Non-Isothermal Plane Couette Flow and Its Stability in an Anisotropic and Inhomogeneous Porous Layer Underlying a Fluid Layer Saturated by Water

Abstract

In this article, the linear stability of non-isothermal plane Couette flow (NPCF) in an anisotropic and inhomogeneous porous layer underlying a fluid layer is investigated. The Darcy model is utilized to describe the flow in the porous layer. The stability analysis indicates that the introduction of media-anisotropy (K∧ *) and media-inhomogeneity (in terms of inhomogeneity parameter, A) still renders the isothermal plane Couette flow (IPCF) in such superposed fluid-porous systems unconditionally stable. For NPCF, three different modes: unimodal (porous or fluid mode), bimodal (porous and fluid mode) and trimodal (porous, fluid and porous mode), are observed along the neutral stability curves, and characterized by the secondary flow patterns. It has been found that the instability of the fluid-porous system increases on increasing the media permeability and inhomogeneity along the vertical direction. Contrary to natural convection, at d ∧ = 0.2 (d ∧ = depth of fluid layer/depth of porous layer) and K∧ * = 1, in which the critical wavelength shows both increasing and decreasing characteristic with increasing values of A (0 = A = 5), here in the present study, the same continuously decreases with increasing values of A. Finally, scale analysis indicates that the onset of natural convection requires a relatively higher temperature difference (ΔT) between lower and upper plates in the presence of Couette flow. However, by including media anisotropy and inhomogeneity in the porous media, the system becomes unstable even for a small critical temperature difference of about 2°C.