Numerical simulation of Rayleigh-Bénard convection in an inclined enclosure under the influence of magnetic field

Abstract

Two-dimensional numerical simulations are performed on the Rayleigh-Bénard convection using the finite element method, and the effect of the magnetic field on a thermally driven flow of a conducting fluid in a rectangular enclosure is studied. The simulations are performed on liquid Sodium with a Rayleigh number of 6 × 106 in a rectangular enclosure (aspect ratio – 4). The effects of the angle of declination of the enclosure and the influence of magnetic field in horizontal and vertical direction are examined. It is observed that the angle of declination of the enclosure (7°–28°) influenced the convection configurations with larger angles restraining the fluid velocity and hampering the formation of vortices. The applied magnetic field (0.001 T–0.003 T) too affected the formation of Bénard cells, and is dependent on the direction and the magnitude of the external field. In the presence of a horizontal magnetic field, a suppression of multiple vortices in favor of a singular cell structure is seen, and the degree of suppression is directly proportional to the magnitude of the field. Higher magnitudes of magnetic field suppressed convection with the isotherms showing lesser irregularities. However, vertical magnetic fields at smaller declination angles improved the circulation inside the enclosure leading to multiple well-defined parallel structures, which caused severe distortions in the temperature distributions. At large declination angles, the vertical magnetic field too suppressed the formation of well-defined Bénard cells. Keywords: Convection, Finite element method, Heat transfer, Magnetohydrodynamics, Transient analysis