The Effects of Radiative Heat Transfer Upon the Melting and Solidification of Semitransparent Crystals

Abstract

Employing the assumptions of one-dimensional energy transfer, equilibrium phase change, and negligible convection in liquid regions, the time-dependent conservation of energy equation is formulated for the general situation of n semitransparent contiguous liquid and solid phases. The dimensionless parameters governing phase change are identified and the effects of their variation are ascertained by a finite difference solution of the rigorously formulated energy and radiative transfer equations. The chief conclusions of this investigation are that for the range of parameters encountered in the melting and solidification of many optical materials, radiant transfer has a significant effect, and that during solidification, radiation can force the temperature profile within the liquid phase to assume a shape which leads to unstable interfacial growth.