Heat Conduction Using Greens Functions

Kevin Cole, James Beck, A. Haji-Sheikh, Bahman Litkouhi

• Publisher: CRC Press
• Year: 2010
• Print ISBN:
  9781439813546
• eBook ISBN:
  9781040060766
• Topic: Physical Sciences
• Subtopic: Differential Equations

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

• Cover
• Half Title
• Series Page
• Title Page
• Copyright Page
• Table of Contents
• Preface to the First Edition
• Preface to the Second Edition
• Authors
• Nomenclature
• Chapter 1 Introduction to Green’s Functions
• Chapter 2 Numbering System in Heat Conduction
• Chapter 3 Derivation of the Green’s Function Solution Equation
• Chapter 4 Methods for Obtaining Green’s Functions
• Chapter 5 Improvement of Convergence and Intrinsic Verification
• Chapter 6 Rectangular Coordinates
• Chapter 7 Cylindrical Coordinates
• Chapter 8 Radial Heat Flow in Spherical Coordinates
• Chapter 9 Steady-Periodic Heat Conduction
• Chapter 10 Galerkin-Based Green’s Functions and Solutions
• Chapter 11 Applications of the Galerkin-Based Green’s Functions
• Chapter 12 Unsteady Surface Element Method
• Appendix B Bessel Functions
• Appendix D Dirac Delta Function
• Appendix E Error Function and Related Functions
• Appendix F Functions and Series
• Appendix I Integrals
• Appendix L Laplace Transform Method
• Appendix P Properties of Selected Materials
• Appendix R Green’s Functions for Radial-Cylindrical Coordinates (r)
• Appendix RΦ Green’s Functions for Cylindrical Coordinates (r, ϕ)
• Appendix Φ Cylindrical Polar Coordinate, ϕ Thin Shell Case
• Appendix RS Green’s Functions for Radial Spherical Geometries
• Appendix X Green’s Functions: Rectangular Coordinates
• Index of Solutions by Number System
• Author Index
• Subject Index