Finite Difference Methods in Heat Transfer, Second Edition

This text 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.

Table of Contents:
Basic Relations Classification of Second-Order Partial Differential Equations Parabolic Systems Elliptic Systems Hyperbolic Systems Systems of Equations Boundary Conditions Uniqueness of the Solution Problems Discrete Approximation of Derivatives Taylor Series Formulation Finite Difference Operators Control-Volume Approach Application of Control-Volume Approach Boundary Conditions Errors Involved in Numerical Solutions Problems Methods of Solving Sets of Algebraic Equations Reduction to Algebraic Equations Direct Methods Iterative Methods Nonlinear Systems Problems One-Dimensional Steady-State Systems Diffusive Systems Diffusive-Convective System Diffusive-Convective System with Flow Problems One-Dimensional Parabolic Systems Simple Explicit Method Simple Implicit Method Crank-Nicolson Method Combined Method Cylindrical and Spherical Symmetry A Summary of Finite-Difference Schemes Problems Multidimensional Parabolic Systems Simple Explicit Method (i) Two-Dimensional Diffusion (ii) Two-Dimensional Steady Laminar Boundary Layer Flow (iii) Two-Dimensional Transient Convection-Diffusion Combined Method (i) Three-Dimensional Diffusion Alternating Direction Implicit (ADI) Method Alternating Direction Explicit (ADE) Method (i) One-Dimensional Diffusion (ii) Two-Dimensional Diffusion Modified Upwind Method (i) Transient Forced Convection Inside Ducts for Step Change in Fluid Inlet Temperature Pressure-Velocity Coupling Problems Elliptic Systems Steady-State Diffusion Velocity Field for Incompressible, Constant Property, Two-Dimensional Flow Vorticity – Stream Function Formulation Problems Hyperbolic Systems Hyperbolic Convection (Wave) Equation Hyperbolic Heat Conduction Equation System of Vector Equations Problems Nonlinear Diffusion Lagging Properties by One Time Step Use of Three-Time Level Implicit Scheme Linearization Method of False Transients for Solving Steady-State Diffusion Simultaneous Conduction and Radiation in Participating Media – Diffusion Approximation Three-Dimensional Simultaneous Conduction and Radiation in Participating Media Problems Phase Change Problems Mathematical Formulation of Phase Change Problems Variable Time Step Approach for Single-Phase Solidification Variable Time Step Approach for Two-Phase Solidification Enthalpy Method Phase Change Problems with Natural Convection Problems Numerical Grid Generation Coordinate Transformation Relations Basic Ideas in Simple Transformations Basic Ideas in Numerical Grid Generation and Mapping Boundary Value Problem of Numerical Grid Generation Finite Difference Representation of Boundary Value Problem of Numerical Grid Generation Steady State Heat Conduction in Irregular Geometry Laminar Forced Convection in Irregular Channels Laminar Free Convection in Irregular Enclosures Problems Hybrid Numerical-Analytic Solutions The Classical (CITT) and the Generalized Integral Transform (GITT) Techniques GITT with Partial Transformation Unified Integral Transforms (UNIT) Algorithm Applications in Heat Conduction Applications in Heat Convection Problems References Appendices Appendix I Discretization Formulae Index