This work investigates solutions of inverse heatsource problems for combined-mode radiation and conduction.The problem consists of finding the heat source distribution inan absorbing-emitting medium that satisfies both thetemperature and the heat flux distributions prescribed on thesurfaces of a two-dimensional rectangular enclosure. Theparticipating medium is gray, the walls are gray emitters andabsorbers, and all the thermal properties are uniform. Thecombined heat transfer mode problem is described by a systemof non-linear equations, which is solved by an iterativeprocedure. At each iteration a system of linear equations issolved, but, as often occurs in inverse problem, the system ofequations is ill-conditioned, and the number of equations andthe number of unknowns are not necessarily the same. Thesolution is obtained by regularizing the system by truncatedsingular value decomposition (TSVD). It is also discussed howto impose additional conditions to satisfy physical constraintsthat govern the heat source itself.
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