MHD Mixed Convective Transport in Square Enclosure with Two Rotating Circular Cylinders

Abstract

This study investigates the two-dimensional hydromagnetic mixed convective transport in a cooled square enclosure filled with an electrically conducting fluid in presence of two inner heated circular cylinders with identical shape. The centers of the two equidiameter cylinders are placed at those of the lower and upper half of the enclosure, respectively, and the gap between the cylinders is kept fixed. The cylinders may be either kept stationary or made to rotate in their own plane about their centroidal axes. Additionally, cylinders may rotate either in the same direction or in the opposite direction. All of the walls of the enclosure are kept isothermal with temperatures less than that of the cylinders. A uniform magnetic field is applied along the horizontal direction normal to the vertical wall. All solid walls are assumed electrically insulated. Simulations are performed by deploying a finite volume technique for various controlling parameters, such as the Rayleigh number (10³ ≤ Ra ≤ 10⁵) and Hartmann number (0 ≤ Ha ≤ 50), keeping the Reynolds number based on the cylinder rotation fixed as Re = 100. The flow and thermal fields are analyzed through streamline and isotherm plots for various Ha, Ra, and different combinations of cylinder rotation. Furthermore, the effects of Ha, Ra, and cylinder rotation on the heat transfer characteristics are portrayed through the local and average Nusselt numbers on all of the cylinder surfaces and the bulk average fluid temperature plots.