Effect of induced electric field on magneto-natural convection in a vertical cylindrical annulus filled with liquid potassium

Laminar steady magneto-natural convection in a vertical cylindrical annulus formed by two coaxial cylinders filled with liquid potassium is studied numerically. The cylindrical walls are isothermal, and the other walls are assumed to be adiabatic. A constant horizontal magnetic field is also applied on the enclosure. The results show that flow is axisymmetric in the absence of the magnetic field; but by applying the horizontal magnetic field, it becomes asymmetric. This is due to the growth of Roberts and Hartmann layers near the walls parallel and normal to the magnetic field, respectively. The applied magnetic field results in a reduction in the Nusselt number in most of the regions of the annulus. This reduction is high in the Hartmann layers but low in the Roberts layers. Moreover, it was found that for a given value of Hartman number, the average Nusselt number is greater in the case of solving the electric potential equation. The results show that there is a large difference in the Nusselt number obtained by solving the electric potential equation, compared with by neglecting the electric potential.