An analysis of the heat and solute transport during solidification of an aqueous binary solution—I. basal plane region

Abstract

A mathematical analysis of the steady, dendritic solidification of an aqueous binary solution has been developed. The energy and solute transport equations were solved using a simple “two-zone” technique. In this procedure, the coupled energy and solute equations are solved first in a zone near the basal plane, and then independently solved in a zone near the dendrite tips, to obtain families of temperature, concentration and dendrite shape profiles in each region. Geometric and thermodynamic matching criteria are employed to determine the specific temperature, concentration and dendrite shape profile in each region that is mutually compatible and satisfies the overall boundary conditions. Heat and mass transport phenomena near the basal plane are analyzed in the present work, while the tip region analysis and matching procedure will be accomplished in an accompanying paper. The results of the basal region analysis indicate that solidification at a higher rate (larger basal heat flux) produces shorter dendrites that are more blunt. A non-dimensional axial similarity variable was found which describes the temperatures and concentration fields independent of the rate of freezing.