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Rayleigh-Bénard convection
KTH, School of Engineering Sciences (SCI), Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics.
2011 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

This report considers Rayleigh-Bénard convection, i.e. the  ow between

two large parallel plates where the lower one is heated. The change in

density due to temperature variations gives rise to a  ow generated by

buoyancy. This motion is opposed by the viscous forces in the  uid.

The balance between these forces determines whether the  ow is stable

or not and the goal of this report is to nd a condition giving this limit

as well as analyzing other aspects of the  ow.

The starting point of the analysis is the incompressible Navier-

Stokes equations and the thermal energy equation upon which the

Boussinesq approximation is applied. Using linear stability analysis

a condition for the stability is obtained depending solely on a nondimensional

parameter, called the Rayleigh number, for a given wavenumber


. This result is conrmed to be accurate after comparison with

numerical simulations using a spectral technique.

Further non-linear two- and three-dimensional simulations are also

performed to analyze dierent aspects of the  ow for various values of

the Rayleigh number.

Place, publisher, year, edition, pages
2011. , 29 p.
National Category
Engineering and Technology
URN: urn:nbn:se:kth:diva-105486OAI: diva2:571135

Examensarbete inom teknisk fysik, grundnivå

Available from: 2012-11-21 Created: 2012-11-21 Last updated: 2013-02-25Bibliographically approved

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