Finite difference heat-transfer modeling for continuous casting

Abstract

A number of solution strategies for heat-flow models of continuous casting processes are developed and compared for interfacing with optimization algorithms. These two-dimensional (2-D) slice models include nonlinear thermodynamic and transport properties. As a result of the compari-son, a number of modifications are applied to enhance the accuracy of the simulation as well as the efficiency of the solution. Here, we found that by applying the Kirchhoff transformation to the heat-flow equations and by iterative adjustment of temperature-dependent properties, fewer calculations are required per time-step and larger time-steps can be taken. Consequently, this leads to approximately a twentyfold reduction in computation time when using 2-D slice models to determine three-dimensional, steady-state temperature fields. As a result, a complex, 2-D heat-flow model for a cast strand can be solved in 2 to 5 minutes on a Micro VAX II and is thus suitable for incorporation into a systematic optimization procedure and for process simu-lation in real time.