3rd Edition

The Finite Element Method in Heat Transfer and Fluid Dynamics

By J. N. Reddy, D.K. Gartling Copyright 2010
    524 Pages 195 B/W Illustrations
    by CRC Press

    As Computational Fluid Dynamics (CFD) and Computational Heat Transfer (CHT) evolve and become increasingly important in standard engineering design and analysis practice, users require a solid understanding of mechanics and numerical methods to make optimal use of available software. The Finite Element Method in Heat Transfer and Fluid Dynamics, Third Edition illustrates what a user must know to ensure the optimal application of computational procedures—particularly the Finite Element Method (FEM)—to important problems associated with heat conduction, incompressible viscous flows, and convection heat transfer.

    This book follows the tradition of the bestselling previous editions, noted for their concise explanation and powerful presentation of useful methodology tailored for use in simulating CFD and CHT. The authors update research developments while retaining the previous editions’ key material and popular style in regard to text organization, equation numbering, references, and symbols.

    This updated third edition features new or extended coverage of:

    • Coupled problems and parallel processing
    • Mathematical preliminaries and low-speed compressible flows
    • Mode superposition methods and a more detailed account of radiation solution methods
    • Variational multi-scale methods (VMM) and least-squares finite element models (LSFEM)
    • Application of the finite element method to non-isothermal flows
    • Formulation of low-speed, compressible flows

    With its presentation of realistic, applied examples of FEM in thermal and fluid design analysis, this proven masterwork is an invaluable tool for mastering basic methodology, competently using existing simulation software, and developing simpler special-purpose computer codes. It remains one of the very best resources for understanding numerical methods used in the study of fluid mechanics and heat transfer phenomena.

    Equations of Heat Transfer and Fluid Mechanics
    Present Study
    Mathematical Preliminaries
    Governing Equations of a Continuum
    Governing Equations in Terms of Primitive Variables
    Porous Flow Equations
    Low-Speed Compressible Flow Equations
    Auxiliary Transport Equations
    Chemically Reacting Systems
    Boundary Conditions
    Change of Phase
    Enclosure Radiation
    Summary of Equations

    The Finite Element Method
    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
    Library of Finite Elements
    Numerical Integration
    Modeling Considerations
    Illustrative Examples

    Conduction Heat Transfer
    Semidiscrete Finite Element Model
    Interpolation Functions
    Numerical Integration
    Computation of Surface Flux
    Semidiscrete Finite Element Model
    Solution of Nonlinear Equations
    Radiation Solution Algorithms
    Variable Properties
    Post-Processing Operations
    Advanced Topics in Conduction
    Example Problems

    Flows of Viscous Incompressible Fluids
    Mixed Finite Element Model
    Penalty Finite Element Models
    Finite Element Models of Porous Flow
    Computational Considerations
    Solution of Nonlinear Equations
    Time-Approximation Schemes
    Stabilized Methods
    Least-Squares Finite Element Models
    Free Surface Flows
    Numerical Examples

    Coupled Fluid Flow and Heat Transfer
    Nonisothermal Incompressible Flows
    Mixed Finite Element Model
    Penalty Finite Element Model
    Finite Element Models of Porous Flow
    Nonisothermal, Low-Speed, Compressible Flows
    Solution Methods
    Convection with Change of Phase
    Convection with Enclosure Radiation
    Post-Computation of Heat Flux
    Turbulent Heat Transfer
    Chemically Reacting Systems
    Numerical Examples

    Flows of Non-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
    Additional Models of Differential Form
    Finite Element Model of Integral Form
    Unresolved Problems
    Numerical Examples

    Multiphysics Problems
    Coupled Boundary Value Problems
    Fluid Mechanics and Heat Transfer
    Solid Mechanics
    Coupled Problems in Mechanics
    Implementation of Coupled Algorithms
    Numerical Examples

    Parallel Processing
    Parallel Systems
    FEM and Parallel Processing


    Subject Index


    J.N. Reddy earned a Ph.D. in Engineering Mechanics from the University of Alabama in Huntsville, worked as a Postdoctoral Fellow at the University of Texas at Austin, was Research Scientist for Lockheed Missiles and Space Company during l974.75, and taught at the University of Oklahoma from 1975 to 1980 and Virginia Polytechnic Institute & State University from 1980 to 1992. Currently, he is a Distinguished Professor and the inaugural holder of the Oscar S. Wyatt Endowed Chair at Texas A&M University, College Station. Dr. Reddy has published over 400 journal papers and 16 textbooks on theoretical formulations and numerical simulations of problems in solid and structural mechanics, computational fluid dynamics, numerical heat transfer, computational biology, geology and geophysics, mechanics of nanosystems, and applied mathematics.

    Dr. Reddy is the recipient of numerous honors and awards, including the 1998 Nathan M. Newmark Medal from the American Society of Civil Engineers, the 2003 Computational Solid Mechanics award from the U.S. Association of Computational Mechanics, the 2004 Distinguished Research Award from the American Society for Composites, and an honorary degree (Honoris Causa) from the Technical University of Lisbon, Portugal (2009). Dr. Reddy is a fellow of the American Academy of Mechanics, the American Institute of Aeronautics and Astronautics, the American Society of Civil Engineers, the American Society of Mechanical Engineers, the American Society for Composites, International Association of Computational Mechanics, U.S. Association of Computational Mechanics, the Aeronautical Society of India, and the Institution of Structural Engineers, U.K. Dr. Reddy serves on the editorial boards of two dozen journals, and as the Editor-in-Chief of Applied Mechanics Reviews, Mechanics of Advanced Materials and Structures, International Journal of Computational Methods in Engineering Science and Mechanics, and International Journal of Structural Stability and Dynamics. As a result of his extensive publications of archival journal papers and books, Dr. Reddy is recognized by ISI Highly Cited Researchers with over 10,000 citations and an H-index of over 40 to his credit. A more complete resume with links to journal papers can be found at http://authors.isihighlycited.com/ or http://www.tamu.edu/acml.

    D.K. Gartling is a senior scientist in the Engineering Sciences Center at Sandia Nationa Laboratories, Albuquerque, New Mexico. He earned his B.S. and M.S. in Aerospace Engineering at the University of Texas at Austin and completed the diploma course at th von Karman Institute for Fluid Dynamics in Brussels, Belgium. After completion of his Ph.D. in Aerospace Engineering at the University of Texas at Austin, he joined the technical staff at Sandia National Laboratories. Dr. Gartling was a Visiting Associate Professor in the Mechanical Engineering Department at the University of Sydney, Australia, under a Fulbright Fellowship, and later he was a Supervisor in the Fluid and Thermal Sciences Department at Sandia National Laboratories. Dr. Gartling has published numerous papers dealing with Þnite element model development and finite element analysis of heat transfer and fluid dynamics problems of practical importance. He is the recipient of the 2001 Computational Fluid Dynamics Award from the U.S. Association of Computational Mechanics and is a fellow of the American Society of Mechanical Engineers. Dr. Gartling is presently a member of several professional societies, serves on the editorial boards o several journals, and is the Co-Editor of International Journal for Numerical Methods I Fluids.

    "This third edition is an updated and extended version of a bestselling monograph, written by two well-known authors, about numerical simulation of the two disciplines heat transfer and fluid dynamics, closely couple in many engineering and scientific applications, by the finite element method. The text is based on graduate lectures and extended courses for a wide spectrum of engineering students and on own practical experiences. Also professionals in modeling of heat transfer, incompressible viscous flow, and heat convection and corresponding codes can profit from the book."
    –– Georg Hebermehl, Zentralblatt MATH