Abstract Numerical simulation of time-dependent magneto-convection flows in a liquid metal breeding blanket unit cell prototypical to the geometry of Water-Cooled Lithium-Lead (WCLL) breeding blanket is performed by COMSOL Multiphysics. Its modeling capability for fully coupled magnetohydrodynamic (MHD)/heat transfer flows in a complex geometry under fusion relevant conditions is tested with the demonstration of the main flow features and temperature profiles. Here, the magneto-convection flow in the bulk region is dominated by the effect of natural convection, leading to two columnar-like, counter-rotating circulations which occupy the whole plenum region of the breeding zone along the external magnetic field direction. High velocity flow jets with the magnitude of 1–2 orders greater than inlet velocity are formed near structural walls that are parallel to the applied magnetic field and break into unsteady sidewall vortices that are mainly confined in boundary layers. Due to the buoyancy effect, the hot fluid particles are stratified near the top structure wall where the cooling effect is the least. The calculated maximum temperature at the wall is lower than the structure’s temperature limit but still exceeds the corrosion temperature limit.