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

Abstract

Thermal convection in a two-layer system with the presence of a plane Couette flow is investigated. The system comprises a fluid layer overlying a porous layer saturated with the same fluid and the lower plate is maintained warmer than the upper. A shear is generated by moving the upper wall horizontally at a constant speed. Both convection modes including longitudinal and transverse rolls are considered. Numerical results show that the neutral curves of both modes may be bimodal which depends on the depth ratio ͑i.e., the ratio of the depth of fluid layer to that of porous layer͒. The longitudinal rolls are always preferred at the onset of convection and the stability of this mode is independent of Reynolds and Prandtl numbers. But the transverse rolls may have the same stability as the longitudinal rolls when Reynolds number or Prandtl number approaches zero. Either increase of Reynolds number or Prandtl number raises its stability, and both produce the same effects on the stability behaviors of transverse rolls and the critical convection mode of transverse rolls tends to be within the porous layer with long wavelength.

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 of a Fluid Overlying a Porous Medium

“…Nield 1977Nield , 1983Nield , 1991Nield , 1998Chen & Chen 1988;Straughan 2002;Carr & Straughan 2003;Carr 2004;Chang 2005Chang , 2006Nield & Bejan 2006;Hirata et al 2007). A key finding was made by Chen & Chen (1988) who employed a Navier-Stokes fluid overlying a Darcy porous medium and discovered that the linear instability curves for the onset of thermal convection may be bi-modal.…”

A thermo-mechanical model for flows in superposed porous and fluid layers with interphasial heat and mass exchange

“…Therefore, a single equation, describing the energy balance of the mixture, is needed to determine the temperature inside the porous region (one-equation model). Within this context, various authors have studied the stability of thermal convection in superposed fluid and porous layers; see, for example, [22][23][24][25][26][27][28][29][30][31][32][33] and references therein. More recently, the authors of [34] presented Reynolds-averaged simulations for statistically stationary turbulent heat transfer in such domains.…”