Bound on vertical heat transport at large Prandtl number

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Bound on vertical heat transport at large Prandtl number

We prove a new upper bound on the vertical heat transport in Rayleigh-Bénard convection of the form c Ra 1 3 (lnRa) 2 3 under the assumption that the ratio of Prandtl number over Rayleigh number satisfies Pr Ra ≥ c0 where the non-dimensional constant c0 depends on the aspect ratio of the domain only. This new rigorous bound agrees with the (optimal) Ra 1 3 bound (modulo logarithmic correction) ...

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ژورنال

عنوان ژورنال: Physica D: Nonlinear Phenomena

سال: 2008

ISSN: 0167-2789

DOI: 10.1016/j.physd.2007.11.001