Influence of the difference in the density of solid and liquid phases on the dynamics of an alloy solidification front at crystallization of a finite volume with a moving boundary $$\sqrt t $$

In this paper we obtain the exact analytical solution for a finite solidifying alloy with the upper boundary moving with the time as k _t√ . 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 paper 1]. Unlike the paper indicated, this paper considers the case of different densities in solid ρ_s and liquid ρ_l phases. The exact 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. As an example, we consider the dependences of the local solidification time, the velocity of the liquidus isotherm, the width of the mush zone, and the temperature gradient in the liquid phase on the liquidus isotherm on the parameters k _t and μ = ρ_l/ρ_s.