3D Inverse Boundary Design Problem of Conduction-radiation Heat Transfer

A numerical analysis of a combined heat transfer problem was considered in this study. The inverse boundary design problem of combined conduction-radiation was solved. The aim of this study was to find the strength of heaters in a 3D cubic enclosure to produce desired temperature and heat flux distribution on the design surface. Conjugate gradients method was chosen to perform the iterative search procedure for obtaining the optimal solution. The direct problem was solved using the finite volume method for both energy and radiative transfer equations. Effects of conduction-radiation parameter, extinction coefficient, single scattering albedo and aspect ratio of the enclosure were studied. The results showed that the combination of a direct method and an inverse one could lead to precise estimation of the heater power distribution. Various problems of the pure radiation, pure conduction and combined radiation-conduction were solved and it was observed that estimated heat flux on the design surface was so close to the desired value that the maximum root mean square error was less than 2%.