Multi-dimensional solidification with internal radiation and temperature dependent properties

Abstract

In this study, a two-dimensional radial and axial analytical model was developed and solved to determine the transient temperature distribution and interface location of a semi-transparent, gray, absorbing, emitting and isotropically scattering phase change medium bounded by two finite concentric cylinders when internal energy transfer occurs simultaneously by conduction and thermal radiation. The phase change medium employed in this study was a fluoride salt with a weight composition of LiF — 41.27%, MgF 2 — 48.76% and KF — 8.95%. The principle of conservation of energy where enthalpy and temperature are the dependent variables was coupled with a set of moment equations that were derived from radiative transfer equations and Marshak type boundary conditions by applying the spherical harmonics or P-1 differential approximation. An iterative finite difference numerical scheme was used to solve the non-linear difference equations. Results that show the effects of internal radiation on the temperature distribution, the rate of solidification and the heat extracted are presented. It is seen that internal radiation tends to accelerate the solidification process.