Nonequilibrium Planar Interface Model for Solidification of Semitransparent Radiating Materials

A nonequilibrium solidification model for semitransparent materials is presented. Consideration is given to a planar layer of an 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, with internal emitting, absorbing, and scattering taken into account. A planar interface nonequilibrium solidification is assumed with crystalline phase nucleated on the surface at a given nucleation temperature, which may be significantly lower than the equilibrium melting temperature of the material. A linear kinetics relationship is introduced to correlate the unknown solidification temperature to the interface velocity. A fully implicit finite volume scheme is used to solve the problem with the solidification interface tracked by a modified interface tracking method. The radiative transfer equation is solved using the discrete ordinates 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 solidification process. In the presence of external convective cooling, effect of internal radiation is small in the early stage of solidification. (Author)