Rayleigh-Bénard convection: bounds on the Nusselt number

Camilla Nobili

AutorIn

Camilla Nobili

Titel

Rayleigh-Bénard convection: bounds on the Nusselt number

Zitierfähige Url:

https://nbn-resolving.org/urn:nbn:de:bsz:15-qucosa-202241

Übersetzter Titel (DE)

Rayleigh-Bénard Konvektion: Schranken an die Nusselt-Zahl

Datum der Einreichung

20.04.2015

Datum der Verteidigung

11.09.2016

Abstract (EN)

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).

Freie Schlagwörter (EN)

Rayleigh–Bénard convection, fluid dynamics, Nusselt number, Stokes equation, Navier-Stokes equation, background field method, maximal regularity.

Klassifikation (DDC)

500

GutachterIn