Stability of buoyancy opposed mixed convection in a vertical channel and its dependence on permeability

Abstract

Non-Darcy mixed convective flow of water due to external pressure gradient and buoyancy opposed forces are considered in a vertical channel filled with porous medium, which can be either isotropic or anisotropic. The linear theory of stability analysis has been used to numerically investigate the dependence of the transition behavior of the fully developed basic flow on the permeability of the medium. Numerical experiments indicate that mainly two main instability modes appear: Rayleigh–Taylor (R–T) and buoyant instability. For Darcy numbers ( Da) ⩽10 −9, R–T instability dominates within the entire Reynolds number ( Re) range considered here. It was also found that for the same Re, the fully developed base flow is highly unstable (stable) for porous media with high (low) permeability. Further, it was seen that the disturbance isotherm cells migrate from the channel walls toward the centerline when permeability is reduced. Reducing the permeability by one order of magnitude (corresponding to a decrease of Darcy number from 10 −6 to 10 −7) increases base flow stability approximately 20-fold. For higher Reynolds numbers, buoyant, mixed and shear instability of the basic flow were found when Da was increased from 10 −7 to 10 −3. However, for cases in which permeability and porosity behaved as suggested by Carman–Kozeny relation (CKR), buoyant stability was the only mode of instability. Critical values of the Rayleigh ( Ra) and Darcy ( Da) numbers in the R–T mode of instability were related to each other by the hyperbolic function RaDa = −2.465.