Solving particular class of unsteady heat conductivity problems in the domain with moving boundary by splitting the generalized Fourier transformation

Analytical method is proposed to solve boundary problems of unsteady heat conductivity in a domain with the boundary moving according to the known regularity and with the heat transfer coefficient changing versus time. The method is based on splitting the generalized integral Fourier transformation on a spatial variable. Exact analytical problem solutions for pulse and pulse-periodical modes of heat exchange with environment, are derived. Asymptotic estimations of utmost temperatures on the moving boundary under considered modes of unsteady heat exchange, are given.