Linear stability analysis of fluid flow between two parallel porous stationary plates with small suction and injection

TL;DR

This study investigates how small suction and injection at parallel porous plates influence the linear stability of viscous incompressible fluid flow, using a modified Orr-Sommerfeld equation solved numerically.

Contribution

It introduces a modified Orr-Sommerfeld equation incorporating suction Reynolds number and analyzes its impact on flow stability.

Findings

Small suction Reynolds number affects flow stability.

Numerical solutions reveal stability characteristics under suction and injection.

Modified equation provides new insights into porous flow stability.

Abstract

In this work, the linear stability of the viscous incompressible fluid flow between two parallel horizontal porous stationary plates with the assumption that there is a small constant suction at upper plate and a small constant injection at the lower plate is studied.The Navier-Stokes and continuous equations are reduced to an equation modified by the suction Reynolds number, which we call modified Orr-Sommerfeld equation. This equation is rewritten as an eigenvalue problem and is solved numerically using Matlab (Windows Version). The effect of small suction Reynolds number on the linear stability fluid flow is discussed.