Non-iterative solution of inverse heat conduction problems in one dimension

A model is presented for the inverse determination of the strength of a temporal-spatial-dependent heat source in the one-dimensional heat conduction problem. This model is constructed from the finite difference approximation of the differential heat conduction equation based on the assumption that the temperature measurements are available over the problem domain. In contrast to the traditional approach, the iteration in the proposed model can be done only once and the inverse problem can be solved in a linear domain. In the examples, comparisons between the exact heat sources and the estimated ones (without measurement errors) are made to confirm the validity of the proposed model. The close agreement between the exact solutions and the estimated results shows the potential of the proposed model in finding an accurate value of the heat source in the one-dimensional heat conduction problem. (C) 1997 by John Wiley & Sons, Ltd.