Solidification of a Sphere with Internal Heat Generation and Convective Cooling at the Surface

Abstract

One-dimensional, nonhomogeneous transient conduction equations in both liquid and solid regions of a volumetrically heated sphere subjected to arbitrary time-independent convective cooling condition at the surface are numerically integrated. The results of numerical integration show that, depending on the relative magnitudes of the volumetric heat generation rate and the surface heat removal rate, the initially molten particle may completely solidify, temporarily solidify and then completely remelt, or have a solid outer crust with an inner molten core. The times needed to attain these quasi-stable states and the solidification and remelting rates prior to attaining these physical states are also computed.