<p>Corner/off-corner crack is a common problem that troubles the continuously cast bloom of alloy steels. The heat transfer characteristic in the mold is a decisive factor, and it is determined together by the solidification and shrinkage of the shell and distributions of the mold flux and air gap. Therefore, focusing on the continuous casting of 36Mn2V bloom, the present work developed a multi-interface thermo-mechanical model to dynamically couple calculations of the heat transfer, deformation, thicknesses of mold flux, and air gap along the circumference and height of the copper tube. The results show that the corner shell is the first to depart from the mold causing the expansion of the interfacial gap, the thickening of solid and liquid mold fluxes and the decrease of the heat flux in the corner region. Near the wide and narrow face centers, under the combined effects of the squeezing of the shrunken shell and the confine of the mold, the interfacial gap keeps constant, the liquid mold flux gradually thins and vanishes, and the solid mold flux gradually thickens and fully occupies the interfacial gap. The air gap forms in the off-corner region in the middle and lower part of the mold leading to the fluctuation of the heat flux and surface temperature. With the reduction of the mold inner corner radius, in the corner region, the interfacial gap is narrower, the liquid mold flux is thinner, the solid mold flux is thicker, and the surface temperature of the bloom decreases. As the mold inner corner radius is reduced to 12&#xa0;mm, the corner shell becomes thickest, the off-corner shell is still thinnest, and the surface stress in the corner region becomes lower than that at the face end. The industrial test shows that the grain is refined in the corner region, but it becomes coarser in the off-corner region with the reduction of the mold inner corner radius.</p>