Effect of Hartmann Number on Free Convective Flow of MHD Fluid in a Square Cavity with a Heated Cone of Different Orientation

Abstract

This paper presents the effect of magnetic field, indicated by Hartmann number ( H a ), on the free convective flow of Magneto-hydro-dynamic (MHD) fluid in a square cavity with a heated cone of different orientation. Although similar studies abound, the novelty of this work lies in the presence of the heated cone, whose orientation is varied at different angles. The mathematical model includes the system of governing mass, momentum and energy equations. The system is solved by finite element method. The calculations are performed for Prandtl number Pr = 0.71; the Rayleigh number Ra = 10, 1000, 100,000; and for Hartmann number Ha = 0, 20, 50, 100. The results are illustrated with streamlines, velocity profiles and isotherms. From the results, it is found that for the present configuration, magnetic field (Hartmann number) has no effect on the shape of the streamlines for low Rayleigh numbers. However, for high values of Ra , the effect of Ha becomes quite visible. Magnetic field affects the flow by retarding the fluid movement, and thus affects convective heat transfer. At low Ra , the fluid movement and heat transfer rate are already slowing, thus impressing a magnetic field does not produce much effect. At high Ra , fluid particles move at high velocity and change the stream lines, in absence of any magnetic force. Impressing magnetic field in this situation produced noticeable effect by slowing down the fluid movement and changing the streamlines back to low Ra situations. It is noted that a combination of low Ra with zero or low Ha produces similar effects with the combination of high Ra and high Ha . It can be concluded that with increasing Ha , heat transfer mode in MHD fluid gradually changes toward conduction from convection. It can be surmised that sufficiently large Ha can potentially stop the fluid movement altogether. In that case, heat transfer would be fully by conduction.