# MR1090950,Martinet, Jean ,Thermocińetique approfondie

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Previous Up Next Article Citations From References: 0 From Reviews: 0 MR1090950 (92d:80001) 80-02 (35K05 73B30 80A20) Martinet, Jean (F-POIT) FThermocine´tique approfondie. (French) [Advanced thermokinetics] Technique et Documentation, Paris, 1990. xii+307 pp. 245 F. ISBN 2-85206-577-0 This book brings together the main analytical methods used in heat conduction problems. The mathematical tools needed are recalled in the appendices of the book. Chapter 1 is devoted to the Fourier and Hankel integral transforms and to their applications to 1-D and 2-D heat conduction in finite, semi-infinite and infinite slabs, in cylindrical and spherical geometries. In Chapter 2, the Laplace transform is used for problems similar to the ones of Chapter 1, for bimaterial walls, for moving boundaries (simulation of sublimation, ablation, erosion or material deposit), for thermal control, exchangers and regenerators. The method involving the Laplace transform is rather straightforward for all types of boundary conditions but is less efficient for problems with more than one space variable. Thermal applications of the Duhamel method are presented in Chapter 3; this method is used to determine the time evolution of temperature in a solid under the influence of transient boundary conditions, in the cases where the solutions are known for constant boundary conditions. This is based on the linearity of the transfer equation, which holds when the thermal characteristics are temperature-independent. Chapter 4 uses the methods of fixed or movable sources of thermal energy in a three-dimensional field; the sources are instantaneous, continuous or periodic in time, point-like, linear or surface-like, or even doublets. The image method, well known in electrostatics, is also developed. Different Green functions and their applications are outlined in Chapter 5. Analytic solutions do not always exist or are difficult to put in closed form or to compute; in these cases, approximate analytical approaches must be used. Amon

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