Steady laminar natural convection flow is studied numerically. The flow domain is a differentially heated square cavity with two partitions that is exposed to a constant horizontal magnetic field. A finite volume-based code is developed by the SIMPLER algorithm. A parametric study is carried out, using different values of the Rayleigh numbers, partition positions, partition heights, and the Hartmann numbers (from zero to 200). It is found that the Nusselt number is an increasing function of the Rayleigh number, but a decreasing function of the partition height and Hartmann number. The position of the partitions affects the streamlines and isotherms, but has a minimal effect on the mean Nusselt number. In addition, the results show that for low partition heights convective heat transfer in a cavity is significant, the braking effect of the Lorentz force is more pronounced, and the mean Nusselt number decreases considerably with increasing magnetic field strength.
Similar content being viewed by others
References
G. D. Davis, Natural convection of air in a square cavity: A benchmark numerical solution, Int. J. Numer. Methods Fluids, 3, 249–263 (1983).
T. Basak, S. Roy, and I. Pop, Heat flow analysis for natural convection within trapezoidal enclosures based on heatline concept, Int. J. Heat Mass Transf., 52, 2471–2483 (2009).
R. S. Kaluri, R. Anandalakshmi, and T. Basak, Bejan's heatline analysis of natural convection in right-angled triangular enclosures: Effects of aspect ratio and thermal boundary conditions, Int. J. Therm. Sci., 49, 1576–1592 (2010).
E. M. Alawadhi, Phase change process with free convection in a circular enclosure: Numerical simulations, Comput. Fluids, 33, 1335–1348 (2004).
Yu. E. Karyakin, Yu. A. Sokovishin, and O. G. Martynenko, Transient natural convection in triangular enclosures, Int. J. Heat Mass Transf., 31, 1759–1766 (1988).
Yu. E. Karyakin, Transient natural convection in prismatic enclosures of arbitrary cross section, Int. J. Heat Mass Transf., 32, 1095–1103 (1989).
J. P. Garandet, J. P. Alboussiere, and T. Moreau, Buoyancy driven convection in a rectangular cavity with a transverse magnetic field, Int. J. Heat Mass Transf., 35, 741–748 (1992).
N. Rudraiah, R. M. Barron, M. Venkatachalappa, and C. K. Subbaraya, Effect of a magnetic field on free convection in a rectangular cavity, Int. J. Eng. Sci., 33, 1075–1084 (1995).
N. M. Al-Najem, K. M. Khanafer, and M. M. El-Refaee, Numerical study of laminar natural convection in tilted cavity with transverse magnetic field, Int. J. Numer. Methods Heat Fluid Flow, 8, 651–672 (1998).
M. Pirmohammadi and M. Ghassemi, Effect of magnetic field on convection heat transfer inside a tilted square enclosure, Int. Commun. Heat Mass Transf., 36, 776–780 (2009).
M. N. Kherief, K. Talbi, and F. Berrahil, Effects of inclination and magnetic field on natural convection flow induced by a vertical temperature, J. Appl. Fluid Mech., 5, 113–120 (2012).
F. Selimefendigil, H. F. Oztop, and K. Al-Salem, Natural convection of ferrofluids in partially heated square enclosures, J. Magn. Magn. Mater., 372, 122–133 (2014).
N. S. Bondareva and M. A. Sheremet, Influence of uniform magnetic field on laminar regimes of natural convection in an enclosure, Thermophys. Aeromech., 22, 203–216 (2015).
A. Malvandi, M. R. Safaei, M. H. Kaffash, and D. D. Ganji, MHD mixed convection in a vertical annulus filled with Al2O3–water nanofluid considering nanoparticle migration, J. Magn. Magn. Mater., 382, 296–306 (2015).
A. Malvandi, Film boiling of magnetic nanofluids (MNFs) over a vertical plate in presence of a uniform variabledirectional magnetic field, J. Magn. Magn. Mater., 406, 95–102 (2016).
A. Malvandi and D. D. Ganji, Magnetic field effect on nanoparticles migration and heat transfer of water/alumina nanofluid in a channel, J. Magn. Magn. Mater., 362, 172–179 (2014).
M. A. Sheremet, I. Pop, and N. C. Rosca, Magnetic field effect on the unsteady natural convection in a wavy-walled cavity filled with a nanofluid: Buongiorno's mathematical model, J. Taiwan Inst. Chem. Eng., 61, 211–222 (2016).
R. Jelti, S. Acharya, and E. Zimmerman, Influence of baffle location on natural convection in partially divided enclosure, Numer. Heat Transf. A, 10, 521–536 (1986).
S. H. Tasnim and M. R. Collins, Suppressing natural convection in a differentially heated square cavity with an arc shaped baffle, Int. Commun. Heat Mass Transf., 32, 94–106 (2005).
A. Ben-Nakhi and A. J. Chamkha, Conjugate natural convection in a square enclosure with inclined thin fin of arbitrary length, Int. J. Therm. Sci., 46, 467–478 (2007).
N. Ben Cheikh, A. J. Chamkha, and B. Ben Beya, Effect of inclination on heat transfer and fluid flow in a finned enclosure fi lled with a dielectric liquid, Numer. Heat Transf. A, 56, 286–300 (2009).
A. J. Chamkha, M. Mansour, and S. E. Ahmed, Double diffusive natural convection in inclined fi nned triangular porous enclosures in the presence of heat generation/absorption effects, Heat Mass Transf., 46, 757–768 (2010).
V. A. F. Costa, Natural convection in partially divided square enclosures: Effects of thermal boundary conditions and thermal conductivity of the partitions, Int. J. Heat Mass Transf., 55, 7812–7822 (2012).
H. Heidary, M. J. Kermani, and M. Pirmohammadi, Partition effect on thermomagnetic natural convection and entropy generation in inclined porous cavity, J. Appl. Fluid Mech., 19, 119–130 (2016).
S. A. M. Mehryan, M. Ghalambaz, M. A. Ismael, and A. J. Chamkha, Analysis of fluid–solid interaction in MHD natural convection in a square cavity equally partitioned by a vertical flexible membrane, J. Magn. Magn. Mater., 424, 161–173 (2017).
S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington DC (1980).
A. Al-Amiri, K. Khanafer, and I. Pop, Buoyancy-induced flow and heat transfer in a partially divided square enclosure, Int. J. Heat Mass Transf., 52, 3818–3828 (2009).
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 93, No. 5, pp. 1300–1309, September–October, 2020.
Rights and permissions
About this article
Cite this article
Pirmohammadi, M., Salehi-Shabestari, A. Parametric Study of Natural Convection inside a Partitioned Cavity in the Presence of a Magnetic Field. J Eng Phys Thermophy 93, 1255–1265 (2020). https://doi.org/10.1007/s10891-020-02229-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10891-020-02229-x