MHD mixed convection in a lid-driven cavity including heat conducting circular solid object and corner heaters with Joule heating

A two-dimensional finite-volume based numerical approach is adopted to solve the hydro-magnetic mixed convection in a horizontal lid-driven square cavity with a circular solid object. The object is located centrally within the enclosure. Part of the bottom and the right walls are taken to be constant temperature heaters. The top boundary of the cavity is moving with uniform speed and kept at a constant temperature lower than the heaters. All other boundary segments are considered thermally insulated. For simulation purposes, the corner heater sizes are altered (XL = YL = 0.25, 0.50, 0.75), keeping the overall sizes of the cavity and the solid object fixed. The mixed convection is studied for the Richardson number range (0.1 ≤ Ri ≤ 10) keeping the Reynolds number based on the lid velocity fixed as Re = 100. The magnetic effect is brought in by varying the Hartmann number (0 ≤ Ha ≤ 50) along with the variation of Joule heating parameter (0 ≤ J ≤ 5). The results indicate a major influence of the prevailing convection method and the applied magnetic field on the flow as well as the thermal field, while the effect of Joule heating is found to be of very small significance.