Efficient computation of heat flux signals to ensure the reproduction of prescribed temperatures at several interacting heat sources

A general and efficient converging iterative process is used to determine the heat flux emanating from heat sources kept at prescribed temperatures. The algorithm uses analytical models, whose source is represented by a Neumann boundary condition or a source term. As a final result, the algorithm provides a heat flux signal that ensures the reproduction of a prescribed temperature signal at a source. The algorithm can manage several interacting sources and can handle different time varying temperatures at each source. To account for time-varying heat flux, the temporal superposition principle is used and expressed as a convolution product, and then solved with a fast Fourier transform to significantly cut down the computation time. It is shown that the proposed algorithm is fast and accurate.