The Finite Element Method in Heat Transfer and Fluid Dynamics: 3rd Edition (Hardback) book cover

The Finite Element Method in Heat Transfer and Fluid Dynamics

3rd Edition

By J. N. Reddy, D.K. Gartling

CRC Press

524 pages | 195 B/W Illus.

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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.


"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

Table of Contents

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

About the Authors

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 or

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.

About the Series

Applied and Computational Mechanics

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Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Mechanics / General
SCIENCE / Mechanics / Dynamics / Thermodynamics