Application of thermal potentials to solving heat conduction problems in a layer

Abstract

We solve the boundary-value problem of nonstationary heat conduction in a layer between parallel planes by joint application of Fourier-Laplace integral transforms and thermal potentials. A relationship is established between the original multidimensional problem and some special one-dimensional problem of nonstationary heat conduction, which is solved numerically. As a result, we obtain a solution of the original multidimensional problem of heat conduction which can be conveniently used in practical calculations.