Steady Finite-Amplitude Rayleigh-Bénard-Taylor Convection of Newtonian Nanoliquid in a High-Porosity Medium

  • P. G. SiddheshwarEmail author
  • T. N. Sakshath
Conference paper
Part of the Trends in Mathematics book series (TM)


Two-dimensional, steady, finite-amplitude Rayleigh-Bénard-Taylor convection of a Newtonian nanoliquid-saturated porous medium is studied using rigid-rigid isothermal boundary condition. The nanoliquid is assumed to conform to a single-phase description and occupies a loosely packed porous medium. Critical Rayleigh number and Nusselt number as functions of various parameters are analyzed, and this is depicted graphically. A non-zero Taylor number demands a higher temperature difference between the horizontal boundaries compared to that of a zero Taylor number case in order to initiate instability in the system and thus inhibits advection of heat. The isothermal boundaries of the rigid-rigid type do not allow as much heat to pass through as that by the free-free type, and hence we see a reduced heat transfer situation in the former case.


Nanoliquid Rayleigh-Bénard convection Rotation Porous medium Linear Non-linear Stability Single-phase 



One of the authors (TNS) would like to thank the Department of Backward Classes Welfare, Government of Karnataka, for providing fellowship to carry out his research work. The authors would like to thank Bangalore University for their support.


  1. 1.
    Agarwal, S., Bhadauria, B. S., Siddheshwar, P. G.: Thermal instability of a nanofluid saturating a rotating anisotropic porous medium. Spec. Topics Rev. Porous Med. 2(1), 53–64 (2011).CrossRefGoogle Scholar
  2. 2.
    Balasubramanian, S., Ecke, R. E.: Experimental study of Rayleigh-Bénard convection in the presence of rotation. Int. J. Mater. Mech. Manuf. 1, 148–152 (2013).Google Scholar
  3. 3.
    Bhadauria, B. S., Agarwal, S.: Natural convection in a nanofluid saturated rotating porous layer: A nonlinear study. Transp. Porous Med. 87, 585–602 (2011).MathSciNetCrossRefGoogle Scholar
  4. 4.
    Busse, F. H.: Thermal Convection in rotating systems. Proc. US Natl. Congr. Appl. Mech. Amer. Soc. Mech. Eng. 299–305 (1982).Google Scholar
  5. 5.
    Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Stability. Clarendon Press, London (1961).zbMATHGoogle Scholar
  6. 6.
    Chandrasekhar, S., Reid, W. H.: On the expansion of functions which satisfy four boundary conditions. Proc. Natl. Acad. Sci. U. S. A. 43, 521–527 (1957).MathSciNetCrossRefGoogle Scholar
  7. 7.
    Desaive, T., Hennenberg, M., Lebon, G.: Thermal instability of a rotating saturated porous medium heated from below and submitted to rotation. The Eur. Phys. J. B. 29, 641–647 (2002).CrossRefGoogle Scholar
  8. 8.
    Lopez, J. M., Marques, F.: Centrifugal effects in rotating convection: nonlinear dynamics. J. Fluid Mech. 628, 269–297 (2009).MathSciNetCrossRefGoogle Scholar
  9. 9.
    Nagata, M.: Bifurcations at the Eckhaus points in two-dimensional Rayleigh-Bénard convection. Phys. Rev. E. 52, 6141–6145 (1995).MathSciNetCrossRefGoogle Scholar
  10. 10.
    Nield, D. A., Bejan, A.: Convection in Porous Media. Third Edition, Springer Science and Business Media, New York (2006).zbMATHGoogle Scholar
  11. 11.
    Riahi, D. H.: The effect of Coriolis force on nonlinear convection in a porous medium. Int. J. Math. Math. Sci. 17(3), 515–536 (1994).MathSciNetCrossRefGoogle Scholar
  12. 12.
    Siddheshwar, P. G., Meenakshi, N.: Amplitude equation and heat transport for Rayleigh-Bénard convection in Newtonian liquids with nanoparticles. Int. J. Appl. Comput. Math. 2, 1–22 (2015).CrossRefGoogle Scholar
  13. 13.
    Siddheshwar, P. G., Sakshath, T. N.: Rayleigh-Bénard convection of Newtonian nanoliquids in a saturated, rotating high porous medium. Math. Sci. Int. Res. J. 6(1), 35–38 (2017).Google Scholar
  14. 14.
    Siddheshwar, P. G., Sakshath, T. N.: Rayleigh-Bénard-Taylor convection of Newtonian nanoliquid. WASET. Int. J. Mech. Aero. Ind. Mech. Manuf. Eng. 11(6), 1131–1135 (2017).Google Scholar
  15. 15.
    Vadasz, P.: Coriolis effect on gravity-driven convection in a rotating porous layer heated from below. J. Fluid Mech. 376, 351–375 (1998).MathSciNetCrossRefGoogle Scholar
  16. 16.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsBangalore UniversityBangaloreIndia

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