**ABSTRACT**

In this paper, the free convective flow and heat transfer in a porous rectangular enclosures filled with Cu-water nanofluid is studied and analyzed. The cavity side-walls are exposed to a constant heat flux and the horizontal walls are assumed to be adiabatic. The governing equations describing the problem are solved using a finite difference method. The main parameters of our problem are: aspect ratio, volume fraction of nanoparticles, types of media, porosity of the medium, and Rayleigh number. The results indicate that an increase in aspect ratio from 0.1 to 0.7 leads to a significant increase of Nusselt number, which then reaches a maximum value. However, the heat transfer rate progressively decreases for aspect ratios greater than 0.7. Moreover, the addition of Cu-nanoparticles weakens the heat transfer. As a result, when the porous medium has low thermal conductivity, the solid matrix porosity becomes particularly more effective in improving heat transfer. Also, a correlation was established between the average Nusselt number and the influencing parameters. Results show that the governing parameters impact the flow regime.

**KEYWORDS**

PAPER SUBMITTED: 2023-04-05

PAPER REVISED: 2023-07-12

PAPER ACCEPTED: 2023-07-17

PUBLISHED ONLINE: 2023-09-02

**THERMAL SCIENCE** YEAR

**2024**, VOLUME

**28**, ISSUE

**Issue 2**, PAGES [929 - 939]

- Nield, D. A., Bejan, A., Convection in Porous Media, Springer International Publishing, Cham, New York, USA, 2017
- Vafai, K., Handbook of Porous Media, CRC Press, Boca Raton, Fla., USA, 2005
- Chamkha, A. J., Al-Naser, H., Double-Diffusive Convection in an Inclined Porous Enclosure with Oppos-ing Temperature and Concentration Gradients, International Journal of Thermal Sciences, 40 (2001), 3, pp. 227-244
- Chamkha, A. J., Al-Naser, H., Hydromagnetic Double-Diffusive Convection in a Rectangular Enclosure with Uniform Side Heat and Mass Fluxes and Opposing Temperature and Concentration Gradients, Inter-national Journal of Thermal Sciences, 41 (2002), 10, pp. 936-948
- Chamkha A. J., et al., Mixed Convection Heat Transfer of Air inside a Square Vented Cavity with a Heated Horizontal Square Cylinder, Numerical Heat Transfer, Part A: Applications, 59 (2011), 1, pp. 58-79
- Khanafer, K. M., Chamkha, A. J., Hydromagnetic Natural Convection from an Inclined Porous Square Enclosure with Heat Generation, Numerical Heat Transfer, Part A: Applications, 33 (1998), 8, pp. 891-910
- Jung, S. Y., Park, H., Experimental Investigation of Heat Transfer of Al2O3 Nanofluid in a Microchannel Heat Sink, International Journal of Heat and Mass Transfer, 179 (2021), 121729
- Sharifpur, M., et al., Optimum Concentration of Nanofluids for Heat Transfer Enhancement Under Cavity Flow Natural Convection with TiO2-Water, International Communications in Heat and Mass Transfer, 98 (2018), Nov., pp. 297-303
- Anwar, M., et al., Numerical Study for Heat Transfer Enhancement Using CuO Water Nanofluids Through Mini-Channel Heat Sinks for Microprocessor Cooling, Thermal Science, 24 (2020), 5A, pp. 2965-2976
- Keblinski, P., et al., Nanofluids for Thermal Transport, Materials Today, 8 (2005), 6, pp. 36-44
- Asmadi, M. S., et al., Nanoparticle Shape Effect on the Natural-Convection Heat Transfer of Hybrid Nanofluid Inside a U-shaped Enclosure, Thermal Science, 26 (2022), 1B, pp. 463-475
- Rahimi, A., et al., A Comprehensive Review on Natural Convection Flow and Heat Transfer: The Most Practical Geometries for Engineering Applications, International Journal of Numerical Methods for Heat & Fluid Flow, 29 (2018), 3, pp. 834-877
- Sadeghi, M. S., et al., On the Natural Convection of Nanofluids in Diverse Shapes of Enclosures: An Exhaustive Review, Journal of Thermal Analysis and Calorimetry, 147 (2022), 1, pp. 1-22
- Izadi, S., et al., A Comprehensive Review on Mixed Convection of Nanofluids in Various Shapes of En-closures, Powder Technology, 343 (2019), Feb., pp. 880-907
- Hashemi-Tilehnoee, M., et al., Magnetohydrodynamic Natural Convection and Entropy Generation Anal-yses Inside a Nanofluid-Filled Incinerator-Shaped Porous Cavity with Wavy Heater Block, Journal of Thermal Analysis and Calorimetry, 141 (2020), 5, pp. 2033-2045
