Mathematical Modelling and Application to Solidification in vertical continuous Casting Mould

Abstract

Various features of a mathematical model are describes along with its limitations and advantages. Essential steps to cevelop a mathematical model for a physical problem are stated. To identify independent parameters controlling the process involved in the physical problem, use of simil-arity and dimensional analyses is presented. Methods of solutions applied particularly to conduction with and without phase-change are suggested. A mathematical model is developed for solidification with air-gap formation in the vertical mould of a cont-inuous casting machine. similarity analysis predicts that this modelis controlled by two independent para-meters, the stefan number, St and the ratio of densities of solid liquid phases. The governing equation along with non-linear boundary condition due to moving solid-liquid interface is solved using the heat balance integral and the quasi-steady methods. They yielded closed form solutions for solidified-shell thickness, air-gap and mould wall temperature in terms of these two parameters. The validity of the model is confirmed with the exper-imental results and theoretical analysis for no air gals formation in the continuous casting.