Analysis of Solidification of a Semitransparent Planar Layer Using the Lattice Boltzmann Method and the Discrete Transfer Method

Abstract

ABSTRACT This article deals with the analysis of solidification of a semitransparent material. The solidification was assumed to occur at a range of temperatures and thus the presence of a mushy zone was considered. The governing energy equation in terms of an enthalpy formulation was considered. The equivalence of the enthalpy-based governing equation in the continuum approach was derived for the lattice Boltzmann method (LBM). The radiative component of the energy equation in the LBM formulation was computed using the discrete transfer method. The LBM formulation was first validated by solving solidification of a radiatively opaque planar material. Next, effects of various parameters such as the extinction coefficient, the scattering albedo, the anisotropy factor, the conduction-radiation parameter, and the latent heat on temperature distribution in three zones and the location of the mushy zone were studied. These parameters were found to have significant bearing on the results.