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Rayleigh-Bénard convection: bounds on the Nusselt number / Rayleigh-Bénard Konvektion: Schranken an die Nusselt-Zahl

We examine the Rayleigh–Bénard convection as modelled by the Boussinesq equation. Our aim is at deriving bounds for the heat enhancement factor in the vertical direction, the Nusselt number, which reproduce physical scalings. In the first part of the dissertation, we examine the the simpler model when the acceleration of the fluid is neglected (Pr=∞) and prove the non-optimality of the temperature background field method by showing a lower bound for the Nusselt number associated to it. In the second part we consider the full model (Pr<∞) and we prove a new upper bound which improve the existing ones (for large Pr numbers) and catches a transition at Pr~Ra^(1/3).

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:15-qucosa-202241
Date28 April 2016
CreatorsNobili, Camilla
ContributorsUniversität Leipzig, Fakultät für Mathematik und Informatik, Professor Dr. Felix Otto, Professor Dr. Charles Doering
PublisherUniversitätsbibliothek Leipzig
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:doctoralThesis
Formatapplication/pdf

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