## THERMAL SCIENCE

International Scientific Journal

### TURBULENT NATURAL-CONVECTION HEAT TRANSFER IN A SQUARE CAVITY WITH NANOFLUIDS IN PRESENCE OF INCLINED MAGNETIC FIELD

**ABSTRACT**

In this paper, we present a numerical study of turbulent natural-convection in a square cavity differentially heated and filled with nanofluid and subjected to an inclined magnetic field. The standard k-ε model was used as the turbulence model. The transport equations were discretized by the finite volume method using the SIMPLE algorithm. The influence of the Rayleigh number, the Hartmann number, the orientation angle of the applied magnetic field, the type of nanoparticles as well as the volume fraction of nanoparticles, on the hydrodynamic and thermal characteristics of the nanofluid was illustrated and discussed in terms of streamlines, isotherms and mean Nusselt number. The results obtained show that the heat transfer rate increases with increasing Rayleigh number and orientation angle of the magnetic field but it decreases with increasing Hartmann number. In addition, heat transfer improves with increasing volume fraction and with the use of Al2O3 nanoparticles.

**KEYWORDS**

PAPER SUBMITTED: 2021-08-25

PAPER REVISED: 2021-09-29

PAPER ACCEPTED: 2021-10-04

PUBLISHED ONLINE: 2021-11-06

**THERMAL SCIENCE** YEAR

**2022**, VOLUME

**26**, ISSUE

**Issue 4**, PAGES [3201 - 3213]

- Ghasemi, B., et al., Magnetic field effect on natural convection in a nanofluid-filled square enclosure, International Journal of Thermal Sciences, 50 (2011), pp. 1748-1756
- Nemat, H., et al., Magnetic field effects on natural convection flow of nanofluid in a rectangular cavity using the Lattice Boltzmann, Scientia Iranica, 19 (2012), pp. 303-310
- Mejri, I., et al., MHD Natural Convection in a Nanofluid-filled Enclosure with Non-uniform Heating on Both SideWalls, FDMP, 10 (2014), 1, pp.83-114
- Mahmoudi, A., et al., MHD natural convection in a nanofluid-filled cavity with linear temperature distribution, Journal of Computational Methods in Sciences and Engineering,14 (2014), pp. 291-313
- Mansour, M. A., et al., MHD Natural convection in the localized heat sources of an inclined trapezoidal Nanofluid-filled enclosure, American Journal of Engineering Research (AJER), 2 (2013), 9, pp. 140-161
- El Hammami, Y., et al., Numerical Study of Natural Convection of Nanofluid in a Square Enclosure in the Presence of the Magnetic Field, International Journal of Engineering and Advanced Technology (IJEAT), 4 (2015), 4, pp. 230-239
- Sourtiji , E., et al., Heat transfer augmentation of magnetohydrodynamics natural convection in L-shaped cavities utilizing nanofluids, Thermal Science, 16 (2012), No. 2, pp. 489-501
- Islam, T., et al., Numerical Study of Magnetohydrodynamic Natural Convection Heat Transfer and Fluid Flow of Nanofluid in a Skewed Cavity, Journal of Engineering Mathematics & Statistics, 4 (2020), pp.14-36
- Sajjadi, H. and Kefayati, G. H. R., MHD Turbulent and Laminar Natural Convection in a Square Cavity utilizing Lattice Boltzmann Method, Heat Transfer—Asian Research, 45 (2016), 8, pp. 795-814
- Rahmati, A. R., et al., Numerical simulation of turbulent natural convection of nanofluid with thermal radiation inside a tall enclosure under the influence of magnetohydrodynamic, Heat Transfer—Asian Research, (2018), pp. 1-19
- Lafdaili, Z., et al., Numerical study of turbulent natural convection of nanofluids in differentially heated rectangular cavities, Thermal Science, 25 (2021), 1B, pp. 579-589
- Lafdaili, Z., et al., Numerical study of the turbulent natural convection of nanofluids in a partially heated cubic cavity, Thermal Science, 25 (2021), 4A, pp. 2741-2754
- Shahzad, F., et al., Numerical simulation of magnetohydrodynamic Jeffrey nanofuid flow and heat transfer over a stretching sheet considering Joule heating and viscous dissipation, AIP Advances, 8 (2018), pp. 065316
- Brinkman, H. C., The Viscosity of Concentrated Suspensions and Solutions, Journal of Chemical Physics, 20 (1952), pp. 571-581
- Maxwell, J. C., A Treatise on Electricity and Magnetism, second ed., Oxford University Press, Cambridge, UK, 1904
- Pak, B. C., Cho, Y. I., Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, Exp. Heat Transfer, 11 (1998), 2, pp. 151-170
- Henkes et al., Comparison of the standard case for turbulent natural convection in a square enclosure, Proceeding, turbulent natural convection in enclosures: a computational and experimental benchmark study, (ed. Henkes R. A. W. M. and Hoogendoorn, C. J.), Delft, Netheriands, (1992), pp. 185-213
- Patankar, S. V., Numerical heat transfer and fluid flow, Hemisphere Publishing Corporation, New York, Taylor and Francis Group., 1980
- Baϊri, A., et al., Nusselt-Rayleigh correlations for design of industrial elements Experimental and numerical investigation of natural convection in tilted square air filled enclosures, Energy Conversion and Management, 49 (2008), 4, pp.771-782
- Barakos, G. and Mitsoulis, E., Natural convection flow in a square cavity Revisited: laminar and turbulent models with wall functions, International journal for numerical methods in fluids, 18 (1994), pp. 695-719
- Dixit, H. N., et al., Simulation of high Rayleigh number convection in a square cavity using the lattice Boltzmann method, Int. J. Heat and Mass Transfer, 49 (2006), 3-4, pp.727-739
- Ampofo, F. and Karayiannis, T.G., Experimental benchmark data for turbulent natural convection in an air filled square cavity, Int. J. Heat Mass Transfer, 46 (2003), 19, pp. 3551-3572