Influence of a magnetic field on liquid metal free convection in an internally heated cubic enclosure

Numerical simulations were conducted for the magnetohydrodynamic free convection flow of a liquid metal in a differentially heated cubic enclosure under the influence of a horizontal magnetic field of different intensities. The Prandtl number was 0.0321, characteristic of 17 % lithium-83 % lead (a tritium breeding medium currently being considered for the blanket of nuclear fusion reactors). The Rayleigh number was 104 so that the base flow in the absence of MHD effects was steady and symmetric. The enclosure was assumed to be surrounded by a thin electrically conducting wall giving a wall-to-fluid conductance ratio of 0.01. The Hartmann number M, which is a measure of the relative importance of MHD effects, was made to vary in a broad range from 1 to 2000, but emphasis was placed on the incipient effects of the magnetic field on the flow structure, i.e. on the lower end of the above M spectrum. Prevailing velocities were found to depend little on M at low Hartmann numbers (M<10) and to decrease as M−2 for large Hartmann numbers (M>100). Electric currents were found to increase about linearly with M at low Hartmann numbers and to decrease as M−1 at high Hartmann numbers, exhibiting a maximum for M≈100. The related case of an internally heated enclosure is discussed in a separate paper