Solidification of a Sphere: The Effects of Thermal Contraction and Density Change Upon Freezing

Abstract

The stress and internal pressure in a solidifying sphere are calculated as a function of heat transfer rate and the density change upon freezing. A numerical solution to the heat transfer problem and a linear isotropic thermoelastic model for the solid are used to describe the solidification process. Results are presented for a model material with typical metallic properties. Heat transfer effects alone cause compression and the density increase upon freezing by itself produces tension within the liquid core. Thermal compression effects can dominate during the early stages of solidification, but only at relatively high rates of heat transfer. The effect of the density change dominates in the later stages and the liquid core goes into tension. It is unlikely that sustained high pressures can be generated within solidifying spheres. The model indicates regimes of low stress where the solid shell may be expected to remain intact during the initial stages of solidification.