MHD natural convection of Fe₃O₄- MWCNT/Water hybrid nanofluid filled in a porous annulus between a circular cylinder and Koch snowflake

In this work, the numerical investigation was conducted for the MHD natural convection and entropy generation characteristics of water-based hybrid nanofluid (Fe₃O₄-MWCNT) in a porous annulus between a cooled circular cylinder and a heated Koch snowflake subjected to a uniform magnetic force. The novelty of this work is presented by the special shape and different studied positions of the hot barrier. The governing equations are explained by employing the Finite Element Method. The impacts of nanoparticle volume fraction (φ = 2 %, 3%,4%, and 5 %), Rayleigh number (Ra = 10³ to 10⁶), Hartman number (Ha = 0,25,50,100), Darcy number (Da = 10^-2, 10^-3, 10^-4, and 10^-5), and the position of the Koch snowflake (four cases) on the distributions of isotherms, streamlines, average Nusselt number (Nu_avg) as well as on total entropy generation and Bejan number are thoroughly examined. The computational outcomes indicate that increasing the Ra number is possible by changing the temperature between the hot and cold sources. By increasing this parameter, the buoyancy force of the fluid is strengthened. As the Da number increases, the penetration of the flow cross-section in the cavity increases, and the flow circulates in the cavity with less depreciation due to the buoyancy force. Applying Lorentz force, if not in the direction of natural flow, causes the flow velocity to be depleted and fluid flow in the cavity to be facilitated. With increasing Ra number, the application of Lorentz force with different intensities becomes important due to the importance of fluid circulation in the cavity. Applying a Lorentz force with a higher Ha number at high Ra numbers reduces heat transfer due to junction balance and flow separation on hot and cold surfaces. In the lower Ra numbers, the Bejan number tends to 1, indicating a significant increase in the temperature gradient in the cavity and the expansion of the thermal boundary layer at low fluid velocities. At the highest Ra, increasing Ha from 0 to 100 decreases Nu_avg by 50 %, while decreasing Da from 10⁻² to 10⁻⁵ reduces Nu_avg by 70 %.