A computational analysis based upon the kinetic, mesoscopic numerical tool is adapted for elucidating the buoyancy-driven convection in the square shaped open cavity having the partially active wall under the influence of the uniform magnetic field (B). A heater (size-half of the height of the cavity) is positioned along the vertical, no-slip wall of the cavity (while another vertical end is open to the atmosphere). Other regions of no-slip partially heated vertical wall, as well as top and bottom walls, are thermally insulated. The significance of heater location (bottom, middle and top), the angle of magnetic field (0°, 45° and 90°), Hartmann number (0–100) and Rayleigh number (103–105) on natural convection have been illustrated. The interpretation of results have been carried out by studying the streamlines, isotherms, centreline variation of temperature; velocity component profiles and Nusselt number (local, average). The dependence of the Nusselt number with the magneto-convective parameter is presented and discussed. Heat transfer rate increases with the angle of the magnetic field. © Springer Nature India Private Limited 2019.