Anisotropic Half-Space Temperature Field with its Moving Boundary Being under Local Pulse-periodic Heat Action in Heat Exchange Conditions with External Environment

Abstract

A noticeably raising interest in analytical research methods in the mathematical theory of the thermal conductivity of solids [1-3] was initiated by various causes, among which, as the most significant, special mention should go to the widespread practical engineering application of computer technology, mathematical modelling techniques and anisotropic materials of various origin. At present, the "anisotropic section" [3, 4] holds a most unique position in the mathematical theory of the thermal conductivity of solids, due both to the specificity of the mathematical models used in it, and to the fair-minded development need in fundamentally new high-performance and absolutely stable computational methods [4-6] to solve real, practically important engineering tasks.The spectrum of practical use of solutions to problems of the mathematical theory of the thermal conductivity, presented in an analytically closed form, is quite wide. In particular, such solutions are used to test new computational algorithms, and the problems generating these solutions are called test problems. And if in the traditional sections of the mathematical theory of the thermal conductivity a set of test problems is very extensive [1-3, 7], then test problems of the "anisotropic thermal conductivity" in regions with fixed and moving boundaries are inconsiderable in number [4, 8-14].The main objective of the research is to solve the problem of determining the temperature field of an anisotropic half-space, the boundary of which moves linearly and is subject to local pulse-periodic thermal action under conditions of heat exchange with the external environment.