Time-dependent heat transfer in a plate with anisotropy of general form under the action of pulsed heat sources

Abstract

An analytical solution to the problem of the theory of heat conduction in an anisotropic band under the pulsed (point) action of heat sources has been obtained for the first time by constructing the boundary influence function from using the Fourier and Laplace integral transforms. An arbitrary orientation of the principal axes of the thermal conductivity tensor and arbitrary (including negative) values of the off-diagonal components of the thermal conductivity tensor are taken into account. The found solution is extended to piecewise continuous densities of heat fluxes at the free boundaries of an anisotropic plate. The influences of the principal components and the orientation of the principal axes of the thermal conductivity tensor on time-dependent temperature fields in the anisotropic plate are determined. It is established that there are saddle points and separatrices dividing the temperature field into regions of influence of the boundary heat fluxes. The results are used to solve problems involving the thermal state of thermal protection made of anisotropic materials.