Skip to main content
SpringerLink
Log in

Effect of an ascendant magnetic field on Rayleigh–Bénard convection for non-Newtonian power-law fluids in a horizontal rectangular cavity submitted to vertical temperature gradient

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

We approach the effect of an external magnetic field on induced natural convection flows within a horizontal rectangular cavity heated from below and containing electrically conducting non-Newtonian fluids. The vertical walls of this cavity are assumed to be insulated. The rheological behavior of the fluids considered is modeled by the power-law of Ostwald-De-Weale. The centered finite difference method is used to solve the governing equations. The parameters on which this problem depends are the aspect ratio of the cavity, A, the Rayleigh number, Ra, the Prandtl number, Pr, the fluid behavior index, n and the Hartmann number, Ha. The effect of magnetic field, rheology and their interaction on flow and heat transfer is examined and discussed in detail.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig.1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Data availability

No associated data in the manuscript.

Abbreviations

A :

Aspect ratio

\(\overrightarrow {{B^{\prime}_{0} }}\) :

Applied magnetic field

g :

Gravitational acceleration

\(H^{\prime}\) :

Width of the enclosure

Ha :

Hartmann number

\(\vec{J^{\prime}}\) :

Electric current density

k :

Consistency index for a power-law fluid

\(L^{\prime}\) :

Length of the enclosure

n :

Behavior index of power-law fluid

Nu :

Average Nusselt number

Pr :

Prandtl number

Ra :

Rayleigh number

T :

Dimensionless temperature

(u, v):

Dimensionless axial and transverse velocities

(x, y):

Dimensionless axial and transverse co-ordinates

α :

Thermal diffusivity of fluid

\(\beta\) :

Thermal expansion coefficient of fluid

λ :

Thermal conductivity of fluid

\(\mu_{a}\) :

Dimensionless apparent viscosity of fluid

\(\Omega\) :

Dimensionless vorticity

\(\psi\) :

Dimensionless stream function

ρ :

Density of fluid

\(\sigma\) :

Electrical conductivity of fluid

\(\phi^{\prime}\) :

Electrical potential

\(\nabla\) :

Nabla operator

':

Dimensional variable

C:

Cold wall

H:

Hot wall

max:

Maximum value

References

  1. A.M. Soward, C.A. Jones, D.W. Hughes, N.O. Weiss, Fluid Dynamics and Dynamos in Astrophysics and Geophysics (2005)

  2. S. Rashidi, J.A. Esfahani, M. Maskaniyan, Applications of magnetohydrodynamics in biological systems-a review on the numerical studies. J. Magn. Magn. Mater. 439, 358–372 (2017). https://doi.org/10.1016/j.jmmm.2017.05.014

    Article  ADS  Google Scholar 

  3. V.R. Gowariker, N.V. Viswanathan, J. Sreedhar, Polymer science. Br. Polym. J. (1988)

  4. M. Sathiyamoorthy, A. Chamkha, Effect of magnetic field on natural convection flow in a liquid gallium filled square cavity for linearly heated side wall(s). Int. J. Therm. Sci. 49, 1856–1865 (2010). https://doi.org/10.1016/j.ijthermalsci.2010.04.014

    Article  Google Scholar 

  5. G.M. Oreper, J. Szekely, The effect of an externally imposed magnetic field on buoyancy driven flow in a rectangular cavity. J. Cryst. Growth 64, 505–515 (1983). https://doi.org/10.1016/0022-0248(83)90335-4

    Article  ADS  Google Scholar 

  6. T.P. Garandet, T. Alboussiere, Buoyancy driven convection in a rectangular enclosure with a transverse magnetic field. Int. J. Heat Mass Transf. 35, 741–748 (1992). https://doi.org/10.1016/0017-9310(92)90242-K

    Article  MATH  Google Scholar 

  7. S. Alchaar, P. Vasseur, E. Bilgen, Natural convection heat transfer in a rectangular enclosure with a transverse magnetic field. J. Heat Transf. Asme 117, 668–675 (1995). https://doi.org/10.1115/1.2822628

    Article  Google Scholar 

  8. N. Rudraiah, R.M. Barron, M. Venkatachalappa, C.K. Subbaraya, Effect of a magnetic field on free convection in a rectangular enclosure. Int. J. Eng. Sci. 33, 1075–1084 (1995). https://doi.org/10.1016/0020-7225(94)00120-9

    Article  MATH  Google Scholar 

  9. M. Pirmohammadi, M. Ghassemi, Effect of magnetic field on convection heat transfer inside a tilted square enclosure. Int. Commun. Heat Mass Transf. 36, 776–780 (2009). https://doi.org/10.1016/j.icheatmasstransfer.2009.03.023

    Article  Google Scholar 

  10. S. Alchaar, P. Vasseur, E. Bilgen, The effect of a magnetic field on natural convection in a shallow cavity heated from below. Chem. Eng. Commun. 134, 195–209 (1995). https://doi.org/10.1080/00986449508936332

