Magnetoconvection in a square cavity with partially active vertical walls: Time periodic boundary condition

Magnetoconvection of an electrically conducting fluid in a square cavity with partially thermally active sidewalls is investigated numerically. Temperature of one of the thermally active regions of the side walls is periodic in time while the opposite wall is isothermal. The horizontal walls and the remaining parts of the side walls are thermally inactive. Nine different combinations of the relative positions of the active zones are considered. The governing equations are discretized by the control volume method with QUICK scheme and solved numerically by SIMPLE algorithm for the pressure–velocity coupling together with under relaxation technique. The tests were carried out for various values of amplitude, period, Grashof number, Hartmann number and Prandtl number. The heat transfer characteristics are presented in the form of streamlines, isotherms and velocity profiles both for transient and steady state. It is observed that the flow and the heat transfer rate in the cavity are affected by the sinusoidal temperature profile and by the magnetic field at lower values of Grashof number. The rate of heat transfer oscillates for increasing periods but it is maximum for Ω = 3 and it is found to be an increasing function of amplitude but decreases for higher values of Hartmann number. The heat transfer rate is maximum for the middle–middle thermally active locations while it is poor for the top heating and bottom cooling active locations. The average Nusselt number decreases with an increase of Hartmann number and increases with increase of Prandtl number and Grashof number.