A numerical investigation has been performed to visualize the magnetohydrodynamic natural convective heat transfer from a heated square cylinder situated within a square enclosure subjected to nonuniform temperature distributions on the left wall. The flow inside the enclosure is unsteady, incompressible, and laminar and the working fluid is micropolar fluid with constant Prandtl number (Pr = 7). The governing equations of the flow problem are the conservation of mass, energy, and linear momentum, as well as the angular momentum equations. Governing equations formulated in dimensionless velocity and pressure form has been solved by Marker and Cell method with second-order accuracy finite difference scheme. Comprehensive verification of the utilized numerical method and mathematical model has shown a good agreement with numerical data of other authors. The results are discussed in terms of the distribution of streamlines and isotherms and surface-averaged Nusselt number, for combinations of Rayleigh number, Ra (103–106), Vortex viscosity parameter, K (0–5), and Ha parameter (0–50). It has been shown that an increase in the vortex viscosity parameter leads to attenuation of the convective flow and heat transfer inside the cavity. © 2021 Wiley Periodicals LLC