Brownian motion’s impact on MHD CuO - A l 2 O 3 / H 2 O hybrid nanofluid flow and heat transfer through annular duct

Abstract

The present numerical work is to explore the effect of variable electrically conductivity on magneto-hydrodynamic, $\left(\mathrm{MHD}\right)$ hybrid nanofluid flow through annular sector duct, for both $H$ 1 and $T$ thermally fully developed conditions. The nanofluid consists of basefluid water and aluminum oxide, (i.e. $A{l}_2{O}_3$ / $H_{2}O$ nanofluid). The addition of copper oxide, $\left(\mathrm{CuO}\right)$ nanoparticles in $A{l}_2{O}_3$ / $H_{2}O$ nanofluid, $n$ , is known as hybrid nanofluid. Koo–Kleinstreuer–Li ( $\mathrm{KKL}$ ) model correlations are used to examine the effective dynamics viscosity and thermal conductivity of the resulting hybrid nanofluid. In this way, the Brownian motion’s impact of $\mathrm{CuO}$ and $A{l}_2{O}_3$ nanoparticles are also accounted. The finite volume based method, $\left(\mathrm{FVBM}\right)$ and strongly implicit procedure, $\left(\mathrm{SIP}\right)$ are adopted for the discretization and the numerical solution of the governing non-linear problem respectively. For this purpose, the well known technique ’the semi implicit method for pressure linked equations, $\left(\mathrm{SIMPLE}\right)$ revised’ is utilized. Accordingly $\mathrm{SIMPLER}$ , the continuity equation is transformed into Poisson equation in term of the pressure by replacing the cross section velocity components’ discretized form. During the work, it has been observed that the velocity contours and isotherms against pertinent parameters, $n$ and $M$ , have inversely and directly impacts respectively, for different values of apex angle, $2\alpha$ and the ratio of radii, $\hat{R}$ . Therefore, the velocity decreases and the temperature of the fluid increases. At $M=5$ and $10$ , the maximum addition of $\mathrm{CuO}$ nanoparticles in hybrid nanofluid, enhances the fanning friction factor, $\mathrm{fRe}$ , nearly up to 7.92 $\mathrm{\%}$ and 8.04 $\mathrm{\%}$ , while average Nusselt number, $\mathrm{Nu}$ , nearly up to 6.82 $\mathrm{\%}$ and 6.79 $\mathrm{\%}$ at $\hat{R}=0.25$ and $0.50$ respectively, for all values of $2\alpha$ . Furthermore, the limiting case results are also examined for code validating and showed the good agreement with the literature results.