Effect of an External Magnetic Field on Rayleigh-Bénard Convection of Liquid Metal in a Rectangular Enclosure
Effect of an external magnetic field on the Rayleigh-Bénard convection of liquid metal within a rectangular enclosure was numerically studied. The liquid metal filled in the enclosure is heated from a horizontal bottom wall and cooled from an opposing top wall both isothermally, whereas vertical walls are adiabatic. The direction of the magnetic field is either in vertical or horizontal. The governing parameters of such Rayleigh-Bénard convection in the presence of a magnetic field are the
... field are the Rayleigh number, Ra, the Prandtl number, Pr, the Hartmann number, Ha, and the electric conductance of walls, c. The numerical computations have been carried out for Pr = 0.025 (approximately mercury or gallium) and c = 0 (insulating walls) by using the HSMAC algorithm for correction of both pressure and electric potential, and also by using a third-order upwind scheme for inertial terms in the Navier-Stokes equation. The numerical results exhibit significant differences depending on the direction of the applied magnetic field. When the vertical magnetic field is applied, the magnetic damping effect is quite strong and the convection structure is different from an ordinary Rayleigh-Bénard convection. On the other hand, when the horizontal magnetic field is applied, a quasi-two-dimensional roll cell structure is organized along the direction of the magnetic field. Once, such a convection structure is organized, the magnetic damping effect is much weaker than that of the vertical magnetic field. For the case of the horizontal magnetic field with the high Hartmann number, the modeling of the Hartmann layer is used in order to make computations more accurate and to save the computational meshes and time. The numerical results are plotted in a graph of Nu versus Ra for the various Hartmann numbers, and finally compared with some data previously reported.