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Journal of Porous Media
IF: 1.752 5-Year IF: 1.487 SJR: 0.43 SNIP: 0.762 CiteScore™: 2.3

ISSN Print: 1091-028X
ISSN Online: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v8.i4.20
pages 347-354

Porous Solid Model to Describe Heat-Mass Transfer near Phase Transition Interface in Crystal Growth from Melt Simulations

ABSTRACT

In simulating the process of crystal growing from the melt it is of crucial importance to describe correctly convective heat-mass transfer in the melt, especially at the crystallization front. Most models use the Navier-Stokes equation in the Boussinesq approximation. The approximation is based on all properties of the melt being independent of pressure and represents the heat-mass transfer process very well when the flow is laminar.
In dealing with non-stationary models, however, account should be taken of the presence of a transitional boundary layer near the crystallization front whose thermal properties may differ greatly from those of a pure melt. As a rule it is assumed that the thickness of the layer with transitional properties is small and all properties of the material being simulated are changed abruptly at the interface. In reality, the boundary layer thickness depends on the crystallization front velocity and temperature gradients in the region and may be not so small. As the properties of the melt in this region differ from those of the rest of the melt an additional term appears in the equation to describe the frictional force which impedes the flow along the crystallization boundary.
A model where the additional frictional force originating in the boundary layer near the crystallization front is described in terms of porous solid approximation is presented. The force is proportional to the crystallization front velocity and the Solid-to-liquid phase ratio in the boundary layer region, the share of each phase is calculated using the specific enthalpy value for the melt in the region.


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