The solidification of pure metals (and eutectics) under uni-directional heat flow conditions: II. Solidification in the presence of superheat

Abstract

The generalized integral-profile method previously developed² to predict the solidification rates of pure metals and eutectic alloys under a range of cooling conditions has been extended to treat solidification rates in the presence of super heat. Heat transfer within the liquid metal has been characterized in terms of a single parameter for which a heat balance on the liquid yields an ordinary nonlinear equation. This equation is additional to the two equations derived previously for the growth of the solid metal, and the three equations have been solved simultaneously using a Runge-Kutta technique. Solutions have been obtained for heat transfer conditions that can be reproduced accurately in laboratory experiments. The results of a series of such experiments are also presented and shown to agree very well with the theoretical predictions.

In carrying out the analysis, it has been shown that a number of different cooling and solidification modes can occur during the solidification of superheated liquid metal, the solidification process following one of two possible routes through these modes. This presents a useful approach to the analysis of this solidification problem and, indeed, of more complicated problems since the logic of the computer program used in the analysis is closely related to the logic of the solidification process.