Assessment of mathematical models for the flow in directional solidification
Resource
Journal of Crystal Growth 171 (3-4): 601-613
Journal
Journal of Crystal Growth
Journal Issue
171
Pages
601-613
Date Issued
1997
Date
1997
Author(s)
Lu, Jay W.
Abstract
In a binary solution unidirectionally solidified from below, the bulk melt and the eutectic solid is separated by a dendritic mushy zone. The mathematical formulation governing the fluid motion shall thus consist of the equations in the bulk melt and the mushy zone and the associated boundary conditions. In the bulk melt, assuming that the melt is a Newtonian fluid, the governing equations are the continuity equation, the Navier-Stokes equations, the heat conservation equation, and the solute conservation equation. In the mushy layer, however, the formulation of the momentum equation and the associated boundary conditions are diversified in previous investigations. In this paper, we discuss three mathematical models, which had been previously applied to study the flow induced by the solidification of binary solutions cooling from below. The assessment is given on the bases of the stability characteristics of the convective flow and the comparison between the numerical and experimental results.
SDGs
Other Subjects
Binary mixtures; Boundary conditions; Cooling; Crystal growth from melt; Flow of fluids; Mathematical models; Molten materials; Navier Stokes equations; Newtonian liquids; Separation; Stability; Convective flow; Dendritic mushy zone; Directional solidification; Eutectic solid; Heat conservation equation; Momentum equation; Solute conservation equation; Solidification
Type
journal article
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