11R13. Boundary Element Method for Heat Conduction: With Applications in Non-Homogeneous Media. Topics in Engineering, Volume 44. - EA Divo and AJ Kassab (Univ of Central Florida, Orlando FL). WIT Press, Southampton, UK. Distributed in USA by Comput Mech, Billerica MA. 2003. 245 pp. CD-Rom included. ISBN 1-85312-771-X. $138.00.

Reviewed by DP Sekulic (Col of Eng, Univ of Kentucky, 210B CRMS Bldg, Lexington KY 40506-0108).

This interesting work is published by WIT Press as the 44th volume in the series Topics in Engineering edited by CA Brebbia of the Wessex Institute of Technology, and JJ Connor of the Massachusetts Institute of Technology. The aim of the series is to provide a rapid and informal dissemination of significant new work in engineering. This book represents a monograph in the series devoted to an important numerical tool known under the name boundary element method (BEM). The authors are known contributors to that field, and this monograph represents a segment of their work devoted to development of the boundary element methods for heat conduction problems in nonhomogeneous media.

The monograph provides a detailed account of the developed method including: (1) steady-state (isotropic, anisotropic and axisymmetric), and (2) transient formulations. In addition, the method is illustrated by applications to nonlinear heat conduction and inverse problems (parameter estimation in heat conduction).

The book is organized in nine chapters as follows. The opening chapter provides a very brief introduction accompanied by a list of references related to BEM and the corresponding theoretical background important for heat conduction applications in both isotropic and anisotropic heterogeneous media. The Introduction concludes with the statement of the book’s purpose, namely, “to formulate a general technique for the development of a boundary integral equation for steady-state and transient heat conduction in heterogeneous isotropic and anisotropic media.” Chapter 2 offers a brief review of a BEM formulation for spatially uniform thermal conductivity cases. As a counterpoint, the following Chapter 3 offers the steady state anisotropic formulation, while in Chapter 4 an extension to axisymmetric cases is provided. A transient fundamental solution is discussed in Chapter 5 by using two approaches: (1) the authors’ dual-reciprocity method, and (2) a combination of the Laplace transforms and dual-reciprocity methods. An application to nonlinear heat conduction is addressed in (a very short) Chapter 6, including some illustrations of the method’s application to cases of one- and two-dimensional temperature fields, in both regular and irregular regions. Chapter 7 is devoted to the problem of identification of an unknown thermal conductivity of a nonhomogeneous medium. In a fairly detailed and well-documented introduction, the inverse problems and the application of BEM to such important engineering topics are presented. Subsequently the related optimizations methods, genetic algorithms, and series expansions are discussed. The chapter concludes, as do most of the other chapters, with examples. The last two chapters, Chapter 8 and 9, together with appendices, offer a presentation of two computer codes ready for implementation.

This demanding technical subject is presented in a well-organized manner. The authors did a good job in setting the text with appealing graphics, including all the color-coded graphic files for each figure provided in the attached CD-ROM. The Fortran codes, given explicitly in the set of appendices, a software included in the CD-ROM, and detailed estimations of the calculation errors in the examples are quite convincing in supporting the author’s claim that the proposed method works well.

The authors and their publisher are to be congratulated for the decision to include a CD-ROM. Implementation of the provided software goes smoothly if the reader has proper supporting software drivers. A more prominent note in the main body of the text and/or a separate appendix regarding the software installation and its use would be beneficial, but the reader can get around the related problems relatively easily by exploring the software itself. A number of illustrative examples supported by data generated using the included software are a very good educational tool.

The book does not have an index. An additional drawback (that would have been easily eliminated by a small but importanteffort) is a lack of a detailed explanation of the technical vocabulary. Such an addition is not mandatory, it is rather rarely included in professional technical books, but this reviewer believes that such new and still somewhat esoteric topics like the one presented in this book desperately need a good terminology explanation, in addition to a complete and detailed nomenclature. The technical language is well utilized and nothing is wrong with an inherent need to use it. Still, an effort of the authors in many fields to disseminate new ideas would better be served if a conscious effort to provide a complete and well-defined technical vocabulary (including brief illustrations of most important new concepts), and better cross-referencing (including the index) would be a great addition to any such publication. This book does not have either. The nomenclature is not complete, and numerous omissions are apparent.

In conclusion, this reviewer recommends, without reservations, this book to engineers and researchers in a need for numerical modeling of heat conduction in nonhomogeneous media. Boundary Element Methods for Heat Conduction: With Applications in Non-Homogeneous Media (and the provided software) should find an easy way to classrooms of advanced heat transfer and numerical modeling classes in engineering schools.