Heat Conduction Using Green's Functions

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.

Kevin D. Cole received his MS in aerospace engineering and mechanics from the University of Minnesota in 1979 and his PhD 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. He is the creator of the Green’s Function Library Internet site.

James V. Beck received his SM in mechanical engineering from MIT in 1957 and his PhD from Michigan State University in 1964. Dr. Beck is currently professor emeritus of mechanical engineering at Michigan State University. 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 referred journal articles and books.

A. Haji-Sheikh received his MS in ME, MA in Mathematics from the University of Michigan and a PhD 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 a 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-step models, inverse problems, and Galerkin-based integral methods.

Bahman Litkouhi received his MS and PhD 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 industrial consultant.