<p>The corner region, being a critical area where defects often occur, was given particular attention. To accurately describe the solidifying corner shell, we developed a mathematical model of boundary heat flux to determine the solidifying behaviors of steel in the continuous casting mold. The model demonstrated robustness in predicting the solidification behavior across a range of scenarios, which is crucial for optimizing the casting process. The model's ability to predict the thermal behavior in this region has led to the development of strategies to mitigate such defects, thereby improving the overall quality of the cast product. In addition, two parameters, decreasing region length and corner edge’ heat flow, have been proposed and coupled in this finite element model (FEM). Boltzmann functions are added to the decreasing trend of heat flow around the solidifying shell corner region. The results show that the shell surface temperature of hot spots increases significantly with enlarging the decreasing length, especially in the corner region. Further, the mathematical model is also validated by actually measured breakout shell data. It has been observed that the proposed heat flux estimation results in accurate solidifying corner shell, and the mathematical model of boundary heat flux is suitable to investigate the solidifying corner shell in the continuous casting mold effectively.</p>