The effect of finite–rate heat release on the solidification of an undercooled pure liquid

Abstract

A mathematical model is formulated to describe the effect of finite rate heat release on solidification in an undercooled pure liquid, and to predict the macroscopic propagation speed of a solidification front through the bulk material. The problem is formulated in terms of continuum equations that describe heat and mass transport in a volumetrically averaged mixture of solid and liquid. A relatively thin phase transformation region, called the solidification zone, exists between thicker regions of pure liquid and solid. The solidification zone is examined on a length scale larger than any microstructural detail, yet smaller than macroscopic thermal conduction length scales in the pure liquid and solid regions. The continuum equations used in this ‘mesoscale’ model contain source terms representing the volumetrically averaged, finite rate phase transformation process occurring within the solidification zone. Solutions are obtained for a source term of the Arrhenius type, derived from an application of nucleation theory. Front speed variation with degree of undercooling is found to be quantitatively similar to that in relevant experiments in pure metals.