Melting of a Free Solid in a Spherical Enclosure: Effects of Subcooling

Abstract

The melting process within a spherical enclosure with the solid phase uniformly subcooled initially has been studied. The preliminary analysis of the problem is similar to a previous study where the degree of subcooling was zero. However, the heat transfer equation has been modified to include the effects of a temperature gradient in the solid core. As a result, a closed-form solution cannot be obtained. At every time step, the unsteady conduction equation has been solved numerically using a toroidal coordinate system, which has been suitably transformed to immobilize the moving boundary and to transform the infinite domain into a finite one. The temperature gradient at the surface is now used to solve the film equation numerically. The melt time, Nusselt number, and melt flux distributions have been obtained over a range of the parameters (Sb, Ste/Cp*, and 1 /Prα*) normally encountered in solar thermal systems.