Thermal convection in superposed fluid and porous layers subjected to a plane Poiseuille flow

Abstract

Thermal convection in a two-layer system comprised by a fluid layer overlying a layer of porous media saturated with the same fluid has been investigated. The system is heated from below and subjected to a horizontally plane Poiseuille flow. The interaction between both instability mechanisms, the unstably stratification and the shear arising from the plane Poiseuille flow, is studied and a completely linear stability analysis has been carried out by considering both longitudinal rolls ͑LRs͒ and transverse rolls ͑TRs͒. It is found that the neutral curves of both modes may be bimodal, which is dependent on the depth ratio, the ratio of the depth of fluid layer to that of the porous layer. The stability characteristics of LRs are found to be invariant with the Reynolds number based on the horizontal Poiseuille velocity and the Prandtl number of the fluid, and the instability is always dominated by this mode if the Reynolds number is within low or moderate strength. The superimposed Poiseuille flow seems to exert a stabilizing effect on the traveling TRs and the critical transverse mode tends to be within the porous layer with low propagating speed. However, if the Reynolds number is sufficiently large, a shear instability mode appears abruptly with higher propagating speed and then dominates the system instability.

Global stability for thermal convection in a fluid overlying a highly porous material

“…Flow of a fluid overlying a porous medium saturated with the same liquid is encountered in a wide range of industrial and geophysical applications, and has consequently received much attention in the literature (see Nield 1977Nield , 1991Nield , 1998Chen & Chen 1988, 1992Chen 1990;Lu & Chen 1997;Das et al 2002;Discacciati et al 2002;Layton et al 2003;Miglio et al 2003;Chang 2004Chang , 2005Chang , 2006Riviere 2005;Chang et al 2006;Das & Lewis 2007;Hirata et al 2007;Hoppe et al 2007;Mu & Xu 2007;Hill & Straughan 2008;Straughan 2008).…”

Poiseuille flow in a fluid overlying a highly porous material

“…The reduction of d from 0.2 to 0.15 results in the disappearance of the local minimum associated with the porous mode. This means that the bimodal structure, which exists in all previous comparable stability studies [10,11,25,32], is no longer present. The structure of the neutral curves atd ¼ 0:15; 0:2; 0:3 suggest that they are composed of two intersecting curves.…”

Combined Effect of Magnetic field and Internal Heat Generation on the Onset of Marangoni Convection

“…Copious literature is available on coupled Benard-Marangoni convection in a horizontal ordinary viscous fluid layer with uniform distribution of internal heat generation (Char and Chiang [4], Wilson [8], Bachok and Arifin [9] and references therein). The problem of penetrative convection in an ordinary viscous fluid-saturated porous layer has also received considerable attention in the recent past because of its applications in many science and engineering problems (with current highly relevant literature including Carr [10], ), Gangadharaiah and Suma [14], ).…”