Numerical analysis of Al2O3/water nano-fluid natural convection in a square cavity filled with an anisotropic porous medium under a magnetic field

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Authors

  • S. Safi Department of Climatic Engineering, Faculty of Sciences Technology, University of Constantine 1 and LEAP Laboratory, Department of Mechanical Engineering, Faculty of Sciences Technology, Algeria
  • F. Berrahil LEAP Laboratory, Department of Mechanical Engineering, Faculty of Sciences Technology and Department of Mechanical and Electromechanical Engineering, Sciences and Technology Institute, University Center Abdelhafid Boussouf, Algeria
  • A. Filali Laboratoire de Mécanique et de systèmes énergétiques avancés, École Nationale Polytechnique de Constantine and Chemical Engineering Department, Imperial College London, Algeria
  • S. Benissaad LEAP Laboratory, Department of Mechanical Engineering, Faculty of Sciences Technology, Algeria

Abstract

Natural convection in porous media is crucial for applications such as geothermal energy cooling systems and energy storage, where efficient heat transfer is essential. However, the combined effect of anisotropy in the porous matrix and an inclined magnetic field on nanofluid heat transfer remains poorly understood hence, this study addresses numerically the unexplored combined effects of anisotropy and inclined magnetic field on the natural convection of water-based Al2O3 nanofluid. The Darcy–Brinkman–Forchheimer model and energy transport equations describe nanofluid motion and heat transfer in a porous medium. The mathematical equations are discretized using the finite volume method in an in-house computer code. The governing parameters are the Rayleigh number the Darcy number, the Hartmann number, solid volume fraction, the permeability ratio K (a measure of porous medium anisotropy) and an inclination angle with the magnetic field. Results are reported for streamlines, temperature contours, and the average Nusselt number under different parametric conditions. It was found that increasing the Rayleigh and Darcy numbers shifts the system from conduction to convection, improving the heat transfer rate. The nanoparticle volume fraction enhances heat transfer in conduction-dominated flows but reduces it in convection-dominated regimes. A higher Hartmann number decreases the average Nusselt number, with a more pronounced effect when the magnetic field is oriented horizontally. A higher permeability ratio reduces flow resistance and enhances convective heat transfer, but beyond K > 10, further increases in permeability have minimal impact on the heat transfer rate.

Keywords:

natural convection, anisotropic porous medium, nanofluid, numerical study, magnetic field

References


  1. S.U.S. Choi, J.A. Eastman, Enhancing thermal conductivity of fluids with nanoparticles, (No. ANL/MSD/CP-84938; CONF-951135-29), Argonne National Lab. (ANL), Argonne, IL, United States of America, 1995.

  2. M.A.A. Hamad, Analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field, International Communications in Heat and Mass Transfer, 38, 4, 487–492, 2011, https://doi.org/10.1016/j.icheatmasstransfer.2010.12.042.

  3. M. Gürbüz-Çaldağ, E. Çelık, Stokes flow in lid-driven cavity under inclined magnetic field, Archives of Mechanics, 74, 6, 549–564, 2022, https://doi.org/10.24423/aom.4013.

  4. K. Kahveci, Buoyancy driven heat transfer of nanofluids in a tilted enclosure, Journal of Heat Transfer, 132, 6, 062501, 2010, https://doi.org/10.1115/1.4000744.

  5. E. Bilgen, Natural Convection in Cavities with a thin fin on the hot wall, International Journal of Heat and Mass Transfer, 48, 17, 3493–3505, 2005, https://doi.org/10.1016/j.ijheatmasstransfer.2005.03.016.

  6. B. Ghasemi, S.M. Aminossadat, A. Raisi, Magnetic field effect on natural convection in a nanofluid-filled square enclosure, International Journal of Thermal Sciences, 50, 9, 1748–1756, 2011, https://doi.org/10.1016/j.ijthermalsci.2011.04.010.

  7. K. Khanafer, K. Vafai, M. Lightstone, Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids, International Journal of Heat and Mass Transfer, 46, 19, 3639–3653, 2003, https://doi.org/10.1016/S0017-9310(03)00156-X.

