Instability of Poiseuille Flow of Viscoelastic Fluids in a Porous Medium of Brinkman-Darcy-Kelvin-Voigt Type with Slip Effect

Abstract

This study delves into the temporal instability of Poiseuille flow of fluids within a porous medium, focusing on a fluid characterised by Brinkman-Darcy-Kelvin-Voigt viscoelastic properties. In particular, the effect of slip boundary conditions on linear instability is studied. To investigate the flow's instability, a numerical analysis of the stability eigenvalue problem is conducted. This involves linearising the equations that govern perturbations and extending Squire's theorem suitably to justify focusing solely on the stability equations for two-dimensional perturbations. In order to find the instability thresholds, the stability eigenvalue issue is numerically solved. Two Chebyshev collocation methods (CCM) are employed to approximate the eigenvalue system in conjunction with the QZ algorithm. Critical Reynolds number Rec, critical wavenumber ac, and critical wave speed cc are computed by this technique, illustrating their dependency on the Darcy number M and the Kelvin-Voigt parameter η.