Solution of heat transfer problems for stochastic boundary conditions

Abstract

Solutions are known for a great deal of heat transfer problems with stationary or analytically given transient boundary conditions. In this paper the well-known Duhamel theorem will be extended for boundary conditions not stated analytically. The fact that the energy supply to a system depends on time in a stochastic manner is a problem in many technical applications. It will be shown by comparison with well-known analytical calculations, that the extended method of Duhamel can be used for calculating the temperature distributions and heat fluxes in any case of transient variations of heat supply or temperatures forced upon the system. The method leads to a long series of error or trigonometrical functions. In order to compute these in real time, an EDP with high capacity and velocity is necessary. But that should be no problem nowadays.