Temperature distribution profiles during vertical continuous casting process

A vertical continuous casting model is considered to analysis the temperature distribution profiles during the casting process. Heat flux is applied at the interface between the liquid layer and the solid layer to overcome the deficient of insufficiency boundary conditions. By combining the general solution of time dependent heat transfer partial differential equation and heat flux at the interface generate linear systems, and linear systems determine the temperature distribution profiles at each layer. The width of liquid layer and enough time interval are important factors in controlling the casting process and yield profound influence on the mechanisms.