Thermal effect of surface tension on the inward solidification of spheres

Abstract

Effect of surface tension (Gibbs–Thomson effect) on the inward solidification of a liquid in a spherical container is investigated analytically by solving the unsteady heat equation via a small-time series expansion technique. A nonlinear Shanks transformation is adopted to improve the convergence property of the series solution at large time. The results show that at fixed Stefan number, the effect of surface tension is to increase the growth rate of the freezing front. A local minimum in the freezing rate is found to develop for all surface tension parameter values considered in this study. Also, analytic expressions for the relations between the growth rate of the freezing front, Stefan number and surface tension parameter are derived under the asymptotic condition of small Stefan number.