Analytical solutions of two-phase region equations in the presence of an incoming flow
DOI:
https://doi.org/10.33910/2687-153X-2026-7-3-111-122Keywords:
directional solidification, two-phase region, weak flow, heat and mass transfer, precise analytical solutions, nonlinear systems of equationsAbstract
This paper describes theory behind the process of directional crystallization with a two-phase region, taking into account the presence of a two-phase region (a layer of mixed solid and liquid phases), as well as a weak outgoing or incoming flow. The analytical solution to high non-linear heat and mass transfer model is found analytically in a parametric form. The impurity concentration profile, temperature distribution, the solid phase portion, the solidification velocity, and the thickness of the two-phase region are determined analytically. The dependencies of impurity concentration versus the solid phase portion are plotted and compared with experimental data. In addition, the permeability of the two-phase region is plotted versus the spatial coordinate, and the interdendritic distance is plotted versus the crystallization rate and compared with the experimental data. In all cases, the theory discussed in this paper is in agreement with the experimental data.
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