Continuous casting (CC) is nowadays the world-leading technology for steel production. The thin slab casting (TSC) is featured by a slab shape close to the final products and a high casting speed. The quality of the thin slabs strongly depends on the uniformity of the turbulent flow and the superheat distribution, defining the solid shell growth against a funnel-shaped mold. In most studies, it is commonly assumed that the submerged entry nozzle (SEN) is properly arranged, and the melt inflow is symmetric. However, the misalignment or clogging of the nozzle can lead to an asymmetric flow pattern. Herein, the asymmetry is imposed via a partial SEN clogging: a) a local porous zone inside the nozzle reflects the presence of the clog material; b) the resistance of the clog is varied from low to high values. The solidification during TSC is modeled, including the effects of the turbulent flow. The variation of the flow pattern and the solidified shell thickness are studied for different permeability values of the SEN clogging. These effects are considered with and without the applied electromagnetic brake (EMBr) using an in-house magnetohydrodynamics (MHD) and solidification solver developed within the open-source package OpenFOAM.