Mathematical model of solidification process in steel continuous casting taking into account the convective heat transfer at liquid–solid interface

•Metal continuous casting.•Calculation of solidified crust thickness and convection coefficient at interface.•Calculation of depth solidification cone.•Solidification model based on convective heat transfer at S-L interface.•Validation of experimental results using Visual C++ program.

The aim of the paper is to develop a mathematical model of solidification process in steel continuous casting taking into account the convective heat transfer at liquid–solid interface. The obtained mathematical model is the starting point for determining relationships for (a) thickness of crust solidified and for (b) the temperature distribution in the solid fraction and (c) coefficient convection, at the interface liquid–solid. Based on obtained mathematical equations, we have drawn a graphical interface that can monitor the evolution of the materials in the crystallizer through a process computer. This mathematical model contributes to the understanding the solidification phenomena that occur for semifinished continuous casting at level of crystallizer.