Mathematical modelling of fluid flow,heat transfer and solidification phenomena in continuous casting of steel

A steady state, two-dimensional mathematical model for continuous billet casting operations has been developed. Towards this, governing equations of fluid flow and heat transfer together with their appropriate set of boundary conditions were derived and solved numerically via a control volume based implicit finite difference procedure (e.g., SIMPLE). The effect of various assumptions and procedures applied to modelling of turbulence phenomena, thermal buoyancy, flow through the mushy zone, free surface conditions etc., on the sensitivity of the computed results was investigated computationally. Of all these, modelling of heat and fluid flow phenomena in the mushy region was found to have relatively more effect on the predicted results. In addition to these, a set of three different billet casting operations reported in literature were simulated mathematically and direct comparisons were made between predicted and observed solidified shell profiles. Such comparisons demonstrated reasonable to excellent agreement between theory and experiments.