- Xu, L., et al., Numerical Investigating the Effect of Al2O3-Water Nanofluids on the Thermal Efficiency of Flat Plate Solar Collectors, Energy Reports, 8 (2022), Nov., pp. 6530-6542
- Alklaibi, A. M., et al., Experimental Investigation on the Performance of Hybrid Fe3O4 Coated MWCNT/Water Nanofluid as a Coolant of a Plate Heat Exchanger, International Journal of Thermal Sciences, 171 (2022), 107249
- Yao, S., et al., The Study of Natural Convection Heat Transfer of Nanofluids in a Partially Porous Cavity Based on Lattice Boltzmann Method, Thermal Science, 23 (2019), 2B, pp. 1003-1015
- Dogonchi, A. S., et al., A Numerical Investigation of Magnetohydrodynamic Natural Convection of Cu-Water Nanofluid in a Wavy Cavity Using CVFEM, Journal of Thermal Analysis and Calorimetry, 135 (2019), 4, pp. 2599-2611
- Chamkha, A. J., et al., Magnetohydrodynamic Nanofluid Natural Convection in a Cavity under Thermal Radiation and Shape Factor of Nanoparticles Impacts: A Numerical Study Using CVFEM, Applied Sci-ences, 8 (2018), 12, 2396
- Alsabery, A. I., et al., Mixed Convection of Al2O3-Water Nanofluid in a Double Lid-Driven Square Cavity with a Solid Inner Insert Using Buongiorno's Two-Phase Model, International Journal of Heat and Mass Transfer, 119 (2018), Apr., pp. 939-961
- Belabid, J., et al., Numerical Simulation for Impact of Copper/Water Nanofluid on Thermo-Convective Instabilities in a Horizontal Porous Annulus, J. of Ther. Anal. and Calor., 138 (2019), 2, pp. 1515-1525
- Oztop, H. F., Abu-Nada, E., Numerical Study of Natural Convection in Partially Heated Rectangular En-closures Filled with Nanofluids, Int. Journal of Heat and Fluid Flow, 29 (2008), 5, pp. 1326-1336
- Redouane, F., et al., Heat Flow Saturate of Ag/MgO-Water Hybrid Nanofluid in Heated Trigonal Enclo-sure with Rotate Cylindrical Cavity by using Galerkin Finite Element, Scientific Reports, 12 (2022), 1, 2302
- Tiwari,R. K., Das, M. K., Heat Transfer Augmentation in a Two-Sided Lid-Driven Differentially Heated Square Cavity Utilizing Nanofluids, Int. Journal of Heat and Mass Transfer, 50 (2007), 9, pp. 2002-2018
- Abu-Nada, E., Oztop, H. F., Effects of Inclination Angle on Natural Convection in Enclosures Filled with Cu-Water Nanofluid, International Journal of Heat and Fluid Flow, 30 (2009), 4, pp. 669-678
- Haddad, Z., et al., A Review on Natural Convective Heat Transfer of Nanofluids, Renewable and Sustain-able Energy Reviews, 16 (2012), 7, pp. 5363-5378
- Sheremet, M. A., et al., Free Convection in a Square Cavity Filled with a Porous Medium Saturated by Nanofluid Using Tiwari and Das' Nanofluid Model, Transport in Porous Media, 106 (2015), 3, pp. 595-610
- Bejan, A., On the Boundary Layer Regime in a Vertical Enclosure Filled with a Porous Medium, Letters in Heat and Mass Transfer, 6 (1979), 2, pp. 93-102
- Gross, R. J., et al., The Application of Flux-Corrected Transport (fct) to High Rayleigh Number Natural Convection in a Porous Meduim, Begel House Inc., Danbury, Conn., USA, 1986
- Manole, D. M., Lage, J. L., Numerical Benchmark Results for Natural Convection in a Porous Medium Cavity, Proceedings, In Heat and Mass Transfer in Porous Media, ASME Conference 1992, Lakeland, Fla., USA, Vol. 216, pp. 55-60
- Baytas, A. C., Pop, I., Free Convection in Oblique Enclosures Filled with a Porous Medium, International Journal of Heat and Mass Transfer, 42 (1999), 6, pp. 1047-1057
- Sun, Q., Pop, I., Free Convection in a Tilted Triangle Porous Cavity Filled with Cu-Water Nanofluid with Flush Mounted Heater on the Wall, International Journal of Numerical Methods for Heat & Fluid Flow, 24 (2014), 1, pp, 2-20
- Sivasankaran, S., et al., Natural Convection in an Inclined Porous Triangular Enclosure with Various Thermal Boundary Conditions, Thermal Science, 23 (2019), 2A, pp. 537-548
- Rao, P. S., Barman, P., Natural Convection in a Wavy Porous Cavity Subjected to a Partial Heat Source, International Communications in Heat and Mass Transfer, 120 (2021), 105007
- Ghalambaz, M., et al., Free Convection in a Parallelogrammic Porous Cavity Filled with a Nanofluid Using Tiwari and Das' Nanofluid Model, Plos One, 10 (2015), 5, e0126486