Influence of through flow on binary fluid convection

Abstract

The influence of an externally imposed lateral Poiseuille through flow on linear, nonlinear, and transient behavior of transverse convective rolls in a horizontal layer of binary fluids heated from below is investigated. The convective roll solutions are determined numerically for realistic boundary conditions with a many-mode Galerkin expansion as well as with a finite-difference method. Bifurcation diagrams of various quantities like Nusselt number, frequency, and mixing behavior are determined as functions of heating rate and wave number for several through flow rates and Soret coupling strengths for ethanol-water parameters. The growth dynamics of small convective perturbations into different, strongly nonlinear convective states and the transition between the latter is studied also.

Convective and absolute instabilities in Rayleigh–Bénard–Poiseuille mixed convection for viscoelastic fluids

“…From the phenomenological standpoint, there is a fairly close analogy between the RBP problem for viscoelastic fluids and for Newtonian binary fluid mixtures. Indeed, Jung et al (1996), Büchel & Lücke (2000a) and Hu et al (2007) carried out a spatio-temporal linear stability analysis of RBP flows with binary fluids taking into account the Soret effect. Moreover, the same problem has been addressed by Büchel & Lücke (2000b) and Hu et al (2009) through fully nonlinear two-dimensional numerical simulations initiated by a localized perturbation.…”

“…the RB convection of a viscoelastic fluid, to the RBP configuration as well as an extension of RBP problem of Newtonian fluids to viscoelastic fluids. From a phenomenological standpoint, there is a close analogy between the current problem and the RBP convection of a Newtonian binary mixture with Soret effects (Jung, Lücke & Büchel 1996;Büchel & Lücke 2000a;Hu, Ben Hadid & Henry 2007).…”

Linear onset of convective instability for Rayleigh-Bénard-Couette flows of viscoelastic fluids

“…The interaction between LRs and TRs in a flow through a rectangular channel heated from below was analyzed using a weakly nonlinear stability framework for both clear fluids [6] and in a porous medium [7] . Recently, there had been a renewed interest in RBP and RBC systems as prototype problems to understand convective and absolute instabilities [8][9][10][11] , viscous dissipation induced thermal instabilities [12,13] , binary fluid systems [14,15] as well as the influence of thermal stratification on transient growth [16] .…”

Harmonic mechanical excitations of steady convective instabilities: A means to get more uniform heat transfers in mixed convection flows?

“…As the Nusselt numbers (13) slightly oscillates in time, it is in addition averaged as is done in Eq. (14).…”

“…Very recently, Barletta and Nield [11] have analyzed the consequences of a uniform internal heat source on the thermal instability of the PRB mixed convection. Finally the stability of PRB flows in binary fluids, with and without Soret effect, is studied in [12][13][14][15] for instance.…”