Dependence of aspect ratio on magnetic damping of natural convection in low-conducting aqueous solution in a rectangular cavity

Magnetic damping of natural convection in low-conducting aqueous solution was numerically studied for 0⩽Hartmann number (Ha)⩽36.67, 1000⩽Grashof number (Gr)⩽39810 and 0.1⩽the aspect ratio of a container (AR)⩽1.0. The ratio of averaged Nusselt number (Nuave) with and without magnetic field, Nur=(NuaveB−1)/(Nuave0−1), was used to quantify the damping efficiency of natural convection. The results reveal that the magnetic damping of natural convection is strongly dependent on the aspect ratio of the container and there exists an optimum AR for minimizing natural convection. The optimum value of AR is almost independent of Ha and shows the tendency to decrease with increasing Gr. Correlation equations for Nur and the ratio of averaged velocity with and without magnetic field with AR, Gr and Ha were given.