  8. G.C. Bourantas, E.D. Skouras, V.C. Loukopoulos, V.N. Burganos, Heat transfer and natural convection of nanofluids in porous media, European Journal of Mechanics – B/Fluids, 43, 45–56, 2014, https://doi.org//10.1016/j.euromechflu.2013.06.013.

  9. D. Yadav, R. Bhargava, G.S. Agrawal, Boundary and internal heat source effects on the onset of Darcy–Brinkman convection in a porous layer saturated by nanofluid, International Journal of Thermal Sciences, 60, 244–254, 2012, https://doi.org/10.1016/j.ijthermalsci.2012.05.011.

  10. W.J. Chang, C.F. Hsiao, Natural convection in a vertical cylinder filled with anisotropic porous media, International Journal of Heat and Mass Transfer, 36, 13, 3361–3367, 1993, https://doi.org/10.1016/0017-9310(93)90017-Z.

  11. P. Nithiarasu, K.S. Sujatha, K. Ravindran, T. Sundararajan, K.N. Seetharamu, Non-Darcy natural convection in a hydrodynamically and thermally anisotropic porous medium, Computer Methods in Applied Mechanics and Engineering, 188, 1-3, 413–430, 2000, https://doi.org/10.1016/S0045-7825(99)00163-2.

  12. D.J. Krishna, T. Basak, S.K. Das, Natural convection in a heat generating hydrodynamically and thermally anisotropic non-Darcy porous medium, International Journal of Heat and Mass Transfer, 51, 19-20, 4691–4703, 2008, https://doi.org/10.1016/j.ijheatmasstransfer.2008.02.019.

  13. M.A. Abdelraheem, S.E. Ahmed, An incompressible smoothed particle hydrodynamics method for natural/mixed convection in a non-Darcy anisotropic porous medium, International Journal of Heat and Mass Transfer, 77, 1155–1168, 2014, https://doi.org/10.1016/j.ijheatmasstransfer.2014.06.044.

  14. R. Chand, G.C. Rana, S. Kumar, Variable gravity effects on thermal instability of nanofluid in anisotropic porous medium, International Journal of Applied Mechanics and Engineering, 18, 3, 631–642, 2013, https://doi.org/10.2478/ijame-2013-0038.

  15. S. Safi, S. Benissaad, Double-diffusive convection in an anisotropic porous layer using the Darcy–Brinkman–Forchheimer formulation, Archives of Mechanics, 70, 1, 89–102, 2018.

  16. I.S. Shivakumara, M. Dhananjaya, Penetrative Brinkman convection in an anisotropic porous layer saturated by a nanofluid, Ain Shams Engineering Journal, 6, 2, 703–713, 2015, https://doi.org/10.1016/j.asej.2014.12.005.

  17. S.E. Ahmed, A.M. Rashad, Natural convection of micropolar nanofluids in a rectangular enclosure saturated with anisotropic porous media, Journal Porous Media, 19, 8, 737–750, 2016, https://doi.org/10.1615/JPorMedia.v19.i8.60.

  18. S. Maheshwari, Y.D. Sharma, O.P. Yadav, Study of Heat Transfer in Anisotropic Porous Enclosures Saturated with Casson Fluid, Journal of Porous Media, 26, 10, 85–107, 2023, https://doi.org/10.1615/JPorMedia.2023044926.

  19. G.C. Bourantas, V.C. Loukopoulos, MHD natural-convection flow in an inclined square enclosure filled with a micropolar-nanofluid, International Journal of Heat and Mass Transfer, 79, 930–944, 2014, https://doi.org/10.1016/j.ijheatmasstransfer.2014.08.075.

  20. M. Sheikholeslami, R. Ellahi, Three dimensional mesoscopic simulation of magnetic field effect on natural convection of nanofluid, International Journal of Heat and Mass Transfer, 89, 779–808, 2015, https://doi.org/10.1016/j.ijheatmasstransfer.2015.05.110.

  21. W.M. El-Maghlany, M.M. Abo Elazm, M. Elhelw, S. Bayoumi, The constraints on nanoparticles addition in natural convection heat transfer at highly magnetic field, Journal of Thermophysics and Heat Transfer, 32, 1, 2017, https://doi.org/10.2514/1.T5183.

