Numerical computation of magnetothermal convection of water in a vertical cylindrical enclosure

Numerical computations were carried out to clarify the effect of Kelvin force on the flow of water in a vertical cylindrical enclosure heated from below and cooled from above under a vertical magnetic field gradient. Since the Kelvin force that is produced by the magnetic field gradient depends on the position and the size of a circular electric coil, the coil was placed at either the hot or the cold plate and the coil diameter was set to be 2.5 or 5 times that of the enclosure. First, to understand the mechanism of the generation of the magnetothermal convection induced by the Kelvin force alone, the transition of velocity and temperature fields were visualized under a non-gravitational field. Under a gravitational field, the average Nusselt number decreased with increase of magnetic strength when the coil was placed at the lower end plate which was heated isothermally so that the generation of natural convection was suppressed by the Kelvin force. On the contrary, the average Nusselt number increased with increase of magnetic strength when the coil was placed at the upper end plate which was cooled isothermally so that the natural convection was enhanced by the Kelvin force.