Natural Convection in an Enclosure with a Partially Active Magnetic Field

Abstract

Chaotic natural convection flow of a molten gallium in a square enclosure with the upper and lower surfaces being insulated was studied by two-dimensional numerical simulation. Constant temperatures are imposed along the left and right walls of the enclosure with a volumetrically heated enclosure. In addition, a nonuniform partially active magnetic field is applied in a vertical direction. The flux lines spread out into a fringing field so the effective cross-sectional area of the gap is larger than that of the pole face. A chaotic regime is considered under steady state boundary condition. This study was done for an internal Rayleigh number of 10⁷, external Rayleigh number of 10⁵, and Prandtl number of 0.024. The study covers various magnet pole effect widths of 1/4, 1/2, and 3/4 from enclosure width and the magnetic field strength ranges 0.0 ≤ B _o  ≤ 10 Tesla. The transport equations for continuity, momentum, and energy are solved. The numerical results are reported for the effect of the partially active magnetic field on the velocity vectors, counters of temperature, streamline, and heat transfer coefficient. The numerical study shows that a magnetic field is damping chaotic oscillation behavior and decreases the amplitude of oscillation. Also, at a certain magnetic field strength the chaotic flow tend to becomes periodic flow at certain amplitude and frequency, and at high magnetic field strength the flow in the square enclosure flow tends to become steady laminar flow with stable average Nusselt number values; so, the random oscillation behavior disappeared. The effect of a nonuniform magnetic field tends to push the fluid to flow away from magnetic field region.