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A semi-infinite material under a solidification process with theSolomon-Wilson- Alexiades's mushy zone model with a heat flux condition at thefixed boundary is considered. The associated free boundary problem isoverspecified through a convective boundary condition with the aim of thesimultaneous determination of the temperature, the two free boundaries of themushy zone and one thermal coefficient among the latent heat by unit mass, thethermal conductivity, the mass density, the specific heat and the twocoefficients that characterize the mushy zone. Bulk temperature andcoefficients which characterize the heat flux and the heat transfer at theboundary are assumed to be determined experimentally. Explicit formulae for theunknowns are given for the resulting six phase-change problems, besidenecessary and sufficient conditions on data in order to obtain them. Inaddition, relationship between the phase-change process solved in this paperwith an analogous process overspecified by a temperature boundary condition ispresented, and this second problem is solved by considering a large heattransfer coefficient at the boundary in the problem with the convectiveboundary condition. Formulae for the unknown thermal coefficients correspondingto both problems are summarized in two tables.

Determination of one unknown thermal coefficient through a mushy zone model with a convective overspecified boundary condition