Effect of a magnetic field on free convection in a rectangular enclosure

Abstract

Natural convection of an electrically conducting fluid in a rectangular enclosure in the presence of a magnetic field is studied numerically. The two vertical side walls are held isothermally at temperatures θ h and θ c, while the horizontal top and bottom walls are adiabatic. A finite difference scheme consisting of modified ADI (Alternating Direction Implicit) method and SLOR (Successive Line Over Relaxation) method is used to solve the vorticity-stream function formulation of the problem. Numerical predictions are obtained for a wide range of Grashof number Gr and Hartmann number Ha at the Prandtl number Pr = 0.733. At low Grashof number regime with weak magnetic field, a circulating flow is formed in the enclosure. When the magnetic field is relatively strengthened, the thermal field resembles that of a conductive distribution, and the fluid in much of the interior is nearly stagnant. Further, when the magnetic field is weak and the Grashof number is high, the convection is dominant and vertical temperature stratification is predominant in the core region. However, for sufficiently large Ha, the convection is suppressed and the temperature stratification in the core region diminishes. The numerical results show that the effect of the magnetic field is to decrease the rate of convective heat transfer. The average Nusselt number decreases with an increase of Hartmann number.