Advertisement

Rayleigh–Bénard Convection

  • Antonio BarlettaEmail author
Chapter

Abstract

The onset of convection cells in a horizontal fluid layer heated from below is a classical phenomenon of thermally induced flow. The generally accepted denomination of this phenomenon is Rayleigh–Bénard convection. Its cause is the buoyancy force, so that the classification of this type of flow and heat transfer is natural convection. The well-known dynamics of the Rayleigh–Bénard convection is one where the fluid maintains its state of rest until the temperature difference between the lower and the upper boundaries of the fluid layer exceeds a critical value. In dimensionless terms, the parameter governing the onset of the cellular flow by exceeding a critical value is the Rayleigh number. This chapter will describe the theoretical foundations of this phenomenon in its different variants, as well as its extension to the domain of seepage flows in porous media.

References

  1. 1.
    Bénard HC (1901) Les tourbillons cellulaires dans une nappe liquide - Méthodes optiques d’observation et d’enregistrement. Journal de Physique Théorique et Appliquée 10:254–266CrossRefGoogle Scholar
  2. 2.
    Chandrasekhar S (1981) Hydrodynamic and hydromagnetic stability. Dover, New YorkGoogle Scholar
  3. 3.
    Drazin PG, Reid WH (2004) Hydrodynamic stability, 2nd edn. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  4. 4.
    Getling AV (1998) Rayleigh–Bénard convection: structures and dynamics. World Scientific, SingaporeCrossRefGoogle Scholar
  5. 5.
    Horton CW, Rogers FT Jr (1945) Convection currents in a porous medium. J Appl Phys 16:367–370MathSciNetCrossRefGoogle Scholar
  6. 6.
    Koschmieder EL (1993) Bénard cells and Taylor vortices. Cambridge University Press, CambridgezbMATHGoogle Scholar
  7. 7.
    Lapwood ER (1948) Convection of a fluid in a porous medium. Math. Proc. Camb. Philos. Soc. 44:508–521MathSciNetCrossRefGoogle Scholar
  8. 8.
    Mutabazi I, Wesfreid JE, Guyon E (2006) Dynamics of spatio-temporal cellular structures: Henri Bénard centenary review. Springer, New YorkCrossRefGoogle Scholar
  9. 9.
    Nield DA, Bejan A (2017) Convection in porous media, 5th edn. Springer, New YorkCrossRefGoogle Scholar
  10. 10.
    Normand C, Pomeau Y, Velarde MG (1977) Convective instability: a physicist’s approach. Rev Mod Phys 49:581–624MathSciNetCrossRefGoogle Scholar
  11. 11.
    Pearson JRA (1958) On convection cells induced by surface tension. J Fluid Mech 4:489–500CrossRefGoogle Scholar
  12. 12.
    Pellew A, Southwell RV (1940) On maintained convective motion in a fluid heated from below. Proc R Soc Lond A Math Phys Eng Sci 176:312–343MathSciNetzbMATHGoogle Scholar
  13. 13.
    Rayleigh L (1916) On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side. Lond Edinb Dublin Philos Mag J Sci 32:529–546CrossRefGoogle Scholar
  14. 14.
    Rees DAS (2000) The stability of Darcy–Bénard convection. In: Vafai K (ed) Handbook of porous media, vol 1. Marcel Dekker, New York, pp 521–588Google Scholar
  15. 15.
    Schmidt RJ, Milverton SW (1935) On the instability of a fluid when heated from below. Proc R Soc Lond Ser A Math Phys Sci 152(877):586–594Google Scholar
  16. 16.
    Tyvand PA (2002) Onset of Rayleigh–Bénard convection in porous bodies. In: Ingham DB, Pop I (eds) Transport Phenomena in porous media II, Pergamon Press, London, pp 82–112CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Industrial EngineeringAlma Mater Studiorum Università di BolognaBolognaItaly

Personalised recommendations