Springer Nature is making SARS-CoV-2 and COVID-19 research free View research | View latest news | Sign up for updates

Onset of Rayleigh-Bénard convection in gases - classical and extended thermodynamics

  • 48 Accesses

  • 2 Citations

Abstract.

This paper deals with the determination of the critical parameters that induce instability in the Rayleigh-Bénard arrangement, viz. a gas confined between two rigid plates and heated from below. In order to compute the critical values of the parameters, classical thermodynamics with the Navier-Stokes and Fourier constitutive relations and extended thermodynamics with thirteen moments are used. Linear stability analysis is performed. The results of both theories are illustrated and compared.

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

References

  1. 1

    Lord Rayleigh: On convective currents in a horizontal layer of fluid when the higher temperature is on the under side. Philos. Mag. 32, 529-546 (1916)

  2. 2

    Chandrasekar, S.: Hydrodynamic and Hydromagnetic Stability, Oxford University Press Oxford (1961)

  3. 3

    Müller, I., Ruggeri, T.: Extended Thermodynamics. Springer Tracts in Natural Philosophy, Vol. 37, New York (1993)

  4. 4

    Müller, I., Ruggeri, T.: Rational Extended Thermodynamics (2nd edn.) Springer Tracts in Natural Philosophy, Vol. 37, New York (1998)

  5. 5

    Grad, H.: Principles of the kinetic theory of gases. Handbuch der Physik, Vol. XII, Springer Heidelberg (1958)

  6. 6

    Below, S.Ya., Vladimirov, V.A.: On the analogues and generalizations of Squire’s theorem. PMM U.S.S.R. 52, 314-319 (1987)

  7. 7

    Jeng, J., Hassard. B.: The critical wave number for the planar Bénard problem is unique. Int. J. Nonlinear Mech. 34, 221-229 (1999)

  8. 8

    Bormann, A.: The onset of convection in the Rayleigh-Bé nard problem for compressible fluids. Continuum. Mech. Thermodyn. 13, 9-23 (2001)

  9. 9

    Barbera, E.: Tesi di dottorato. Universitá di Messina (1999)

Download references

Author information

Correspondence to E. Barbera.

Additional information

Received: 26 August 2003, Accepted: 1 September 2003, Published online: 5 December 2003

Communicated by I. Müller

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Barbera, E. Onset of Rayleigh-Bénard convection in gases - classical and extended thermodynamics. Continuum Mech. Thermodyn. 16, 337–346 (2004). https://doi.org/10.1007/s00161-003-0155-z

Download citation

Keywords:

  • Extended thermodynamics
  • Bénard convection
  • thermal instability