Similarity Solution of the 3-phase Stefan Problem for Alloys with   Arbitrary Temperature Dependent Properties
  In this paper a 3-phase Stefan problem solution method for 1D semi-infinity alloy is developed. The problem is first solved for full enthalpy of the system and then the thermal diffusivity has been eliminated from the divergence operator by Kirchoff transformation. Moreover, we introduce a similarity independent variable $\eta=x^{2}/\tau$ and original problem transforms to ordinary differential equations (ODE) for each phase separately. These ODEs have Dirichlet's type boundary conditions. 
Evgeniy N. Kondrashov