Finite element simulation for MHD ferro-convective flow in an inclined double-lid driven L-shaped enclosure with heated corners

Abstract

The main objective of this study is to simulate magnetohydrodynamics (MHD) ferro-convective flow in an inclined double-lid driven L-shaped enclosure with heated corners. The dimensionless forms of the partial governing equations are solved numerically using the Galerkin finite element method. The L-shaped enclosure is heated from the corner with variations on the heated lengths of the left and bottom walls. The other boundaries are insulated except the top and right boundaries of the L-walls, which are cooled with a lid-driven velocity. The magnetic field acts on the horizontal direction of an inclined L-shaped enclosure. Heat generation/absorption, shear forces through lid motion and magnetic forces are considered. Simulations are performed for several physical parameters including Richardson parameter Ri, an inclination angle α, Hartman parameter Ha, solid volume fraction ϕ and heat generation/absorption parameter Q. The results revealed that the isothermal distributions are increased strongly as the lengths of the heated corner increase. For a fixed value of the heat generation parameter (Q=2), the average Nusselt number is reduced by 4.66% when lengths of the active parts is varied from 0.2 to 0.8. Also, rate of the heat transfer is minimized by 30.66% in case of the ferrofluid with concentration 5% as the Hartmann number increases from 0 to 50.