Air gaps in vertical continuous casting in round moulds

A recent asymptotic thermomechanical model for the formation and evolution of air gaps in vertical continuous casting is extended from an idealized geometry to a cylindrical one that is of actual industrial relevance. The differences between the models, in particular as regards the criterion for the onset of air-gap formation for the two geometrical configurations, are noted. Parameter regimes for which the thermal and mechanical problems decouple are discussed. In such cases, corresponding to thermal stresses dominating viscosplastic ones, asymptotic analysis helps to reduce the model to a moving-boundary problem for the temperature, along with a boundary condition in integro-differential form that describes the evolution of the air gap. Sample computations are carried out using parameters for the continuous casting of copper, and the value of the model results as a new and useful benchmark for verifying 3D numerical codes describing the thermomechanics in continuous casting models is highlighted.