Buoyancy-driven nonlinear convection in a square cavity in the presence of a magnetic field

The effect of a magnetic field on the buoyancy-driven flow of water inside a square cavity with differentially heated side walls is studied numerically. A finite difference scheme consisting of ADI (Alternating Direction Implicit) and SOR (Successive Over Relaxation) methods are used to solve the coupled nonlinear equations. The flow pattern and the heat transfer characteristics inside the cavity are presented for Hartmann number Ha varying over 0 to 100, while the vertical walls are maintained at uniform but different temperatures with theta(c) = 0 degrees C (cold walt) and 4 degrees C less than or equal to theta(h) less than or equal to 12 degrees C (hot wall), while the horizontal walls are thermally insulated. The magnetic field dampens the flow field and the heal transfer. As the Hartmann number Ha increases, the temperature field resembles that of conduction type. The average Nusselt number <(Nu)over bar>, the heat transfer coefficient, decreases with the increase of the Hartmann number Wa. The temperature distribution and flow fields are depicted in the form of streamlines, isotherms and mid-height velocity profiles in the graphs attached for 0 less than or equal to Ha less than or equal to 100, varying the hot wall temperatures from 0 degrees C to 12 degrees C.