  The simultaneous determination of two unknown thermal coefficients for a
semi-infinite material under a phase-change process with a mushy zone according
to the Solomon-Wilson-Alexiades model is considered. The material is assumed to
be initially liquid at its melting temperature and it is considered that the
solidification process begins due to a heat flux imposed at the fixed face. The
associated free boundary value problem is overspecified with a convective
boundary condition with the aim of the simultaneous determination of the
temperature of the solid region, one of the two free boundaries of the mushy
zone and two thermal coefficients among the latent heat by unit mass, the
thermal conductivity, the mass density, the specific heat and the two
coefficients that characterize the mushy zone. The another free boundary of the
mushy zone, the bulk temperature and the heat flux and heat transfer
coefficients at the fixed face are assumed to be known. According to the choice
of the unknown thermal coefficients, fifteen phase-change problems arise. The
study of all of them is presented and explicit formulae for the unknowns are
given, beside necessary and sufficient conditions on data in order to obtain
them. Formulae for the unknown thermal coefficients, with their corresponding
restrictions on data, are summarized in a table.