    Article  Google Scholar 

  11. R. Bajaj, S.K. Malik, Rayleigh-Bénard convection and pattern formation in magnetohydrodynamics. J. Plasma Phys. 60, 529–539 (1998). https://doi.org/10.1017/S0022377898006989

    Article  ADS  Google Scholar 

  12. M.K. Reddy, Numerical simulation of Rayleigh-Bénard convection in an inclined enclosure under the influence of magnetic field. J. King Saud Univ. Sci. 32, 486–495 (2020). https://doi.org/10.1016/j.jksus.2018.07.010

    Article  Google Scholar 

  13. U. Burr, U. Muller, Rayleigh Bénard convection in liquid metal layers under the influence of a horizontal magnetic field. J. Fluid Mech. 453, 345–369 (2002). https://doi.org/10.1017/S002211200100698X

    Article  ADS  MATH  Google Scholar 

  14. B. Ghasemi, S.M. Aminossadati, A. Raisi, Magnetic field effect on natural convection in a nanofluid-filled square enclosure. Int. J. Therm. Sci. 50, 1748–1756 (2011). https://doi.org/10.1016/j.ijthermalsci.2011.04.010

    Article  Google Scholar 

  15. G. Kefayati, Lattice Boltzmann simulation of natural convection in nanofluid-filled 2D long enclosures at presence of magnetic field. Theor. Comput. Fluid Dyn. 27, 865–883 (2013). https://doi.org/10.1007/s00162-012-0290-x

    Article  Google Scholar 

  16. M. Benzemaa, Y.K. Benkahlaa, S. Ouyahiaa, Rayleigh-Bénard MHD convection of Al2O3–water nanofluid in a square enclosure: magnetic field orientation effect. Energy Procedia 139, 198–203 (2017). https://doi.org/10.1016/j.egypro.2017.11.196

    Article  Google Scholar 

  17. T. Zürner, F. Schindler, T. Vogt, S. Eckert, J. Schumacher, Flow regimes of Rayleigh Bénard convection in a vertical magnetic field. J. Fluid Mech. (2020). https://doi.org/10.1017/jfm.2020.264

    Article  MATH  Google Scholar 

  18. G. Kefayati, Simulation of magnetic field effect on natural convection of non-Newtonian power-law fluids in a sinusoidal heated cavity using FDLBM. Int. Commun. Heat Mass Transf. 53, 139–153 (2014). https://doi.org/10.1016/j.icheatmasstransfer.2014.02.026

    Article  Google Scholar 

  19. G. Kefayati, FDLBM simulation of magnetic field effect on natural convection of non-Newtonian power-law fluids in a linearly heated cavity. Powder Technol. 256, 87–99 (2014). https://doi.org/10.1016/j.powtec.2014.02.014

    Article  Google Scholar 

  20. G. Kefayati, Mesoscopic simulation of magnetic field effect on natural convection of power-law fluids in a partially heated cavity. Chem. Eng. Res. Des. 94, 337–354 (2015). https://doi.org/10.1016/j.cherd.2014.08.014

    Article  Google Scholar 

  21. M. Poonia, Computational study on MHD power-law fluid in tilted enclosure having sinusoidal heated sidewall. Multidiscip. Model. Mater. Struct. (2020). https://doi.org/10.1108/MMMS-08-2019-0154

    Article  Google Scholar 

  22. M. Lamsaadi, M. Naimi, M. Hasnaoui, Natural convection of non-Newtonian power law fluids in a shallow horizontal rectangular cavity uniformly heated from below. Heat Mass Transf. 41, 239–249 (2005). https://doi.org/10.1007/s00231-004-0530-8

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Team of Modern and Applied Physics, Laboratory of Search in Physics and Science for Engineer, Polydisciplinary Faculty, Sultan Moulay Slimane University, B.P. 592, Béni-Mellal, Morocco

    T. Makayssi

  2. Team of Research in Renewable Energies and Technological Innovation, Laboratory of Search in Physics and Science for Engineer, Polydisciplinary Faculty, Sultan Moulay Slimane University, B.P. 592, Béni-Mellal, Morocco

    M. Lamsaadi

  3. Laboratory of Industrial Engineering and Surface Engineering, Faculty of Science and Technologies, Sultan Moulay Slimane University, B.P. 523, Béni-Mellal, Morocco

    M. Kaddiri & Y. Tizakast

Authors
  1. T. Makayssi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Lamsaadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Kaddiri
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Y. Tizakast
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. Makayssi.

Ethics declarations

Conflict of interest

The authors declare no competing financial interests.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Makayssi, T., Lamsaadi, M., Kaddiri, M. et al. Effect of an ascendant magnetic field on Rayleigh–Bénard convection for non-Newtonian power-law fluids in a horizontal rectangular cavity submitted to vertical temperature gradient. Eur. Phys. J. Plus 138, 650 (2023). https://doi.org/10.1140/epjp/s13360-023-04290-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-023-04290-w

Search

Navigation