Natural doubly diffusive convection with vibration

Abstract

We present a numerical and analytical study of doubly di usive convection driven by horizontal thermal and solutal gradients in square and rectangular enclosures with no-slip walls subjected to high-frequency vibration. The two vertical walls of the enclosure are maintained at di erent but uniform temperatures and concentrations while the horizontal walls are assumed to be impermeable and insulating. The resulting system is described by time-averaged Boussinesq equations. These equations possess a doubly di usive quasi-equilibrium solution provided the thermal and solutal buoyancy forces are equal and opposite. This solution is linearly stable up to a critical value of the stability parameter independently of the strength and orientation of the vibration. The solutions in the neighborhood of the bifurcation point are described analytically as a function of the strength and orientation of the vibration, and the larger amplitude states are computed numerically using a spectral collocation method. For vertical oscillation increasing the vibration amplitude decreases the subcriticality of the solutions and may even reverse it; the opposite occurs with horizontal vibration.

Chaotic Convection in a Porous Medium Under Temperature Modulation

“…12a. But, as for gravity modulation case these results are quite opposite given by Srivastava et al (2013), where modulated flows transport less heat than their corresponding unmodulated flows conform the results of Bar- (2000), Bardana et al (2001); Mojtabi et al (2004); Govender (2005Govender ( , 2006Govender ( , 2010; Gresho and Sani (1970); Davis (1976) and Bhadauria and Kiran (2015). The following relation can generalize the above Nu temperature modulation > Nu unmodulation > Nu gravity modulation…”

05/00906 Rayleigh Bénard convective instability of a fluid under high-frequency vibration

“…When the aspect ratio equals 8 or more, the character of the bifurcation is practically the same as in the limiting case of an infinitely long layer. The latter statement was confirmed by Khallouf et al [12], Liz ee [13], Bardan et al [14] for a binary mixture when they studied the non-linear regimes of two-dimensional thermovibrational convection in rectangular cavities subjected to a longitudinal temperature gradient and transversal axis of vibration. It was shown that the transition from a four-vortex regime to inversional symmetry took place at some critical value of Ra v .…”

“…The temporal integration, therefore, transforms the systems into a Helmholtz problem arising from Eq. (14) coupled to the Poisson problems (15), (16) with appropriate boundary conditions. Eqs.…”

“…where K is a constant which depends on G v [14]. For each value of G v , as Nu 2 ¼ KðGr À Gr c Þ, a simply extrapolation technique allows us to determine an accurate value of Gr c .…”

Averaging method and long-wave asymptotics in vibrational convection in layers with an interface

“…The effect of admixture presence was discovered as the result: vibrational thermoconcentrational convection in weightless conditions can occur at any vibrational angle. Averaged equations of binary-mixture convection were analyzed in [22], where the Soret effect was investigated; vibrational convection in a vertical layer [23][24][25], where linear stability analysis was done in the case of a rectangular stripe and the bifurcation points of the nonlinear problem were also calculated. The influence of high-frequency vibration on convection of miscible fluids was investigated in [26], where the results of the solutions of total and averaged systems were compared, and the value of the frequency, which corresponds to high-frequency asymptotics, was calculated.…”