Numerical simulation of a non-Newtonian nanofluid on mixed convection in a rectangular enclosure with two rotating cylinders

Abstract

Non-Newtonian fluid flows are a present advancement in industrial heat transfer and fluid mechanics, with numerous applications in engineering field as well as in real life such as food industry, petroleum refiners, biological processes, biomedical engineering, chemical engineering, etc. As a result, this numerical investigation explore the heat transfer and fluid flow behaviour of a mixed convective non-Newtonian power-law nanofluid (${\mathrm{Al}}_2{\mathrm{O}}_3$-${\mathrm{H}}_2\mathrm{O}$) in a rectangular enclosure. The physical model is considered as a two-dimensional rectangular enclosure consisting two rotating hot cylinders ($T_H$)in the middle part of the cavity, where one moving clockwise and the other counter-clockwise directions. The left and right walls of the chamber are taken relatively low temperature ($T_C$) while the remaining top and bottom walls are insulated. The important thermophysical property, viscosity, depends on the fluid shear rate, and the thermal conductivity depends on the fluid temperature. The related governing equations are solved by using the finite element method, and to describe the response surfaces the response surface methodology (RSM) is applied. The influence of the relevant non-dimensional parameters, Prandtl number ($\mathrm{Pr}=6.2$), Reynolds number ($\mathrm{Re}=10$, 100, 200 and 400), power-law index (n = 0.6, 0.8, 1.0 and 1.4), Richardson number ($\mathrm{Ri}=1.0$, 2.0, 4.0 and 6.0), and nanoparticle volume fraction ($\varphi =0.00$, 0.01, 0.02 and 0.04), are explained with physical interpretation by using streamlines, isotherm lines, velocity profile, temperature profile, and average Nusselt number (${\mathrm{Nu}}_{\mathrm{av}}$). To visualise the response surfaces, 2D and 3D contour plots are explained using the RSM. It is concluded that by adding nanoparticle into base fluid, the rate of heat transfer developed significantly. Same phenomena exhibits for larger magnitudes of $\mathrm{Ri}$ and $\mathrm{Re}$. And, by increasing the value of n from 0.6 to 1.4, the ${\mathrm{Nu}}_{\mathrm{av}}$ would go down by 39.8 percent.

KEYWORDS:

• Non-Newtonian fluid
• nanofluid
• rotating cylinder
• mixed convection
• finite element method
• response surface methodology

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

This study is not associate with any third part data.

Additional information

Funding

The corresponding author acknowledges gratefully to the (i) North South University [grant number CTRG-23-SEPS-11], and (ii) the Ministry of Science and Technology, Government of the People's Republic of Bangladesh [grant number EAS/SRG-232406] for the financial support.