A Summary of New Predictive High Frequency Thermo-Vibrational Models in Porous Media

Abstract

In this paper, we consider the effect of mechanical vibration on the onset of convection in porous media. The porous medium is saturated either by a pure fluid or by a binary mixture. The importance of a transport model on stability diagrams is presented and discussed. The stability threshold for the Darcy-Brinkman case in the Ra T c -R and k c -R diagrams is presented (where Ra T c , k c and R are the critical Rayleigh number, the critical wave number and the vibration parameters, respectively). It is shown that there is a significant deviation from the Darcy model. In the thermo-solutal case with the Soret effect, the influence of vibration on the reduction of multi-cellular convection is emphasized. A new analytical relation for obtaining the threshold of mono-cellular convection is derived. This relation shows how the separation factor is related to the controlling parameters of the problem, = f (R, ε * , Le), when the wave number k → 0. The importance of vibrational parameter definition is highlighted and it is shown how, by using a proper definition for vibrational parameter, we may obtain compact relationship. It is also shown how this result may be used to increase component separation.

Study of Heat Transport in a Porous Medium Under G-jitter and Internal Heating Effects

“…Further, this leads to the appearance of a modified gravity, collinear with actual gravity, in the form of a time-periodic gravity field perturbation and is known as gravity modulation or G-jitter in literature. Some of the documented works on gravity modulation in recent times include Yang (1997), Malashetty and Padmavathi (1997), Rees and Pop (2000, 2001, 2003, Malashetty and Basavaraj (2002), Govender (2004Govender ( , 2005a, Kuznetsov (2005Kuznetsov ( , 2006a, Siddhavaram and Homsy (2006), Strong (2008a,b), Razi et al (2009), Purusothaman (2009), Vanishree (2010), Saravanan and Arunkumar (2010), Malashetty and Swamy (2011), and Sivakumar (2010, 2011), . However, most of the studies on thermal instability in a porous medium with gravity modulation concern only linear stability and hence address only questions on onset of convection.…”

Analytical and numerical stability analysis of Soret-driven convection in a horizontal porous layer: The effect of vertical vibrations

“…In some related studies in fluid media, Razi et al [11] showed that the asymptotic analysis results in a closed form relation for the stability threshold. In order to obtain such a relation, a regular perturbation method with the wave number as the small parameter is performed (for simplifying the procedure), we drop the tilde symbol and we expand (ψ , θ, η, ϕ , σ) as…”

Onset of Vibrational Convection in a Binary Fluid Saturated Non-Darcy Porous Layer Heated from Above

“…(19) and (20) are solved then to obtain the marginal curves of Ra T against α for S and SH modes respectively. Prior to that convergence of the continued fractions was verified numerically and the continued fractions were truncated once the desired precision (10 −4 ) is achieved.…”

“…A brief review of the findings related to the above subject have been given by Razi et. al [19]. Recently, Strong [20] brational thermosolutal convection in a horizontal Darcy porous layer and constructed the neutral curves for synchronous, subharmonic and quasiperiodic instability modes.…”