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A model for near-wall dynamics in turbulent Rayleigh-Benard convection

Theerthan, Ananda S and Arakeri, Jaywant H (1998) A model for near-wall dynamics in turbulent Rayleigh-Benard convection. In: Journal of Fluid Mechanics, 373 . pp. 221-254.


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Experiments indicate that turbulent free convection over a horizontal surface (e.g. Rayleigh–Bénard convection) consists of essentially line plumes near the walls, at least for moderately high Rayleigh numbers. Based on this evidence, we propose here a two-dimensional model for near-wall dynamics in Rayleigh–Bénard convection and in general for convection over heated horizontal surfaces. The model proposes a periodic array of steady laminar two-dimensional plumes. A plume is fed on either side by boundary layers on the wall. The results from the model are obtained in two ways. One of the methods uses the similarity solution of Rotem & Classen (1969) for the boundary layer and the similarity solution of Fuji (1963) for the plume. We have derived expressions for mean temperature and temperature and velocity fluctuations near the wall. In the second approach, we compute the two-dimensional flow field in a two-dimensional rectangular open cavity. The number of plumes in the cavity depends on the length of the cavity. The plume spacing is determined from the critical length at which the number of plumes increases by one. The results for average plume spacing and the distribution of r.m.s. temperature and velocity fluctuations are shown to be in acceptable agreement with experimental results.

Item Type: Journal Article
Publication: Journal of Fluid Mechanics
Publisher: Cambridge University Press
Additional Information: Copyright for this article belongs to Cambridge University Press.
Department/Centre: Division of Mechanical Sciences > Mechanical Engineering
Date Deposited: 01 Sep 2004
Last Modified: 19 Sep 2010 04:14
URI: http://eprints.iisc.ac.in/id/eprint/1362

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