Nonequilibrium Planar Interface Model for Solidification of Semitransparent Radiating Materials

Abstract

A nonequilibrium solidie cation model for semitransparent materials is presented. Consideration is given to a planar layer of emitting, absorbing, and scattering medium subject to radiative and convective cooling. The enthalpy method is used to formulate the phase-change problem together with radiative transfer equation taking into account internal emitting, absorbing, and scattering. A planar interface nonequilibrium solidie cation is assumed with crystalline phase nucleated on the surface at a given nucleation temperature, which may be signie cantly lower than the equilibrium melting temperature of the material. A linear kinetics relationship is introduced to correlate the unknown solidie cation temperature to the interface velocity. A fully implicit e nite volume scheme is used to solve the problem with the solidie cation interface tracked by a modie ed interface tracking method. Theradiative transfer equation issolved using the discreteordinates method. Internal radiation enhances the latent heat removal and thus leads to a higher interface velocity and a larger melt undercooling. Optical thickness and the conduction-radiation parameter are two important parameters that affect the solidie cation process. In the presence of external convective cooling, effect of internal radiation is small in the early stage of solidie cation.