2nd Edition
Finite Difference Methods in Heat Transfer
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
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
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.
