Natural convection and heat transmission of two-phase Bingham Fe₃O₄-CoFe₂O₄-water hybrid nanofluid flow in an enclosure with a corrugated heated cylinder

Abstract

The Galerkin weighted residual finite element method (GFEM) has been used to numerically investigate the natural convection flow of two-phase Bingham hybrid nanofluid in a square cavity with a corrugated cylinder at the center. The base fluid here is water. The hybrid nanofluid is made of Fe$_3$O$_4$-CoFe$_2$O$_4$ nanoparticles. The flow inside the enclosure is considered laminar, non-Newtonian, and incompressible. The corrugated cylinder is taken heated. The top and bottom walls of the outer square are considered adiabatic, and the left and right walls are considered cold. Several non-dimensional parameters including the Rayleigh number ($Ra=10^4, 10^5, 10^6$), the Bingham number ($Bn=0, 0.5, 1$), the volume fraction ($\phi=0.00, 0.04$), the Brownian parameter ($Nb=0.1, 0.2, 0.3$), thermophoresis parameter ($Nt=0.1, 0.2, 0.3$), buoyancy ratio ($Nr=0.1, 0.2, 0.3$), corrugation ($N= 5, 6, 7$), the Prandtl number ($Pr=6.2$), and the Lewis number ($Le=1000$) have been numerically simulated. 
The results show that an upsurge in $Ra$ increases the extent of the upper two vortices and decreases the extent of the lower two vortices. All four vortices are seen to increase in dimension for an increase in $Bn$. The same observation is found for an increase in $\phi$. The lower vortices are growing, and the top ones are nearly eliminated for base fluid, while those are visible for nanofluid when corrugation is increased. A further expansion completely destroyed the higher ones and increased the size of the bottom ones. 
The average Nusselt number ($\overline{Nu}$) increases when $Ra$ is incremented. $\overline{Nu}$ rises with rise in $\phi$. An increment in $\phi$ to 0.04 results in $4.43\%$ gain in $\overline{Nu}$. An increase in $Bn$ is causing $\overline{Nu}$ to drop by $18.02\%$. For $Ra=10^5$ and $Bn=2$, $\phi=0.02$ has the maximum heat transfer enhancement between $0.00\le\phi\le0.04$