Solidification with a quasiequilibrium mushy region: exact analytical solution of nonlinear model

Abstract

A set of nonlinear equations describing solidification of a binary melt in the presence of a quasiequilibrium mushy region is solved analytically in the case of an arbitrary dependence of effective coefficients of heat and mass transfer. Concentration, temperature distributions and a bulk fraction of the solid phase in a mushy region are found as functions of a spatial coordinate for unidirectional quasistationary regime of solidification. An algebraic equation for the bulk fraction of the solid phase at the solid–mushy region interface is also deduced. The mushy region width is found as a function of given physical and operating parameters of solidification. On the basis of obtained solutions the regime of solidification with the quasiequilibrium mushy zone is replaced by equivalent discontinuity surface (frontal) regime with new boundary conditions.