete Approximation of Derivatives
• 3. Methods of Solving Systems of Algebraic Equations
• 4. One-Dimensional Steady-State Systems
• 5. One-Dimensional Transient Systems
• 6. Transient Multidimensional Systems
• 7. Nonlinear Diffusion
• 8. Multidimensional Incompressible Laminar Flow
• 9. Compressible Flow
• 10. Phase Change Problems
• 11. Numerical Grid Generation
• 12. Hybrid Numerical–Analytical Solutions
• 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