Development of a mathematical model for

A mathematical model of continuous casting of steel slabs and billets that considers aspects relating to computer capacities was developed. The objective of this study was to create a reliable model capable of predicting temperature profiles and the solidification front during the continuous casting process. Utilizing the finite-difference method, the model began with the solution of a partial differential equation of heat conduction under varying boundary conditions. Implementation was carried out using Pascal and C programming languages on the GNU/Linux operating system, with a comparison of computation speeds conducted. The model's accuracy was verified against approximate solutions derived from two distinct sets of mesh points, analyzing temperatures at four representative spatial locations. Furthermore, the ability of the mathematical model to reliably predict temperature distribution and shell thickness was assessed using actual data from the solidified shell taken from a continuous casting machine for steel billets at Štore Steel in Slovenia. Results indicated that the model is a promising tool for enhancing the understanding and efficiency of continuous casting operations.