Finite Difference Methods in Heat Transfer

DescriptionFinite 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 FeaturesProvides a self-contained approach in finite difference methods for students and professionalsCovers the use of finite difference methods in convective, conductive, and radiative heat transferPresents numerical solution techniques to elliptic, parabolic, and hyperbolic problemsIncludes hybrid analytical–numerical approachesTable of ContentsBasic RelationsClassification of Second-Order Partial Differential EquationsParabolic SystemsElliptic SystemsHyperbolic SystemsSystems of EquationsBoundary ConditionsUniqueness of the Solution ProblemsDiscrete Approximation of DerivativesTaylor Series FormulationFinite Difference OperatorsControl-Volume ApproachApplication of Control-Volume ApproachBoundary ConditionsErrors Involved in Numerical Solutions ProblemsMethods of Solving Sets of Algebraic EquationsReduction to Algebraic EquationsDirect MethodsIterative MethodsNonlinear Systems ProblemsOne-Dimensional Steady-State SystemsDiffusive SystemsDiffusive-Convective SystemDiffusive-Convective System with Flow ProblemsOne-Dimensional Parabolic SystemsSimple Explicit MethodSimple Implicit MethodCrank-Nicolson MethodCombined MethodCylindrical and Spherical SymmetryA Summary of Finite-Difference Schemes ProblemsMultidimensional Parabolic SystemsSimple Explicit MethodTwo-Dimensional DiffusionTwo-Dimensional Steady Laminar Boundary Layer FlowTwo-Dimensional Transient Convection-DiffusionCombined MethodThree-Dimensional DiffusionAlternating Direction Implicit (ADI) MethodAlternating Direction Explicit (ADE) MethodOne-Dimensional DiffusionTwo-Dimensional DiffusionModified Upwind MethodTransient Forced Convection Inside Ducts for Step Change in Fluid InletTemperaturePressure-Velocity Coupling ProblemsElliptic SystemsSteady-State DiffusionVelocity Field for Incompressible, Constant Property, Two-Dimensional FlowVorticity – Stream Function FormulationProblemsHyperbolic SystemsHyperbolic Convection (Wave) EquationHyperbolic Heat Conduction EquationSystem of Vector Equations ProblemsNonlinear DiffusionLagging Properties by One Time StepUse of Three-Time Level Implicit SchemeLinearizationMethod of False Transients for Solving Steady-State DiffusionSimultaneous Conduction and Radiation in Participating Media – DiffusionApproximationThree-Dimensional Simultaneous Conduction and Radiation in Participating MediaProblemsPhase Change ProblemsMathematical Formulation of Phase Change ProblemsVariable Time Step Approach for Single-Phase SolidificationVariable Time Step Approach for Two-Phase SolidificationEnthalpy MethodPhase Change Problems with Natural ConvectionProblemsNumerical Grid GenerationCoordinate Transformation RelationsBasic Ideas in Simple TransformationsBasic Ideas in Numerical Grid Generation and MappingBoundary Value Problem of Numerical Grid GenerationFinite Difference Representation of Boundary Value Problem of Numerical Grid GenerationSteady State Heat Conduction in Irregular GeometryLaminar Forced Convection in Irregular ChannelsLaminar Free Convection in Irregular EnclosuresProblemsHybrid Numerical-Analytic SolutionsThe Classical (CITT) and the Generalized Integral Transform (GITT) TechniquesGITT with Partial TransformationUnified Integral Transforms (UNIT) AlgorithmApplications in Heat ConductionApplications in Heat ConvectionProblemsReferencesAppendicesAppendix I Discretization FormulaeIndexAuthor(s) DescriptionHelcio 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.