Magnetohydrodynamics (MHD) has been a subject of intense research for a long time due to its overwhelming importance in numerous fields ranging from several natural phenomena like geophysics, astrophysics to many engineering applications such as plasma confinement, liquid–metal cooling of nuclear reactors, electromagnetic casting and so on. A strong external magnetic field is known to suppress the velocity fluctuations because of its damping nature. This causes a reduction in the turbulent intensity of the MHD flow, thereby affecting the thermofluidic transport significantly. In applications like nuclear fusion reactors, the liquid metal blankets (required to extract heat to control the reactor temperature) are prone to such magnetic damping phenomena. Hence, there is a chance for the degradation of the heat transfer in such engineering devices. The heat transfer can be augmented by promoting turbulence by placing obstacles inside the blankets. The obstacles may have different geometric shapes such as circular or square cross sections. The thermofluidic transport around the obstacles will strongly depend on the shape of the obstacles. It needs to be emphasized that the flow patterns and the wake structures for the cases of flow over a square object are significantly different from that over a circular one because of the fact that unlike the circular object the square counterpart fixes the separation points, causing differences in the critical flow regimes. Furthermore, the separation mechanisms depending on the shedding frequencies and the aerodynamic forces also differ considerably for the two geometries. These technological and fundamental issues set the motivation for carrying out the study of MHD flow of liquid metal around a square obstacle in a square duct subjected to strong external magnetic field.