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Numerical study of two-dimensional thermovibrational convection in rectangular cavities

Abstract : Two-dimensional thermovibrational convection in rectangular cavities under the condition of weightlessness is studied. The problem is based on the system of equations of the mean fields of velocity, pressure, and temperature. A pseudospeetral Chebyshev collocation method is used. The case of rectangular cavities (a layer of finite length) is considered subject to high-frequency transversal vibrations and a longitudinal temperature gradient. In the case of a square cavity the instability of the main flow exists, and the bifurcation to other symmetry takes place. The same behavior is observed when the cavity is elongated in the direction of the temperature gradient. It is shown that the intensity of the thermovibrational convective flow decreases, in general, while the aspect ratio increases in accordance with linear stability theory, in which it was proven that, in the limiting case of an infinitely long layer subject to a longitudinal temperature gradient and a transversal axis of vibrations, the absolute stability of the quasi-equilibrium state lakes place.
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Hicham Khallouf, Grigori Z. Gershuni, Abdelkader Mojtabi. Numerical study of two-dimensional thermovibrational convection in rectangular cavities. Numerical Heat Transfer, Part A Applications, Taylor & Francis, 1995, 27 (3), pp.297-305. ⟨10.1080/10407789508913701⟩. ⟨hal-01946086⟩

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