INVERSE STEFAN PROBLEM IN A GRAY SEMITRAN SPARENT MEDIUM FITTED WITH 2 BLACK INTERFACES

The Stefan problem is studied for the melting of an one-dimensional pl ane parallel semi-transparent material fitted with black boundaries. T he system is defined for a fixed spatiotemporal [0, 1] x [0, infinity] domain. The inverse problem is solved by an optimization method assoc iated with a sequential method based on a moving time horizon. It allo ws to retrieve the interface position as a function of time from a set of temperature data measured on the fixed boundary. The study is supp orted by solution of the direct problem accounting for the radiative-c onductive coupling solved by means of the discrete ordinates method. F or high initial optical thicknesses, the method provides satisfactory results even with noisy input data. When the medium becomes opticaly, thin the sensitivity coefficient is too weak to insure the inversion.