Based on the use of additional boundary conditions (characteristics) and the integral method of heat balance, a numerical and analytical solution of the heat conduction problem for an infinitely extended plate is obtained under symmetric boundary conditions of the third kind with constant internal heat sources in time. Considering the heat flux on the plate surface as a new sought function, a simple analytical form of the specified problem is obtained. Using the proposed approach is possible for solving partial differential equations that do not allow separation of variables.

Keywords: analytical solution, internal heat sources, non-stationary thermal conductivity, boundary value problem, boundary conditions of the third kind, additional function, integral of heat balance