Title: On the validity of the Oberbeck-Boussinesq approximation in a tall differentially heated cavity with water

Authors: D. Kizildag; I. Rodriguez; J. Castro

Addresses: Centre Tecnològic de Transferència de Calor (CTTC), Universitat Politècnica de Catalunya (UPC), ETSEIAT, Colom 11, 08222, Terrassa, Barcelona, Spain. ' Centre Tecnològic de Transferència de Calor (CTTC), Universitat Politècnica de Catalunya (UPC), ETSEIAT, Colom 11, 08222, Terrassa, Barcelona, Spain. ' Centre Tecnològic de Transferència de Calor (CTTC), Universitat Politècnica de Catalunya (UPC), ETSEIAT, Colom 11, 08222, Terrassa, Barcelona, Spain

Abstract: In the present work, the validity of the Oberbeck-Boussinesq approximation for the resolution of fluid flow and heat transfer phenomena inside a differentially heated cavity filled with water (Pr = 3.44) is submitted to investigation. The cavity models, the integrated solar collector-storage element installed on an advanced façade. According to Gray and Giorgini (1976), the use of the Boussinesq approximation can be considered valid for variations of thermosphysical properties up to 10% with respect to the mean value. In the configuration under this study, there is a variation of about 17% in the dynamic viscosity and 15% in the thermal expansion coefficient. The significance of the Oberbeck-Boussinesq effects is studied comparatively by means of detailed direct numerical simulations (DNS). Numerical results reveal that for the conditions under study, important variations from the Oberbeck-Boussinesq conditions occur. These effects are observed as dissimilarities between boundary layers in hot and cold walls, and as a consequence on the local Nusselt number. In addition, there is a loss of symmetry in the flow within the cavity which is reflected in the temperature and velocity profiles.

Keywords: Boussinesq approximation; turbulent convection; natural convection; turbulence; direct numerical simulation; DNS; computational fluid dynamics; CFD; fluid flow; heat transfer; differentially heated cavities; solar collectors; solar storage; temperature profile; velocity profile.

DOI: 10.1504/PCFD.2012.048257

Progress in Computational Fluid Dynamics, An International Journal, 2012 Vol.12 No.4, pp.251 - 259

Published online: 30 Jul 2012 *

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