Stability of porous-Poiseuille flow with uniform vertical throughflow: High accurate solution

This paper investigates the influence of a uniform vertical throughflow on the stability of Poiseuille flow in a Newtonian fluid-saturated Brinkman porous medium. The solution to the stability eigenvalue problem is obtained numerically using the Chebyshev collocation and the Galerkin methods. The vertical throughflow, irrespective of its direction, imparts an identical stabilizing/destabilizing effect on the fluid flow. The throughflow dependent Reynolds number RT instills both stabilizing and destabilizing effects in a fluid saturated channel of porous medium and the range of RT up to which the system gets destabilized increases with increasing porous parameter. The results for the clear fluid case are also obtained as a particular case from the present study, and contrary to the porous case, throughflow always displays a stabilizing effect. Moreover, the numerical solutions presented will be useful for checking the performance and accuracy of any numerical methodologies.