The Effect of Magnetic Field on Buoyancy-Driven Convection in a Differentially Heated Square Cavity With Two Insulated Baffles Attached to Its Isothermal Walls

Abstract

Steady, laminar, natural-convection flow in the presence of a magnetic field in a differentially heated square cavity which two insulated horizontal baffles attached to its vertical walls is considered. The vertical walls are at different temperatures while the horizontal walls are adiabatic. 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 various Rayleigh number (Ra), Hartmann number (Ha) and baffles position 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.