Steady-state crystallization with a mushy layer: a test of theory with experiments

Motivated by important applications in materials science and geophysics, I develop a non-linear heat and mass transfer model describing a steady-state crystallization scenario with a mushy layer. An exact analytical solution of mushy layer equations is derived in a parametric form where the temperature being the decision variable. The volume fraction of ice, the mass fraction of solute in the interstitial liquid, the spatial coordinate are found as functions of temperature in the mushy layer. Its thickness and temperature distribution in the liquid phase are defined analytically as well. The analytical theory developed well describes experiments on NaCl–H$$_2$$O solutions