Abstract
The purpose of this work is to investigate the influence of the transverse walls on the onset of convection in a horizontal rectangular cavity of infinite length filled with a binary mixture when heated from below. For the first time we take into account the effect of the third dimension without making any approximation and considering realistic boundary conditions. In previous numerical works the width of the cell was either taken to be infinity (bulk mixtures) or different approximations usually valid in the narrow cell limit were assumed (i.e., Hele–Shaw and non-ideal Hele–Shaw approximations). The results we find show that the presence of the walls has a considerable effect on the onset of convection even for intermediate transverse aspect ratio cells. They also show that the approximations generally assumed fail to reproduce the correct behaviour of the critical parameters in an important range of aspect ratio values when the primary bifurcation is oscillatory. We have compared the critical values of the Rayleigh number and the frequency with those reported in the literature (Ohlsen et al. [1]) and we find a quantitative agreement within the experimental error.
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H.J.S. Fernando
PACS
47.20.Bp, 47.27.Te, 47.54.+r
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Alonso, A., Batiste, O. Onset of oscillatory binary fluid convection in three-dimensional cells. Theor. Comput. Fluid Dyn. 18, 239–249 (2004). https://doi.org/10.1007/s00162-004-0130-8
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DOI: https://doi.org/10.1007/s00162-004-0130-8