Skip to main content
SpringerLink
Log in

The onset of double diffusive convection in a sparsely packed porous layer using a thermal non-equilibrium model

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

We examine the effect of local thermal non-equilibrium on double diffusive convection in a fluid-saturated sparsely packed porous layer heated from below and cooled from above, using both linear and nonlinear stability analyses. The Brinkman model is employed as the momentum equation. A two-field model that represents the fluid and solid phase temperature fields separately is used for the energy equation. The onset criterion for stationary, oscillatory and finite amplitude convection is derived analytically. It is found that a small inter-phase heat transfer coefficient has significant effect on the stability of the system. There is a competition between the processes of thermal and solute diffusion that causes the convection to set in through either oscillatory or finite amplitude mode rather than stationary. The effect of solute Rayleigh number, porosity modified conductivity ratio, Lewis number, ratio of diffusivities, Vadasz number and Darcy number on the stability of the system is investigated. The nonlinear theory based on the truncated representation of Fourier series method predicts the occurrence of subcritical instability in the form of finite amplitude motions. The effect of thermal non-equilibrium on heat and mass transfer is also brought out.

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. Nield D.A., Bejan A.: Convection in Porous Media, 3rd edn. Springer, New York (2006)

    Google Scholar 

  2. Trevisan O.V., Bejan A.: Combined heat and mass transfer by natural convection in a porous medium. Adv. Heat Transf. 20, 315–352 (1999)

    Google Scholar 

  3. Mojtabi A., Charrier-Mojtabi M.C.: Double-diffusive convection in porous media. In: Vafai, K. (eds) Handbook of Porous Media, pp. 559–603. Marcel Dekker, New York (2000)

    Google Scholar 

  4. Mojtabi A., Charrier-Mojtabi M.C.: Double-diffusive convection in porous media. In: Vafai, K. (eds) Handbook of Porous Media, 2nd edn, pp. 269–320. Taylor and Francis, New York (2005)

    Google Scholar 

  5. Mamou M.: Stability analysis of double—diffusive convection in porous enclosures. In: Ingham, D.B., Pop, I. (eds) Transport Phenomena in Porous Media II, pp. 113–154. Elsevier, Oxford (2002)

    Chapter  Google Scholar 

  6. Ingham, D.B., Pop, I. (eds): Transport Phenomena in Porous Media. Pergamon, Oxford (1998)

    MATH  Google Scholar 

  7. Ingham, D.B., Pop, I. (eds): Transport Phenomena in Porous Media vol. III. Elsevier, Oxford (2005)

    Google Scholar 

  8. Kuznetsov A.V., Vafai K.: Analytical comparison and criteria for heat and mass transfer models in metal hydride packed beds. Int. J. Heat Mass Transf. 38, 2873–2884 (1995)

    Article  Google Scholar 

  9. Kuznetsov A.V.: A perturbation solution for a non-thermal equilibrium fluid flow through a three-dimensional sensible storage packed bed. Trans. ASME J. Heat Transf. 118, 508–510 (1996)

    Article  Google Scholar 

  10. Vafai K., Amiri A.: Non-Darcian effects in combined forced convective flows. In: Ingham, D.B., Pop, I. (eds) Transport Phenomenon in Porous Media, pp. 313–329. Pergamon, Oxford (1998)

    Chapter  Google Scholar 

  11. Kuznetsov A.V.: Thermal non-equilibrium forced convection in porous Media. In: Ingham, D.B., Pop, I. (eds) Transport Phenomenon in Porous Media, pp. 103–130. Pergamon, Oxford (1998)

    Chapter  Google Scholar 

  12. Rees D.A.S., Pop I.: Local thermal non-equilibrium in porous medium convection. In: Ingham, D.B., Pop, I. (eds) Transport Phenomena in Porous Media, vol. III, pp. 147–173. Elsevier, Oxford (2005)

    Chapter  Google Scholar 

  13. Rees D.A.S., Pop I.: Vertical free convective boundary layer flow in a porous medium using a thermal non-equilibrium model. J. Porous Media 3, 31–44 (2000)

    MATH  Google Scholar 

  14. Rees D.A.S.: Vertical free convective boundary layer flow in a porous medium using a thermal non-equilibrium model: elliptic effects. J. Appl. Math. Phys. 54(3), 437–448 (2003)

    MATH  MathSciNet  Google Scholar 

  15. Banu N., Rees D.A.S.: Onset of Darcy–Benard convection using a thermal non-equilibrium model. Int. J. Heat Mass Transf. 45, 2221–2228 (2002)

