Inverse Heat Source Design Combining Radiation and Conduction Heat Transfer

This work investigates solutions of inverse heat source problems for combined-mode radiation and conduction. The problem consists of finding the heat source distribution in an absorbing-emitting medium that satisfies both the temperature and the heat flux distributions prescribed on the surfaces of a two-dimensional rectangular enclosure. The participating medium is gray, the walls are gray emitters and absorbers, and all the thermal properties are uniform. The combined heat transfer mode problem is described by a system of non-linear equations, which is solved by an iterative procedure. At each iteration a system of linear equations is solved, but, as often occurs in inverse problem, the system of equations is ill-conditioned, and the number of equations and the number of unknowns are not necessarily the same. The solution is obtained by regularizing the system by truncated singular value decomposition (TSVD). It is also discussed how to impose additional conditions to satisfy physical constraints that govern the heat source itself.