a1 DLR – Institute for Aerodynamics and Flow Technology, Bunsenstraße 10, 37073 Göttingen, Germany
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.
(Received August 29 2010)
(Reviewed June 21 2011)
(Accepted August 15 2011)
(Online publication September 27 2011)