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The Rayleigh-Bénard Convection System

  • Emily S. C. ChingEmail author
Chapter
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Abstract

The Rayleigh-Bénard convection system consists of a closed cell of fluid heated from below and cooled from above. We formulate the problem in this chapter. We first introduce the Oberbeck-Boussinesq approximation and derive the equations of motion under this approximation. The boundary conditions are then specified. The dimensionless parameters describing the state of fluid motion are defined. Furthermore, using the equations of motion, we derive two exact relations relating the heat transfer and the mean energy and thermal dissipation rates.

Keywords

Rayleigh-Bénard convection Oberbeck-Boussinesq approximation Rayleigh number Nusselt number Mean energy and Thermal dissipation rates 

References

  1. 1.
    L.D. Landau, E.M. Liftshitz, Fluid Mechanics (Pergamon Press, Oxford, London, 1987)Google Scholar
  2. 2.
    P. Manneville, Rayleigh-Bénard Convection: Thirty Years of Experimental, Theoretical, and Modeling Work, In Dynamics of Spatio-Temporal Cellular Structures: Henri Bénard Centenary Review (Springer Tracts in Modern Physics Vol. 207),(Eds.) by I. Mutabazi, J.E. Wesfreid, E. Guyon (Springer, New York, 2006), pp. 41–65Google Scholar
  3. 3.
    E.D. Siggia, High Rayleigh number convection. Annu. Rev. Fluid Mech. 26, 137–168 (1994)MathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Department of PhysicsThe Chinese University of Hong KongHong KongHong Kong SAR

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