Heat transfer process simulation by finite differences for online control of ladle furnaces

A numerical method for solving the two-dimensional transient heat conduction equation is presented to determine temperature profiles of ladle furnaces during the casting of special steels. The method is based on an explicit formulation of the heat transfer process in finite differences. In order to improve the efficiency of the method, two auxiliary algorithms are added, one for correcting finite difference results from coarse mesh calculations and the other to perform time extrapolation of the temperature behaviour between furnace batches. The calculated steel temperatures are found to be in good agreement with experimental data, obtained at a Brazilian thin steel casting facility. Currently, about 80% of the ladle batches at this facility come out within their commercial specifications, against 45% previously observed without the use of such a model. With average processing times of the order of 100 s in an AMD K6II 300 MHz computer, the method is suitable for real time thermal tracking of ladles and steel