The problem for calculating the temperature distribution in cables, semiconductor devices or electronic tubes if these devices are heated by given time functions of heat flow or temperature, leads to the more general problem to find the solution of a set of n coupled heat conduction equations. This problem can be solved using a generalized Fourier-expansion of the temperature time function which describes the temperature distribution in the considered laminated system for linear, cylindrical and spherical bodies, if the space dependency is described by one coordinate.

Because of the formal identity of the diffusion equation and the equation of heat conduction, the method can also be used to solve analogous diffusion problems. It is furthermore applicable in the theory of heat exchangers, in the general theory of the production of pressed or automatically blown glass and in the theory of slip cast processing.