Heat Transfer Model for Thin Solidified Material in Continuous Casting

Abstract

An asymptotic explicit numerical method was developed for the Stefan problem in which a series of solidification rates and boundary temperatures for the solidified material are given and the boundary heat flux is returned. A spectral method with several basis functions of a specialized shape in the solidification problem was adopted. Combined with multi-dimensional computational fluid dynamics methods for the liquid zone, this method is adequate for resolving the thin solidified material problem for a variety of continuous casting processes e.g. thin slab continuous casting, melt-spinning, twin roll casting, and edge-defined film-fed growth. The method is less expensive than conventional numerical methods and as accurate as a direct numerical approach such as the Finite Difference Method especially in the case of the Stefan number >> 1 or in the case of variable material properties.