A New Unified Space/Time Treatment for Solving Direct and Thermal Design Problems in Radiative and Conductive Transport

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ABSTRACT This proposal is for the development of a numerical method that treats time as the fourth spatial dimension. Preliminary results obtained under a SGER grant demonstrated accurate and stable results for sample heat transfer problems. Because the effect of numerical ill-conditioning is removed by time-collocation, this new method is particularly suitable for solving inverse problems where boundary conditions are usually not known. The proposed work scope involves establishing a set of global basis functions that can be used to expand the time envelop. The goal is to develop the method to a point that it can be used to solve a variety of direct and inverse heat transfer problems.