Skip to main content
SpringerLink
Log in

Hydromagnetic Natural Convection from a Horizontal Porous Annulus with Heat Generation or Absorption

  • Published:
Journal of Engineering Physics and Thermophysics Aims and scope

This paper deals with a numerical study of free convection in a horizontal cylindrical annulus filled with a fluidsaturated porous medium in the presence of a transverse magnetic field and the heat generation or absorption effect. It is assumed that the inner and outer walls of the cylindrical annulus are maintained at constant temperatures Ti and To , respectively, as Ti > To . In addition to the heat equation, the model consists of the equation of motion under the Darcy law and Boussinesq approximation. The system of equations is solved numerically by the alternatingdirection implicit finite difference method. This investigation concerns the effects of the magnetic field inclination angle, Hartmann number, and the heat generation or absorption coefficient on heat transfer and the flow pattern. The results demonstrate that the heat transfer rate and flow regime depend mainly on the characteristics mentioned. The obtained data are presented graphically in terms of the streamlines and isotherms.

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

Similar content being viewed by others

References

  1. K. Vafai (Ed.), Handbook of Porous Media, 3rd edn., CRC Press (2015).

  2. D. A. Nield and A. Bejan, Convection in Porous Media, 5th edn., Springer (2017).

  3. S. Acharya and R. J. Golstein, Natural convection in an externally heated vertical or inclined square box containing internal energy sources, J. Heat Transf., 107, No. 4, 855–866 (1985).

    Article  Google Scholar 

  4. H. Ozoe and K. Okada, The effect of the direction of the external magnetic field on the three-dimensional natural convection in cubical enclosure, Int. J. Heat Mass Transf., 32, No. 10, 1939–1954 (1989).

    Article  Google Scholar 

  5. J. H. Lee and R. J. Goldstein, An experimental study on natural convection heat transfer in an inclined square enclosure containing internal energy sources, J. Heat Transf., 110, No. 2, 345–349 (1988).

    Article  Google Scholar 

  6. T. Fusegi, J. M. Hyun, and K. Kuwahara, Natural convection in a differentially heated square cavity with internal heat generation, Numer. Heat Transf., Part A, 21, No. 2, 215–229 (1992).

    Article  Google Scholar 

  7. M. Venkatachalappa and C. K. Subbaraya, Natural convection in a rectangular enclosure in the presence of a magnetic field with uniform heat flux from the side walls, Acta Mech., 96, 13–26 (1993).

    Article  Google Scholar 

  8. Y. M. Shim and J. M. Hyun, Transient confined natural convection with internal heat generation, Int. J. Heat Fluid Flow, 18, No. 3, 328–333 (1997).

    Article  Google Scholar 

  9. M. A. Hossain and M. Wilson, Natural convection flow in a fluid-saturated porous medium enclosed by non-isothermal walls with heat generation, Int. J. Therm. Sci., 41, No. 5, 447–454 (2002).

    Article  Google Scholar 

  10. N. G. Kafoussias, MHD free convection flow through a nonhomogeneous porous medium over an isothermal cone surface, Mech. Res. Commun., 19, No. 2, 89–94 (1992).

    Article  Google Scholar 

  11. T. K. Aldoss, M. A. Al-Nimr, M. A. Jarrah, and B. J. Al-Sha’er, Magnetohydrodynamic mixed convection from a vertical plate embedded in a porous medium, Numer. Heat Transf., Part A, 28, No. 5, 635–645 (1995).

    Article  Google Scholar 

  12. A. J. Chamkha, Non-Darcy hydromagnetic free convection from a cone and a wedge in porous medium, Int. Commun. Heat Mass Transf., 23, No. 6, 875–887 (1996).

    Article  MathSciNet  Google Scholar 

  13. M. Khan and H. Sardar, Heat generation/absorption and thermal radiation impacts on three-dimensional flow of Carreau fluid with convective heat transfer, J. Mol. Liq., 272, No. 15, 474–480 (2018).

    Article  Google Scholar 

  14. R. M. Kannan, B. Pullepu, and S. A. Shehzad, Numerical solutions of dissipative natural convective flow from a vertical cone with heat absorption, generation, MHD and radiated surface heat flux, Int. J. Appl. Comput. Math., 5, No. 1, 1–21 (2019).

    Article  MathSciNet  Google Scholar 

  15. D. D. Vo, Z. Shah, M. Sheikholeslami, A. Shafee, and T. K. Nguyen, Numerical investigation of MHD nanomaterial convective migration and heat transfer within a sinusoidal porous cavity, Phys. Scr., 94, No. 11, 115225 (2019).

