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 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 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 b solved using the discrete ordinates method. Internal radon 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.