Explicit Solutions for the Solomon-Wilson-Alexiades's Mushy Zone Model with Convective or Heat Flux Boundary Conditions

Abstract

We complete the Solomon-Wilson-Alexiades's mushy zone model (Solomon, 1982) for the one-phase Lame-Clapeyron-Stefan problem by obtaining explicit solutions when a convective or heat flux boundary condition is imposed on the fixed face for a semi-infinite material. We also obtain the necessary and sufficient condition on data in order to get the explicit solutions for both cases which is new with respect to the original model. Moreover, when these conditions are satisfied, the two phase-change problems are equivalent to the same problem with a temperature boundary condition on the fixed face and therefore an inequality for the coefficient which characterized one of the two free interfaces of the model is also obtained.