2nd Edition

# Finite Difference Methods in Heat Transfer

598 Pages 100 B/W Illustrations
by CRC Press

600 Pages 100 B/W Illustrations
by CRC Press

Also available as eBook on:

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
• 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

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

(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

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

### Biography

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. He serves as an Associate Editor for the journals Heat Transfer Engineering, Inverse Problems in Science and Engineering and High Temperatures – High Pressures.

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. Afterwards, he spent one year performing research at UFRJ/COPPE on a prestigious CNPq grant as an Instructor and a researcher. From there, he joined Brazilian Military Institute of Engineering where he was teaching and performing research for five years in numerical algorithms for analysis of MHD flows, EHD flows, solidification problems, optimization algorithms utilizing response surfaces, and fuel research. For the past years, he has been teaching and performing research in Brazil and helping to build a large and unique fuels and lubricants research center at the UFRJ. He is the co-author of some book-chapters, and more than 200 papers in major journals and conferences. He was the recipient of the Young Scientist Award, given by state of Rio de Janeiro, in 2007 and 2009 and the Scientist Award in 2013 and 2015. Prof. Colaço is also member of the Scientific Council of the International Centre for Heat and Mass Transfer.