Effect of property variation and modelling on convection in a fluid overlying a porous layer

Abstract

SUMMARYAn accurate computational analysis is presented for the onset of thermal convection in a two-layer system which is comprised of a saturated layer of porous material described by Darcy's law, over which lies a layer of the same saturating #uid. The two-layer system is heated from below and the upper (#uid) surface is allowed to be "xed or stress free. The onset of convection may have a bi-modal nature in which convection may be dominated by the porous medium or by the #uid depending on the depths of the relative layers, but this is strongly controlled by material parameters. The e!ect of variation of relevant #uid and porous material properties is investigated in detail, as is the e!ect of the interface boundary condition between the #uid and the porous medium.

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

“…In this paper, we allow our highly porous material to be a foametal, which is used extensively in industrial applications such as heat exchangers, chemical reactors and fluid filters. This material has well-documented values for its permeability and porosity (Straughan 2002;Goyeau et al 2003), which we will use in our analyses.…”

Poiseuille Flow of a Fluid Overlying a Porous Medium

“…We could omit the term ∂u b 3 /∂x γ on the left-hand side of (2.10) and this would amount to using a Beavers & Joseph (1967) boundary condition. Straughan (2002) found that the Jones and Beavers-Joseph boundary conditions led to almost the same numerical results. We believe this is true here and so employ the invariant condition (2.10).…”

“…These values have been chosen to be consistent with a porous-layer depth of 3 cm so that a direct comparison can be made with Chang et al (2006), and the experiments of Goharzadeh et al (2005). Although most of the results are derived for a small-scale porous medium, which is highly relevant to practical experimentation, § 3.3 studies length scales of up to 1 m in the context of geological and industrial applications (Straughan 2002;Nield & Bejan 2006). This is achieved by adopting realistic values for the permeabilities of soil and Foametal (which is used extensively in industrial applications such as heat exchangers, chemical reactors and fluid filters).…”

“…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.…”

Onset of surface tension driven convection in a fluid layer overlying a layer of an anisotropic porous medium

“…McKay [10] has considered the onset of buoyancy-driven convection in superposed reacting fluid and porous layers. Straughan [11,12] has studied a fundamental model for convection in a porous-fluid layer system developed originally by Nield [7]. He has obtained the eigenvalues and eigenfunctions numerically by utilizing the Chebyshev tau method.…”