Lattice Boltzmann Simulation of MHD Rayleigh-Bénard Natural Convection in a Cavity Filled With a Ferrofluid

Abstract

In this study, we examine the effect of a uniform external magnetic field on Rayleigh-Bénard convection in a square cavity filled with a ferrofluid. Numerical simulations are based on the Lattice Boltzmann method. The effects of physical parameters, which are the Rayleigh number, the Hartmann number, and the angle of inclination of the magnetic field are studied. The results obtained are graphically illustrated and discussed for a volume fraction of four percent. These results show that the rate of heat transfer decreases by increasing the Hartmann number. For high Rayleigh number values, the maximum heat transfer rate was obtained for a specific Hartmann number when the Lorentz and buoyancy forces are perpendicular.

Rayleigh-Benard Convection Inside Square Cavities Filled with Thermodependent Non-Newtonian Fluids and Subjected to External Magnetic Field

“…Before initiating the problematic research on MHD, extensive studies demonstrated the occurrence of free convection under the influence of a magnetic field across various fluid types and boundary conditions (Dirichlet, Neumann) in both square and rectangular cavities. Research on free convection with Newtonian fluids under the impact of a magnetic field has been conducted for both horizontal thermal conditions in published papers by Oreper and Szekely [8], Pirmohammadi and Ghassemi [9], Ghasemi et al, [10], Kefayati [11], and Alchaar et al, [12] and vertical thermal conditions in other published scientific articles by Liao et al, [13], Benzema et al, [14], Zürner et al, [15], and Chtaibi et al, [16]. The flow of conductive fluids during natural convection is notably affected by the interaction between the magnetic force and buoyancy forces, contributing to flow stabilization and the regulation of oscillatory instabilities.…”

“…However, the influence of 𝑛 becomes less pronounced for high values of 𝐻𝑎, particularly in the presence of strong magnetic fields. Chtaibi et al, [16] presented a preliminary study obtained from numerical simulations of free convection in a square enclosure of the Rayleigh-Benard type filled with a ferrofluid under the impact of an outside magnetic field. The equations describing the physical problem were solved using Boltzmann method.…”