Mathematical Modelling of Heat Transfer

In the continuous casting of steel, heat transfer in the liquid region is more complex than in solidified areas due to various influencing factors such as flow dynamics and electromagnetic stirring. This study aims to develop a comprehensive three-dimensional heat flow model utilizing a novel concept of artificial effective thermal conductivity. By applying established boundary conditions to the governing heat flow equation and solving it through a control-volume based finite difference method, the model's versatility with various geometrical shapes relevant to continuous casting is demonstrated. The sensitivity of results is rigorously analyzed concerning numerical factors including grid configurations, axial conduction, and varying values of effective thermal conductivity (K.ff). The findings reveal significant influences resulting from assumptions and numerical processes on computed results. A comparison of numerical predictions with three experimental data sets from literature regarding shell thickness in industrial casters indicates only a poor to moderate alignment with experimental observations, challenging earlier claims. This work highlights the model's applicability and the critical need for refined numerical approaches in accurately predicting heat transfer phenomena in continuous steel casting.