On the validity of the Oberbeck-Boussinesq approximation in a tall differentially heated cavity with water
by D. Kizildag; I. Rodriguez; J. Castro
Progress in Computational Fluid Dynamics, An International Journal (PCFD), Vol. 12, No. 4, 2012

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.

Online publication date: Tue, 25-Nov-2014

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