Some exact solutions of the heat conduction equation in parallelepiped obtained by the fast expansions method

Abstract

An analytical solution to the boundary value problem for the Poisson equation in a parallelepiped was obtained in general form using the fast expansions method. The construction of exact solutions of the heat conduction equation for the cases of an internal source depending on coordinates was shown in the work. The study of the influence of the variability of the internal source on the propagation of heat in the body at the same initial temperatures at the parallelepiped vertices was carried out. In this case, the heat in the body will be transferred only in those directions in which the internal source is changed.