We capture through numerical simulation the MHD (magnetohydrodynamic) vortex dynamics around a square object in a square duct subjected to a strong externally imposed axial magnetic field. A quasi two-dimensional conditionality allows us to follow a two-dimensional modeling approach. The pertinent MHD control parameters such as the Reynolds and Hartmann numbers are kept in the range 0 < Re <= 6000 and 0 < Ha <= 2160, respectively. The various regimes of the MHD wake are found in-line with those obtained by Dousset and Potherat under similar conditions using a circular object (Dousset and Potherat, 2008). Four different regimes are identified out of which the first three regimes are the classical non-MHD 2D cylinder wakes. The transition from one to another regime is controlled by the friction parameter Re/Ha. The fourth regime is characterized by the vortices evolved from the duct side walls due to the boundary layer separation which strongly disturbs the Karman vortex street. In order to explore the thermal transport phenomena under the action of the axially imposed magnetic field, the channel bottom wall is considered heated while the top wall is maintained at the free stream temperature keeping the cylinder adiabatic. The heat transfer rate from the heated channel wall strongly depends on the imposed magnetic field strength as well as Reynolds number. Additionally, an enhancement in heat transfer is experienced by placing the square cylinder in the channel over the bare channel, however, simultaneously a degradation in heat transfer would occur if the square object is replaced by a same size circular object. (C) 2015 Elsevier Ltd. All rights reserved.