Hydromagnetic Mixed Convective Transport in a Vertical Lid-Driven Cavity Including a Heat Conducting Rotating Circular Cylinder

Abstract

Two-dimensional numerical simulation is performed for the hydromagnetic mixed convective transport in a vertical lid-driven square enclosure filled with an electrically conducting fluid in the presence of a heat conducting and rotating solid circular cylinder. Both the top and bottom horizontal walls of the enclosure are considered thermally insulated, and the left and right vertical walls are kept isothermal with different temperatures. The left wall is moving in the upward direction at a uniform speed, while all other walls are stationary. A uniform magnetic field is applied along the horizontal direction normal to the moving wall. A heat conducting circular cylinder is placed centrally within the outer enclosure. The cylinder is made to rotate in its own plane about its centroidal axis. Both the clockwise and counterclockwise rotations of the cylinder are considered. All solid walls are assumed electrically insulated. Simulations are performed for various controlling parameters, such as the Richardson number (1 ≤ Ri ≤ 10), Hartmann number (0 ≤ Ha ≤ 50), and dimensionless rotational speed (−5 ≤ Ω ≤ 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, Ω, and Ri. Furthermore, the pertinent transport quantities such as the drag coefficient, Nusselt number, and bulk fluid temperature are also computed to understand the effects of Ha, Ω, and Ri on them. It is observed that the heat transfer greatly depends on the rotational speed of the cylinder.