    Article  Google Scholar 

  16. C. Revnic, T. Grosan, I. Pop, and D. B. Ingham, Magnetic field effect on the unsteady free convection flow in a square cavity filled with a porous medium with a constant heat generation, Int. J. Heat Mass Transf., 54, Nos. 9–10, 1734–1742 (2011).

    Article  Google Scholar 

  17. J. P. Garandet, T. Albussoiere, and R. Moreau, Buoyancy driven convection in a rectangular enclosure with a transverse magnetic field, Int. J. Heat Mass Transf., 35, No. 4, 741–748 (1992).

    Article  Google Scholar 

  18. S. Alchaar, P. Vasseur, and E. Bilgen, Natural convection heat transfer in a rectangular enclosure with a transverse magnetic field, J. Heat Transf., 117, No. 3, 668–673 (1995).

    Article  Google Scholar 

  19. J. P. Caltagirone, Thermoconvective instabilities in a porous medium bounded by two concentric horizontal cylinders, J. Fluid Mech., 76, No. 2, 337–362 (1976).

    Article  Google Scholar 

  20. H. H. Bau, Thermal convection in a horizontal, eccentric annulus containing a saturated porous medium — An extended perturbation expansion, Int. J. Heat Mass Transf., 27, No. 12, 2277–2287 (1984).

    Article  Google Scholar 

  21. Y. F. Rao, K. Fukuda, and S. Hasegawa, Steady and transient analyses of natural convection in a horizontal porous annulus with the Galerkin method, J. Heat Transf., 109, No. 4, 919–927 (1987).

    Article  Google Scholar 

  22. J. P. B. Mota, I. A. A. C. Esteves, C. A. M. Portugal, J. M. S. S. Esperanca, and E. Saatdjian, Natural convection heat transfer in horizontal eccentric elliptic annuli containing saturated porous media, Int. J. Heat Mass Transf., 43, No. 24, 4367–4379 (2000).

    Article  Google Scholar 

  23. Z. Alloui and P. Vasseur, Natural convection in a horizontal annular porous cavity saturated by a binary mixture, Comput. Therm. Sci., 3, No. 5, 407–417 (2011).

    Article  Google Scholar 

  24. M. A. Sheremet and I. Pop, Natural convection in a horizontal cylindrical annulus filled with a porous medium saturated by a nanofluid using Tiwari and Das’ nanofluid model, Eur. Phys. J. Plus, 130, No. 6, 107 (2015).

    Article  Google Scholar 

  25. M. C. Charrier-Mojtabi, Numerical simulation of two- and three-dimensional free convection flows in a horizontal porous annulus using a pressure and temperature formulation, Int. J. Heat Mass Transf., 40, No. 7, 1521–1533 (1997).

    Article  Google Scholar 

  26. K. Khanafer, A. Al-Amiri, and I. Pop, Numerical analysis of natural convection heat transfer in a horizontal annulus partially filled with a fluid-saturated porous substrate, Int. J. Heat Mass Transf., 51, Nos. 7–8, 1613–1627 (2008).

    Article  Google Scholar 

  27. M. A. Sheremet and I. Pop, Free convection in a porous horizontal cylindrical annulus with a nanofluid using Buongiorno’s model, Comput. Fluids, 118, No. 2, 182–190 (2015).

    Article  MathSciNet  Google Scholar 

  28. J. P. Barbosa Mota and E. Saatdjian, Natural convection in a porous horizontal cylindrical annulus, J. Heat Transf., 116, No. 3, 621–626 (1994).

    Article  Google Scholar 

  29. J. Belabid, K. Allali, and M. Belhaq, Convection in a horizontal porous annulus with quasi-periodic gravitational modulation, in: Topics in Nonlinear Mechanics and Physics, Springer, Singapore (2019).

    Book  Google Scholar 

  30. K. Himasekhar and H. H. Bau, Two-dimensional bifurcation phenomena in thermal convection in horizontal, concentric annuli containing saturated porous media, J. Fluid Mech., 187, 267–300 (1988).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of Mathematics and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, Po. Box 146, Mohammedia, Morocco

    J. Belabid

Authors
  1. J. Belabid
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Belabid.

Additional information

Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 94, No. 4, pp. 960–966, July–August, 2021.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Belabid, J. Hydromagnetic Natural Convection from a Horizontal Porous Annulus with Heat Generation or Absorption. J Eng Phys Thermophy 94, 934–941 (2021). https://doi.org/10.1007/s10891-021-02370-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10891-021-02370-1

Keywords

Search

Navigation