Magnetohydrodynamic Free Convection Heat Transfer in a Square Enclosure heated from side and cooled from the ceiling

The Magnetohydrodynamic free convection fluid flow and heat transfer in a square cavity filled with a fluid with Prandtl number of Pr = 0.7 is investigated numerically. The left vertical wall and top horizontal wall of the cavity are maintained at a constant temperature Th and Tc respectively with Th > Tc. Other walls of the cavity are insulated. The governing equations written in terms of the primitive variables are solved numerically using the finite volume method and the SIMPLER algorithm. Using the developed code, a parametric study is performed, and the effects of the Rayleigh number and the Hartman number on the fluid flow and heat transfer inside the enclosure are investigated. The results show that temperature distribution and flow pattern inside the enclosure depend both the strength of the magnetic field and Rayleigh number. For all cases a clockwise primary vortex is formed inside the enclosure. The magnetic field decrease the intensity of free convection and flow velocity and for low Rayleigh numbers suppresses free convection.