Inverse determination of heat source distribution in conductive-radiative media with irregular geometry

This work investigates the inverse problem of finding the two-dimensional heat source distribution in an irregular conductive-radiative medium to satisfy the desired temperature and heat flux distributions over the design surface. The participating medium is gray and non-scattering, the walls are diffuse and gray, and all the thermal properties are uniform. The conjugate gradient method is used to minimize an objective function, expressed by the sum of square residuals between estimated and desired heat fluxes over the design surface. A combination of the finite element method with the discrete transfer method is used to solve the direct problem of conductive-radiative heat transfer. The results of the problem are in good agreement with available numerical solution. The performance and ability of the method for irregular geometries is investigated by an example problem.