Bounds on Rayleigh–Bénard convection with an imposed heat flux

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 N...

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Bibliographic Details
Published in:Journal of fluid mechanics 2002-12, Vol.473, p.191-199
Main Authors: OTERO, JESSE, WITTENBERG, RALF W., WORTHING, RODNEY A., DOERING, CHARLES R.
Format: Article
Language:English
Subjects:
Buoyancy-driven instability
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Hydrodynamic stability
Physics
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Summary: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.
ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112002002410