The analytical solution of the one alloy solidification problem

In this paper we obtain the analytical solution for a semi-infinite solidifying alloy. Thus, a three-phase problem including solid, solid–liquid, and liquid phases is analytically solved. Linearization of the heat conduction equation for an alloy is based on the method proposed in our recent papers. Note that the method does not allow one to solve the problem of solidification of an alloy with the given function λ(T) (liquid fraction). The dependence λ(T) is determined from the condition of linearization of the heat conduction equation within the mush zone. The analytical solution presented is an important test example for analysis of the numerical schemes used for systems with moving boundaries, e.g., for programs simulating vacuum arc remelting.