Exact analytical solutions of a steady-state mushy layer model containing heat exchange with the environment

A set of nonlinear equations describing the crystallization of a binary melt in the presence of a quasi-equilibrium mushy layer is analytically solved in the case of heat exchange with the environment. Solute concentration, temperature distributions, and a bulk fraction of the solid phase in a mushy region are found. In addition, the average interdendritic distance in the two-phase region, which characterizes the structural-phase transition and porosity of the material, was analytically determined. The mushy layer's thickness was also found as a function of given the physical and operating parameters of the solidification process. The analytical solutions obtained are compared with experimental data.