<p>Understanding the heat transfer mechanisms among the mold, slag film/air gap and molten steel, as well as characterizing the coupling effects and mutual influences between heat transfer, solidification behavior and slag film distribution, is critical for ensuring smooth continuous casting operations and improving slab quality. This study establishes a numerical model for mold heat transfer and slab solidification based on measured mold temperatures and inverse problem algorithm. A numerical model for slag film/air gap thickness and thermal resistance is further developed to calculate heat flux distribution across the copper plate, shell thickness, and slag film/air gap distribution under industrial conditions. Correlation analysis is applied to quantify the relationships among temperature, heat flux, slag film thickness and air gap along the slab width direction. The results reveal significant non-uniform distributions of heat flux, slag film/air gap and thermal resistance in the mold. The slag channel exhibited an average thickness of 0.91 mm, with the solid slag film contributing 0.83 mm. This slag channel thickness measured approximately 12 times greater than the liquid slag film and 140 times larger than the air gap dimension. The solid slag dominates thermal resistance, contributing 91.5 pct of the total. Mold heat transfer and shell solidification exhibit strong correlations with slag film distribution. Solid slag thickness significantly influences heat flux and shell growth, while liquid slag and air gap exhibit negligible effects. Slab surface temperature critically impacts heat transfer and shell growth. Liquid slag thickness positively correlates with solid slag thickness but negatively correlates with air gap thickness. Solid slag thickness demonstrates pronounced correlations with all variables, emerging as the key factor governing mold heat transfer and slab solidification. These findings provide insights into heat transfer mechanisms and slag film behavior in continuous casting molds.</p>