| Equilibrium and non-equilibrium melting and solidification in semitransparent materials are investigated in this dissertation. Both one- and two-dimensional geometries are considered, including solidification of a slab subject to radiative and convective cooling, and surface melting in a semiinfinite body by collimated irradiation. The material is emitting, absorbing and anisotropically scattering. Two phase change models i.e., the mushy zone model and a new non-equilibrium planar interface model are employed to account for different physical conditions. The phase change problem is formulated using the enthalpy method and is solved using the fully implicit finite volume scheme. Methods to track the planar interface accurately and to locate the mushy zone boundary are developed. The radiative transfer equation is solved using the discrete ordinate method.; In the non-equilibrium model, a planar interface is assumed with a given nucleation temperature and a linear kinetics relationship is introduced to correlate the unknown solidification temperature to the interface velocity. A temperature distribution sharply peaked at the interface is found to exist throughout the solidification process; and the temperature distribution depends strongly on the optical thickness, heat conduction, scattering, and external convection. The linear perturbation theory is used to address the stability of the planar interface. In general, the planar interface is unstable in the early stage of solidification, and the smaller the optical thickness and the stronger the scattering level, the more unstable the planar interface. A stable planar interface may maintain throughout the solidification process in the presence of external convective cooling.; An isothermal mushy region results naturally from the solution when the equilibrium phase change is applied. The thickness of the mushy zone increases with reduced optical thickness and increased scattering. In the presence of external convection, the solidification front approaches a planar interface in the early stage, which is in agreement with the conclusion drawn from planar interface stability study. The incidence irradiation plays an important role in the melting process. A stronger incidence intensity leads to a thinner mushy zone. The distribution of irradiation intensity in the traverse direction affects not only the geometry of the melt pool, but also the formation of the mushy zone. |
