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Modelling the influence of wall roughness on heat transfer in thermal convection

Published online by Cambridge University Press:  27 September 2011

Olga Shishkina  and
Claus Wagner
Olga Shishkina*
Affiliation:
DLR – Institute for Aerodynamics and Flow Technology, Bunsenstraße 10, 37073 Göttingen, Germany
Claus Wagner
Affiliation:
DLR – Institute for Aerodynamics and Flow Technology, Bunsenstraße 10, 37073 Göttingen, Germany
*
†Email address for correspondence: Olga.Shishkina@dlr.de
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Abstract

The objective of this study is to approximate heat transport in thermal convection enhanced by the roughness of heated/cooled horizontal plates. The roughness is introduced by a set of rectangular heated/cooled obstacles located at the corresponding plates. An analytical model to estimate the Nusselt number deviations caused by the wall roughness is developed. It is based on the two-dimensional Prandtl–Blasius boundary layer equations and therefore is valid for moderate Rayleigh numbers and regular wall roughness, for which the height of the obstacles and the distances between them are significantly larger than the thickness of the thermal boundary layers. To validate this model, the transport of heat and momentum in rectangular convection cells is studied in two-dimensional Navier–Stokes simulations, for different aspect ratios of the obstacles. It is found that the model predicts the heat transport with errors for all investigated cases.

JFM classification

Convection: Plumes/thermals Turbulent Flows: Turbulent convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 686 , 10 November 2011 , pp. 568 - 582
Copyright
Copyright © Cambridge University Press 2011

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