Heat Conduction Using Green's Functions  book cover
2nd Edition

Heat Conduction Using Green's Functions

ISBN 9781439813546
Published July 16, 2010 by CRC Press
663 Pages 131 B/W Illustrations

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Book Description

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.

Table of Contents

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)






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