Analytical solution to the equations of a two-phase layer with allowance for the convective heat and mass transfer in a binary liquid

The model equations describing directional crystallization of a binary system with a two-phase layer and taking into account the convective heat and mass transfer mechanism in the liquid phase are formulated. The system of formulated nonlinear heat and mass transfer equations is solved analytically in the case of steady-state crystallization scenario. The temperature and concentration distributions, the solid phase fraction, the two-phase layer thickness and its boundaries, solid phase - mushy layer and mushy layer - liquid phase, are found. The steady-state crystallization velocity is determined as a function of fixed model parameters. The developed model and its analytical solutions describe the case of intensive motions of a binary liquid (the case of turbulent flows in the ocean, for example). © 2019 Author(s)