  22. K.S. Al Kalbani, M.M. Rahman, M.S. Alam, N. Al-Salti, A.I. Eltayab, Buoyancy induced heat transfer flow inside a tilted square enclosure filled with nanofluids in the presence of oriented magnetic field, Heat Transfer Engineering, 39, 6, 511–525, 2018, https://doi.org/10.1080/01457632.2017.1320164.

  23. T. Islam, M.D. Fayz-Al-Asad, M.A. Khatun, N. Parveen, H. Ahmad, S. Askar, Natural convection heat transport performance of nanofluids under the influence of inclined magnetic field, Results in Physics, 5, 8, 107365, 2024, https://doi.org/10.1016/j.rinp.2024.107365.

  24. D.J. Krishna, T. Basak, S.K. Das, Natural convection in a non-Darcy anisotropic porous cavity with a finite heat source at the bottom wall, International Journal of Thermal Sciences, 48, 7, 1279–1293, 2009, https://doi.org/10.1016/j.ijthermalsci.2008.11.022.

  25. A.M. Aly, S.E. Ahmed, An incompressible smoothed particle hydrodynamics method for natural/mixed convection in a non-Darcy anisotropic porous medium, International Journal of Heat and Mass Transfer, 77, 1155–1168, 2014, https://doi.org/10.1016/j.ijheatmasstransfer.2014.06.044.

  26. G. Lauriat, V. Prasad, Non-Darcian effects on natural convection in a vertical porous enclosure, International Journal of Heat and Mass Transfer, 32, 11, 2135–2148, 1989, https://doi.org/10.1016/0017-9310(89)90120-8.

  27. P. Nithiarasu, K.N. Seetharamu, T. Sundararajan, Natural convective heat transfer in a fluid saturated variable porosity medium, International Journal of Heat and Mass Transfer, 40, 16, 3955–3967, 1997, https://doi.org/10.1016/S0017-9310(97)00008-2.

  28. X.B. Chen, P. Yu, S.H. Winoto, H.T. Low, Free convection in a porous wavy cavity based on the Darcy–Brinkman–Forchheimer extended model, Numerical Heat Transfer, Part A, 52, 37–397, 2007, https://doi.org/10.1080/10407780701301595.

  29. M. Kumari, G. Nath, Unsteady natural convection from a horizontal annulus filled with a porous medium, International Journal of Heat and Mass Transfer, 51, 19–20, 5001–5007, 2008, https://doi.org/10.1016/j.ijheatmasstransfer.2008.01.030.

  30. G.H.R. Kefayati, Heat transfer and entropy generation of natural convection on non-Newtonian nanofluids in a porous cavity, Powder Technology, 299, 127–149, 2016, https://doi.org/10.1016/j.powtec.2016.05.032.

  31. H.C. Brinkman, The viscosity of concentrated suspensions and solutions, The Journal of Chemical Physics, 20, 4, 571–581, 1952.

  32. J.C. Maxwell Garnett, Colours in metal glasses and in metallic films, The Philosophical Transactions of the Royal Society A, 203, 385–420, 1904.

  33. J.C. Maxwell, A Treatise on Electricity and Magnetism, 2nd ed., Oxford University Press, Cambridge, 1904.

  34. F. Berrahil, A. Filali, C. Abid, S. Benissaad, R. Bessaih, O. Matar, Numerical investigation on natural convection of Al2O3/water nanofluid with variable properties in an annular enclosure under magnetic field, International Communications in Heat and Mass Transfer, 126, 105408, 2021, https://doi.org/10.1016/j.icheatmasstransfer.2021.105408.

  35. S.V. Patankar, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, 1980.

  36. J. Ni, C. Beckermann, Natural convection in a vertical enclosure filled with anisotropic porous media, Journal of Heat Transfer, 113, 1033–1037, 1991.

  37. R.J. Krane, J. Jessee, Some detailed field measurements for a natural convection flow in a vertical square enclosure, [in:] 1st ASME-JSME Thermal Engineering Joint Conference, 1983.

  38. M.T. Nguyen, A.M. Aly, S.-W. Lee, Natural convection in a non-Darcy porous cavity filled with Cu–Water nanofluid using the characteristic-based split procedure in finite-element method, Numerical Heat Transfer, Part A: Applications, 67, 2, 224–247, 2014, https://doi.org/10.1080/10407782.2014.923225.