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Solving direct and inverse heat conduction problems. (English) Zbl 1122.80001
Berlin: Springer (ISBN 3-540-33470-X/hbk). xxvi, 889 p. with CD-ROM. (2006).
The present book is devoted to direct and inverse heat conduction problems. Solving direct problems is the temperature determination when initial and boundary conditions are known, while solving inverse problems, e.g., search for boundary values when temperature properties are known at selected inner points of a body.
In the first part of the book (Chapters 1–5), the authors discuss theoretically heat conduction in solids, motionless liquids and liquids that move in time. In the second part of the book (Chapters 6–26), they discuss at great length different engineering problems, which are presented together with the proposed solutions in the form of theoretical and practical examples. The authors acquaint the reader in a step-by-step fashion with mathematical derivations and solutions to some of the more significant transient and steady-state heat conduction problems with respect to movable and immovable heat sources and the phenomena of melting and freezing. A lot of attention is paid to nonlinear problems. Exact and approximate analytical methods and numerical methods are discussed in great detail, such as the finite difference method, the finite volume method, the finite element method and the boundary element method. Aside from algorithms, applicable computational programs, written in a FORTRAN language, are given. The accuracy of the results obtained by means of various numerical methods is evaluated by comparison with accurate analytical solutions.
The presented solutions not only allow to illustrate mathematical methods used in thermal conduction but also can be used to solve concrete practical problems, for example in designing and life-time calculations of industrial machinery, combustion engines and in refrigerating and air conditioning engineering.
Many examples refer to the topic of heating and thermo-renovation of apartment buildings. The methods for solving problems involved with welding and laser technology are also discussed in great detail.
The present book is addressed to undergraduate and PhD students of mechanical, power, process and environment engineering. Due to the complexity of the heat conduction problems elaborated in the present text, it can also serve as a reference book to be used by nuclear, industrial and civil engineers.

##### MSC:
 80-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to classical thermodynamics 80A23 Inverse problems in thermodynamics and heat transfer 80M20 Finite difference methods applied to problems in thermodynamics and heat transfer 80M15 Boundary element methods applied to problems in thermodynamics and heat transfer 80M10 Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer 35-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations 35R30 Inverse problems for PDEs 35K05 Heat equation 35-04 Software, source code, etc. for problems pertaining to partial differential equations 76A15 Liquid crystals