The Finite Element Method in Heat Transfer and Fluid Dynamics

EQUATIONS OF HEAT TRANSFER AND FLUID MECHANICS Present Study Governing Equations of a Continuum Governing Equations in Terms of Primitive Variables Porous Flow Equations Auxiliary Transport Equations sChemically Reacting Systems Boundary Conditions sChange of Phase Enclosure Radiation Summary of Equations THE FINITE ELEMENT METHOD: AN OVERVIEW Model Differential Equation Finite Element Approximation Weighted-Integral Statements and Weak Forms Finite Element Model Interpolation Functions Assembly of Elements Time-Dependent Problems Axisymmetric Problems Convective Boundary Conditions Library of Finite Elements Numerical Integration Modeling Considerations Illustrative Examples 3D CONDUCTION HEAT TRANSFER Semidiscrete Finite Element Model Interpolation Functions Numerical Integration Computation of Surface Fluxes Semidiscrete Finite Element Model Solution of Nonlinear Equations Radiation Solution Algorithms Variable Properties sPost-Processing Operations sAdvanced Topics in Conduction sExamples of Diffusion Problems VISCOUS INCOMPRESSIBLE FLOWS Mixed Finite Element Model Penalty Finite Element Models Finite Element Models of Porous Flow Computational Considerations Solution of Nonlinear Equations Time-Approximation Schemes sStabilized Methods Post-Processing sAdvanced Topics Advanced Topics - Turbulence Numerical Examples CONVECTIVE HEAT TRANSFER Mixed Finite Element Model Penalty Finite Element Model Finite Element Models of Porous Flow Solution Methods Convection with Change of Phase Convection with Enclosure Radiation Post-Computation of Heat Flux Advanced Topics - Turbulent Heat Transfer Advanced Topics - Chemically Reacting Systems Numerical Examples sNON-NEWTONIAN FLUIDS Governing Equations of Inelastic Fluids Finite Element Models of Inelastic Fluids Solution Methods for Inelastic Fluids Governing Equations of Viscoelastic Fluids Finite Element Model of Differential Form Finite Element Model of Integral Form Unresolved Problems Numerical Examples sCOUPLED PROBLEMS Coupled Boundary Value Problems Fluid Mechanics and Heat Transfer Solid Mechanics Electromagnetics Coupled Problems in Mechanics Implementation of Coupled Algorithms Numerical Examples sADVANCED TOPICS Parallel Processing Other Topics Note: Chapters also include an Introduction, Exercises, and References APPENDIX A: COMPUTER PROGRAM--HEATFLOW Heat Transfer and Related Problems Flows of Viscous Incompressible Fluids Description of the Input Data A Source Listings of Selective Subroutines Reference sAPPENDIX B: SOLUTION OF LINEAR EQUATIONS Introduction Direct Methods Iterative Methods References for Additional Reading sAPPENDIX C: FIXED POINT METHODS AND CONTRACTION MAPPINGS Fixed Point Theorem Chord Method Newton's Method The Newton-Raphson Method Descent Methods References for Additional Reading