Buoyant viscoelastic flow instability in a vertical anisotropic porous slab

The instability of a buoyancy-driven parallel flow of an Oldroyd-B fluid saturating a vertical anisotropic porous layer with impermeable isothermal boundaries is investigated. The anisotropy in both permeability and thermal diffusivity is considered with their principal directions aligned with the horizontal and vertical coordinate axes. An extended form of Darcy's law is utilized to implement the Oldroyd-B rheological model for the flow in the porous medium. The linear stability of the basic flow is analysed by testing the fate of normal modes of perturbation through the numerical solution of the resulting differential eigenvalue problem. The neutral stability curves and the instability thresholds are obtained for various values of anisotropic and viscoelastic parameters. The results reveal that the mechanical and thermal anisotropy parameters play contrasting roles on the onset of instability, while the relaxation and retardation viscoelastic parameters likewise act in opposite ways. The transition curves defining the stability boundary in the viscoelastic parameters plane are presented for isotropic and anisotropic cases. The results of Newtonian and Maxwellian fluids are retrieved as particular cases from the present study and showed that the instability is not possible for Newtonian fluids.