The Effect of a Magnetic Field on Buoyancy-Driven Convection in Differentially Heated Square Cavity

Steady, laminar, natural-convection flow in the presence of a magnetic field in a cavity heated from left and cooled from right is considered. In our formulation of governing equations, mass, momentum, energy and induction equations are applied to the cavity. To solve the governing differential equations a finite volume code based on Patankar's simpler method is utilized. Numerical predictions are obtained for a wide range of Rayleigh number (Ra) and Hartmann number (Ha) at the Prandtl number Pr = 0.733. At low Rayleigh number regime with weak magnetic field, a circulating flow is formed in the cavity. 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 Rayleigh 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 as Hartmann number increases. The results are presented for Rayleigh number from 104 up to 106 and are in form of streamlines, isotherms as well as Nusselt number for various Rayleigh and Hartman numbers.