    Article  MATH  Google Scholar 

  16. Postelnicu A., Rees D.A.S.: The onset of Darcy–Brinkman convection in a porous layer using a thermal nonequilibrium model-part I: stress-free boundaries. Int. J. Energy Res. 27(10), 961–973 (2003)

    Article  Google Scholar 

  17. Baytas A.C., Pop I.: Free convection in a square porous cavity using a thermal non-equilibrium model. Int. J. Thermal Sci. 41, 861–870 (2002)

    Article  Google Scholar 

  18. Baytas A.C.: Thermal non-equilibrium natural convection in a square enclosure filled with a heat-generating solid phase non-Darcy porous medium. Int. J. Energy Res. 27, 975–988 (2003)

    Article  Google Scholar 

  19. Baytas A.C.: Thermal non-equilibrium free convection in a cavity filled with a non-Darcy porous medium. In: Ingham, D.B., Bejan, A., Mamut, E., Pop, I. (eds) Emerging Technologies and Techniques in Porous Media, pp. 247–258. Kluwer, Dordrecht (2004)

    Google Scholar 

  20. Saeid N.H.: Analysis of mixed convection in a vertical porous layer using non-equilibrium model. Int. J. Heat Mass Transf. 47, 5619–5627 (2004)

    Article  MATH  Google Scholar 

  21. Malashetty M.S., Shivakumara I.S., Sridhar K.: The onset of Lapwood–Brinkman convection using a thermal non-equilibrium model. Int. J. Heat Mass Transf. 48, 1155–1163 (2005)

    Article  Google Scholar 

  22. Malashetty M.S., Shivakumara I.S., Sridhar K.: The onset of convection in an anisotropic porous layer using a thermal non-equilibrium model. Transp. Porous Media 60, 199–215 (2005)

    Article  Google Scholar 

  23. Straughan B.: Global non-linear stability in porous convection with a thermal non-equilibrium model. Proc. Roy. Soc. Lond. A 462, 409–418 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  24. Malashetty, M.S., Swamy, M., Heera, R.: Double diffusive convection in a porous layer using a thermal non-equilibrium model. Int. J. Thermal Sci. (2007). doi:10.1016/j.ijthermalsci.2007.07.015

  25. Vadasz P.: Explicit conditions for local thermal equilibrium in porous media heat conduction. Transp. Porous Media 59, 341–355 (2005)

    Article  Google Scholar 

  26. Horton C.W., Rogers F.T.: Convection currents in a porous medium. J. Appl. Phys. 16, 367–370 (1945)

    Article  MATH  MathSciNet  Google Scholar 

  27. Lapwood E.R.: Convection of a fluid in a porous medium. Proc. Camb. Philos. Soc. 44, 508–521 (1948)

    Article  MATH  MathSciNet  Google Scholar 

  28. Vadasz P.: Coriolis effect on gravity-driven convection in a rotating porous layer heated from below. J. Fluid Mech. 376, 351–375 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  29. Vadasz P., Olek S.: Weak turbulence and chaos for low Prandtl number gravity driven convection in a porous media. Transp. Porous Media 37, 69–91 (1999)

    Article  MathSciNet  Google Scholar 

  30. Vadasz P.: Local and global transitions to chaos hysteresis in porous layer heated from below. Transp. Porous Media 37, 213–245 (1999)

    Article  MathSciNet  Google Scholar 

  31. Vadasz P., Olek S.: Route to chaos for moderate prandtal number convection in a porous layer heated from below. Transp. Porous Media 41, 211–239 (2000)

    Article  Google Scholar 

  32. Vadasz P.: Heat transfer regimes and hysteresis in porous media convection. ASME J. Heat Transf. 123, 145–156 (2001)

    Article  Google Scholar 

  33. Rudraiah N., Srimani P.K., Friedrich R.: Finite amplitude convection in a two component fluid saturated porous layer. Int. J. Heat Mass Transf. 25, 715–722 (1982)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Gulbarga University, Jnana Ganga Campus, Gulbarga, 585 106, India

    M. S. Malashetty & Rajashekhar Heera

Authors
  1. M. S. Malashetty
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rajashekhar Heera
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. S. Malashetty.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Malashetty, M.S., Heera, R. The onset of double diffusive convection in a sparsely packed porous layer using a thermal non-equilibrium model. Acta Mech 204, 1–20 (2009). https://doi.org/10.1007/s00707-008-0036-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-008-0036-4

Keywords

Search

Navigation