Mathematical Modelling of Transport Phen

A steady state, two-dimensional mathematical model for continuous casting of steel has been developed. This study derives governing partial differential equations of fluid flow and thermal energy transport along with the appropriate boundary conditions, outlining a procedure for their non-dimensional representation. The model discusses the turbulence, flows and energy transport within the mushy region, and the bulk motion of the descending strand affecting liquid steel flow and heat transfer phenomena. The governing equations and boundary conditions were numerically solved using a control volume based finite difference procedure, incorporating the SIMPLE algorithm in double precision FORTRAN77. Three different industrial billet casting operations reported in the literature were mathematically modeled, allowing for direct comparisons between predicted and experimental solidified shell thickness. The comparisons demonstrated reasonable to excellent agreement between the predicted and measured values. Additionally, the present estimates were compared with earlier predictions made using an effective thermal conductivity based model, indicating that for mathematical modeling of transport phenomena in continuous casting of steel, a 'conjugate heat and fluid flow model' is the most appropriate.