MHD mixed convection of viscoplastic fluids in different aspect ratios of a lid-driven cavity using LBM

Abstract

In this paper, a two-dimensional simulation of mixed convection in an enclosure with differentially heated sidewalls in the presence of a uniform magnetic field has been performed for different aspect ratios of the enclosure while the enclosure is filled with a viscoplastic fluid. The viscoplastic fluid has been simulated by the exact Bingham model without any regulations. Lattice Boltzmann Method (LBM) has been applied to solve the problem. Heat transfer, fluid flow, and yielded/unyielded zones are investigated for certain pertinent parameters of the Reynolds number (Re = 100, 500, and 1000), the Hartmann number (Ha = 0, 2, and 5), the Bingham number (Bn = 1, 5, and 10), the aspect ratio (AR = 0.25, 1, and 4), and Eckert number (Ec = 0, 10-4,10-3, and 10-2) when the Grashof and prandtl numbers are fixed at Gr = 104 and Pr = 1; respectively. Results show that the increase in the Reynolds number augments the heat transfer and changes the extent of the unyielded section. Furthermore, for fixed studied parameters, an increase in the Bingham number decreases the heat transfer while enlarging the unyielded section. The rise of the aspect ratio alters the size and position of the unyielded/yielded zones. As Hartmann number rises, the heat transfer drops gradually and the unyielded parts increase significantly. The change of the magnetic field angle alters the heat transfer and the unyielded/yielded regions in the cavity. It was observed that the viscous dissipation and the joule heating parts in the energy equation based on the practical values of Eckret numbers have marginal effects on heat transfer and yielded/unyielded sections.