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The buoyancy-driven magnetohydrodynamic flow in a liquid-metal-filled square enclosure is investigated by 2-D numerical simulation. The enclosure is differentially heated at two opposite vertical walls, the horizontal walls being adiabatic, and a uniform magnetic field is applied orthogonal to the gravity vector. To solve the governing nonlinear differential equations (mass, momentum, and energy), a finite-volume code based on Patankar's SIMPLER method is utilized. The results are obtained for a Rayleigh number (Ra) of 5 × 106, with a Prandtl number of 0.0091 (characteristic of Na at 150 °C) and a Hartmann number (Ha) between 100 and 700. The fluid properties are considered as a function of temperature so that the values of these properties at the hot wall are lower than that of the cold wall. It is found that the resistance to fluid motion is stronger near the hot wall and the flow intensity increases in this region. Thus, due to continuity, the form of the streamlines changes, and the symmetry of the isotherms is broken.