MATHEMATICAL-MODELING OF TRANSPORT PHENOMENA IN CONTINUOUS-CASTING OFSTEEL

A steady state, two dimensional mathematical model for continuous cast ing of steel has been developed. Towards this, governing partial diffe rential equations of fluid flow and thermal energy transport together with the appropriate set of boundary conditions were derived and a pro cedure for their non-dimensional representation outlined. The modellin g of (1) turbulence, (2) flows and energy transport within the mushy r egion, and (3) bulk motion of the descending strand on liquid steel fl ow and heat transfer phenomena were also discussed. The governing p.d. e's and the associated boundary conditions were solved numerically via a control volume based finite difference procedure. To this end, inco rporating the SIMPLE algorithm, a computational procedure was develope d in double precision, FORTRAN 77. Finally, three different industrial billet casting operations reported in the literature were mathematica lly modelled and direct comparison were made between predicted and exp erimental solidified shell thickness. Such comparisons demonstrated re asonable to excellent agreement between the two. Present estimates wer e also compared with our earlier predictions derived via an effective thermal conductivity based model. This indicated that for mathematical modelling of transport phenomena in continuous casting of steel, a '' conjugate heat and fluid flow model'' is the most appropriate.