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—
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Expands the introduction to Green’s functions, both steady and unsteady
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Adds a section on the Dirac Delta Function
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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
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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.
Preface
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
Problems
References
Appendices
Index
