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Heat Conduction Using Green's Functions (2nd Edition) by Beck James V., Cole Kevin D., Haji Sheikh A., Litkouhi Bahman
**

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**About this book :- **
**Heat Conduction Using Green's Functions (2nd Edition) ** written by
** Beck James V., Cole Kevin D., Haji Sheikh A., Litkouhi Bahman**.
The purpose of this book is to simplify and organize the solution of heat conduction and diffusion problems and to make them more accessible. This is accomplished using the method of Green’s functions, together with extensive tables of Green’s functions and related integrals. The tables of Green’s functions were first compiled as a supplement to a first-year graduate course in heat conduction taught at Michigan State University. The book was originally envisioned as a reference volume, but it has grown into a heat conduction treatise from a Green’s function perspective.

There is enough material for a one-semester course in analytical heat conduction and diffusion. There are worked examples and student problems to aid in teaching. Because of the emphasis on Green’s functions, some traditional topics such as Fourier series and Laplace transform methods are treated somewhat briefly; this material could be supplemented according to the interest of the instructor. The book can also be used as a supplementary text in courses on heat conduction, boundary value problems, or partial differential equations of the diffusion type.

This book is best for the use as a reference for practicing engineers, applied mathematicians, physicists, geologists, and others. In many cases, a heat conduction or diffusion solution may be assembled from tabulated Green’s functions rather than derived. The book contains the most extensive set of Green’s functions and related integrals that is currently available for heat conduction and diffusion.

The book is organized on a geometric basis because each Green’s function is associated with a unique geometry. For each of the three coordinate systems—Cartesian, cylindrical, and spherical—there is a separate appendix of Green’s functions named Appendix X, Appendix R, and Appendix RS, respectively. Each of the Green’s functions listed is identified by a unique alphanumeric character that begins with either X, R, or RS to denote the x, r, or the spherical r coordinate, respectively. It is important for the reader to know something about this numbering system to use the tables of Green’s functions.Amore detailed numbering system, which covers both Green’s functions and temperature solutions, is discussed in Chapter 2.We find the numbering system very helpful in identifying exactly which solution is under discussion, and all of the solutions discussed in the text are listed in Appendix N indexed according to the numbering system.

The level of treatment is intended for senior and first-year graduate students in engineering and mathematics.We have emphasized solution of problems rather than theorems and proofs, which are generally omitted.Aprerequisite is an undergraduate course in ordinary differential equations. A previous introduction to the method of separation of variables for partial differential equations is also important.

**Book Detail :- **
** Title: ** Heat Conduction Using Green's Functions
** Edition: ** 2nd Edition
** Author(s): ** Beck James V., Cole Kevin D., Haji Sheikh A., Litkouhi Bahman
** Publisher: ** CRC Press
** Series: **
** Year: ** 2010
** Pages: ** 666
** Type: ** PDF
** Language: ** English
** ISBN: ** 9781439813546;9781439895214;9781466501232;9780429109188
** Country: ** US

**About Author :- **
The author ** 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. 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.

The author ** James V. Beck ** received his MS 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 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 referred journal articles and books.

The author ** A. Haji-Sheikh ** received his MS in ME, MAin 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. He is a registered PE in the state of Texas, a fellow of ASME, a recipient of the ASME Memorial Award in Science.

The author ** 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.

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**Book Contents :- **
**Heat Conduction Using Green's Functions (2nd Edition) ** written by
** Beck James V., Cole Kevin D., Haji Sheikh A., Litkouhi Bahman**
cover the following topics.

1. Introduction to Green’s Functions

2. Numbering System in Heat Conduction

3. Derivation of the Green’s Function Solution Equation

4. Methods for Obtaining Green’s Functions

5. Improvement of Convergence and Intrinsic Verification

6. Rectangular Coordinates

7. Cylindrical Coordinates

8. Radial Heat Flow in Spherical Coordinates

9. Steady-Periodic Heat Conduction

10. Galerkin-Based Green’s Functions and Solutions

11. Applications of the Galerkin-Based Green’s Functions

12. Unsteady Surface Element Method

Appendix

B Bessel Functions

D Dirac Delta Function

E Error Function and Related Functions

F Functions And Series

i Integrals

L Laplace Transform Method

P Properties of Selected Materials

R Green’s Functions for Radial-Cylindrical Coordinates (r)

RF Green’s Functions for Cylindrical Coordinates (r, f)

F Cylindrical Polar Coordinate, f Thin Shell Case

RS Green’s Functions for Radial Spherical Geometries

X Green’s Functions: Rectangular Coordinates

Index of Solutions by Number System

Author Index

subject Index

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