MHD Mixed Convection in a Lid-Driven Cavity Including a Heated Source

Abstract

Numerical simulations are performed to understand the thermo-magneto-convective transport of fluid and heat in a vertical lid-driven square enclosure following a finite volume approach based on the SIMPLEC algorithm. The enclosure is filled with an electrically conducting fluid and having a heated source on the right vertical wall. Two different types of sources, such as a semicircular and a rectangular one, are considered. Both the top and bottom horizontal walls and the right vertical wall, except the source of the enclosure, are assumed insulated and the left vertical wall and the sources are kept isothermal with different temperatures. The left vertical wall is also translating in its own plane at a uniform speed, while all other walls are stationary. Two cases of translational lid motion, viz., vertically upward and downward are considered. A uniform magnetic field is applied along the horizontal direction normal to the translating wall. Shear forces due to lid motion, buoyancy forces as a result of differential heating, and magnetic forces within the electrically conducting fluid act simultaneously. Heat transfer due to forced flow, natural convection, and Joule dissipation are taken into account. Simulations are conducted for various controlling parameters, such as the Rayleigh number (10³ ≤ Ra ≤ 10⁵), Hartmann number (0 ≤ Ha ≤ 100), and Joule heating parameter (0 ≤ J ≤ 5), keeping the Reynolds number based on lid velocity fixed as Re = 100. The flow and thermal fields are analyzed through streamline and isotherm plots for various Ha and J. Furthermore, the pertinent transport quantities such as the drag coefficient, Nusselt number, and bulk fluid temperature are also plotted to show the effects of Ha, J, and Ra on them.