Bounds on Rayleigh-Benard convection with general thermal boundary conditions. Part 1. Fixed Biot number boundaries

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dc.creatorWittenberg, Ralf W.
dc.date2008-11-19
dc.date.accessioned2026-07-07T10:19:27Z
dc.date.available2026-07-07T10:19:27Z
dc.descriptionWe investigate the influence of the thermal properties of the boundaries in turbulent Rayleigh-Benard convection on analytical bounds on convective heat transport. Using the Doering-Constantin background flow method, we systematically formulate a bounding principle on the Nusselt-Rayleigh number relationship for general mixed thermal boundary conditions of constant Biot number ηwhich continuously interpolates between the previously studied fixed temperature ($η= 0$) and fixed flux ($η= \infty$) cases, and derive explicit asymptotic and rigorous bounds. Introducing a control parameter R as a measure of the driving which is in general different from the usual Rayleigh number Ra, we find that for each $η> 0$, as R increases the bound on the Nusselt number Nu approaches that for the fixed flux problem. Specifically, for $0 < η\leq \infty$ and for sufficiently large R ($R > R_s = O(η^{-2})$ for small η) the Nusselt number is bounded as $Nu \leq c(η) R^{1/3} \leq C Ra^{1/2}$, where C is an η-independent constant. In the $R \to \infty$ limit, the usual fixed temperature assumption is thus a singular limit of this general bounding problem.
dc.descriptionSubmitted
dc.identifierhttps://arxiv.org/abs/0811.3048
dc.identifierhttp://arxiv.org/abs/0811.3048
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/174513
dc.subjectFluid Dynamics
dc.titleBounds on Rayleigh-Benard convection with general thermal boundary conditions. Part 1. Fixed Biot number boundaries
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