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Bounds on Rayleigh–Bénard convection with an imposed heat flux

Published online by Cambridge University Press:  13 December 2002

JESSE OTERO ,
RALF W. WITTENBERG ,
RODNEY A. WORTHING  and
CHARLES R. DOERING
JESSE OTERO
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA
RALF W. WITTENBERG
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA
RODNEY A. WORTHING
Affiliation:
Breasco LLC, Ann Arbor, MI 48197, USA
CHARLES R. DOERING
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA
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Abstract

We formulate a bounding principle for the heat transport in Rayleigh–Bénard convection with fixed heat flux through the boundaries. The heat transport, as measured by a conventional Nusselt number, is inversely proportional to the temperature drop across the layer and is bounded above according to Nu [les ] cRˆ1/3, where c < 0.42 is an absolute constant and Rˆ = αγβh4/(νκ) is the ‘effective’ Rayleigh number, the non-dimensional forcing scale set by the imposed heat flux κβ. The relation among the parameter Rˆ, the Nusselt number, and the conventional Rayleigh number defined in terms of the temperature drop across the layer, is NuRa = Rˆ, yielding the bound Nu [les ] c3/2Ra1/2.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 473 , 10 December 2002 , pp. 191 - 199
Copyright
© 2002 Cambridge University Press

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