Stability of fluid flow in a porous medium with uniform cross-flow and velocity slip

Abstract

This work examines the evolution of small perturbations in a plane Poiseuille flow through a porous medium bounded by porous walls implemented with the Brinkman flow model. The effect of uniform cross-flow across the channel along with slip imposed on the channel walls is examined for the associated fluid flow. The modified Orr–Sommerfeld equation for the flow system under consideration is derived and then solved numerically using Chebyshev spectral collocation method. The acquired sufficient conditions ensure that fluid motion will remain stable even when the flow system is widely perturbed. The linear stability characteristics and the onset of instability is discussed for a wide range of cross-flow Reynolds number, slip length and porosity parameter. The above mentioned flow parameters have a significant stabilizing effect on the fluid flow that is depicted with neutral stability curves, growth rate dispersion curves and eigenspectrums. Asymmetric slip allows the critical Reynolds number to increase rapidly when the upper channel wall experiences more slip than the lower.