2nd Edition

Heat Conduction Using Green's Functions

    664 Pages 131 B/W Illustrations
    by CRC Press

    Continue Shopping

    Since its publication more than 15 years ago, Heat Conduction Using Green’s Functions has become the consummate heat conduction treatise from the perspective of Green’s functions—and the newly revised Second Edition is poised to take its place. Based on the authors’ own research and classroom experience with the material, this book organizes the solution of heat conduction and diffusion problems through the use of Green’s functions, making these valuable principles more accessible. As in the first edition, this book applies extensive tables of Green’s functions and related integrals, and all chapters have been updated and revised for the second edition, many extensively.

    Details how to access the accompanying Green’s Function Library site, a useful web-searchable collection of GFs based on the appendices in this book

    The book reflects the authors’ conviction that although Green’s functions were discovered in the nineteenth century, they remain directly relevant to 21st-century engineers and scientists. It chronicles the authors’ continued search for new GFs and novel ways to apply them to heat conduction.

    New features of this latest edition—

    • Expands the introduction to Green’s functions, both steady and unsteady
    • Adds a section on the Dirac Delta Function
    • Includes a discussion of the eigenfunction expansion method, as well as sections on the convergence speed of series solutions, and the importance of alternate GF
    • Adds a section on intrinsic verification, an important new tool for obtaining correct numerical values from analytical solutions

    A main goal of the first edition was to make GFs more accessible. To facilitate this objective, one of the authors has created a companion Internet site called the Green’s Function Library, a web-searchable collection of GFs. Based on the appendices in this book, this library is organized by differential equation, geometry, and boundary condition. Each GF is also identified and cataloged according to a GF numbering system. The library also contains explanatory material, references, and links to related sites, all of which supplement the value of Heat Conduction Using Green’s Functions, Second Edition as a powerful tool for understanding.

    Introduction to Green’s Functions

    Heat Flux and Temperature

    Differential Energy Equation

    Boundary and Initial Conditions

    Integral Energy Equation

    Dirac Delta Function

    Steady Heat Conduction in One Dimension

    GF in the Infinite One-Dimensional Body

    Temperature in an Infinite One-Dimensional Body

    Two Interpretations of Green’s Functions

    Temperature in Semi-Infinite Bodies

    Flat Plates

    Properties Common to Transient Green’s Functions

    Heterogeneous Bodies

    Anisotropic Bodies


    Non-Fourier Heat Conduction

    Numbering System in Heat Conduction

    Geometry and Boundary Condition Numbering System

    Boundary Condition Modifiers

    Initial Temperature Distribution

    Interface Descriptors

    Numbering System for g(x, t)

    Examples of Numbering System

    Advantages of Numbering System

    Derivation of the Green’s Function Solution Equation

    Derivation of the One-Dimensional Green’s Function Solution Equation

    General Form of the Green’s Function Solution Equation

    Alternative Green’s Function Solution Equation

    Fin Term m2T

    Steady Heat Conduction

    Moving Solids

    Methods for Obtaining Green’s Functions

    Method of Images

    Laplace Transform Method

    Method Of Separation of Variables

    Product Solution for Transient GF

    Method of Eigenfunction Expansions

    Steady Green’s Functions

    Improvement of Convergence and Intrinsic Verification

    Identifying Convergence Problems

    Strategies to Improve Series Convergence

    Intrinsic Verification

    Rectangular Coordinates

    One-Dimensional Green’s Functions Solution Equation

    Semi-Infinite One-Dimensional Bodies

    Flat Plates: Small-Cotime Green’s Functions

    Flat Plates: Large-Cotime Green’s Functions

    Flat Plates: The Nonhomogeneous Boundary

    Two-Dimensional Rectangular Bodies

    Two-Dimensional Semi-Infinite Bodies

    Steady State

    Cylindrical Coordinates

    Relations for Radial Heat Flow

    Infinite Body

    Separation of Variables for Radial Heat Flow

    Long Solid Cylinder

    Hollow Cylinder

    Infinite Body with a Circular Hole

    Thin Shells, T = T (φ, t)

    Limiting Cases for 2D and 3D Geometries

    Cylinders with T = T (r, z, t )

    Disk Heat Source on a Semi-Infinite Body

    Bodies with T = T (r, φ, t )

    Steady State

    Radial Heat Flow in Spherical Coordinates

    Green’s Function Equation for Radial Spherical Heat Flow

    Infinite Body

    Separation of Variables for Radial Heat Flow in Spheres

    Temperature in Solid Spheres

    Temperature in Hollow Spheres

    Temperature in an Infinite Region Outside a Spherical Cavity

    Steady State

    Steady-Periodic Heat Conduction

    Steady-Periodic Relations

    One-Dimensional GF

    One-Dimensional Temperature

    Layered Bodies

    Two- and Three-Dimensional Cartesian Bodies

    Two-Dimensional Bodies in Cylindrical Coordinates

    Cylinder with T = T (r, φ, z,ω)

    Galerkin-Based Green’s Functions and Solutions

    Green’s Functions and Green’s Function Solution Method

    Alternative form of the Green’s Function Solution

    Basis Functions and Simple Matrix Operations

    Fins and Fin Effect


    Applications of the Galerkin-Based Green’s Functions

    Basis Functions in some Complex Geometries

    Heterogeneous Solids

    Steady-State Conduction

    Fluid Flow in Ducts


    Unsteady Surface Element Method

    Duhamel’s Theorem and Green’s Function Method

    Unsteady Surface Element Formulations

    Approximate Analytical Solution (Single Element)







    Kevin D. Cole received his M.S. in aerospace engineering and mechanics from the University of Minnesota in 1979 and his Ph.D. in mechanical engineering from Michigan State University in 1986. Dr. Cole has held several positions in academia and industry and is currently Associate Professor of Mechanical Engineering at the University of Nebraska—Lincoln. Dr. Cole is active in writing and reviewing in the areas of heat conduction and thermal measurements. He is the creator of the Green’s Function Library internet site.

    James V. Beck received his S.M. in mechanical engineering from MIT in 1957 and his Ph.D. from Michigan State University in 1964. Dr. Beck is currently Professor Emeritus of Mechanical Engineering at Michigan State University. He has been honored with the MSU Distinguished Faculty Award and the ASME Heat Transfer Memorial Award. He is the originator of the Inverse Problems Symposium and is the inventor, with Professor Litkouhi of the numbering system for heat conduction solutions. Dr. Beck has contributed to the field of heat transfer with numerous refereed journal articles and books.

    A. Haji-Sheikh received his M.S. in M.E., M.A. in Math from the University of Michigan and a Ph.D. in 1965 from the University of Minnesota. In 1966, he joined the Department of Mechanical Engineering at the University of Texas at Arlington, and is currently Professor and member of the Distinguished Scholars Academy. His contributions to heat conduction include the floating random walk in Monte Carlo method, Green’s function in two-ste models, inverse problems, and Galerkin-based integral methods. He is a registered PE in the state of Texas, a Fellow of ASME, a recipient of the ASME Memorial Award in Science.

    Bahman Litkouhi received his M.S. and Ph.D. from Michigan State University and is presently Professor and Graduate Program Director of the Mechanical Engineering Department at Manhattan College. Dr. Litkouhi is a registered professional engineer in the state of New York and a member of the American Society of Mechanical Engineers. He has authored several technical publications in heat transfer and has served as an industria consultant.