A mathematical model for air-gap formation in vertical continuous casting: the effect of superheat

The formation of an air gap at the mould-metal interface in continuous casting has long been known to have a detrimental effect on the efficiency of the process, and has therefore attracted many attempts at mathematical modelling. While almost all current efforts consist of complex three-dimensional numerical simulations of the phenomenon, this paper demonstrates the use of elementary asymptotic techniques to derive a quasi-analytical model that captures the essential characteristics. The model allows for full two way coupling between the thermal and mechanical problems: the formation of the air gap affects the heat transfer, whilst the heat transfer affects the stresses that lead to the formation and evolution of the air gap. In particular, this paper extends a recent model [1] by including the effects of superheat. Sample computations are performed using parameters for the continuous casting of the copper, and the results, qualitative trends and possible extensions are discussed.