Linear Stabily analysis of hydromagnetic Couette flow with small injection/suction through the modified Orr-Sommerfeld equation

TL;DR

This study investigates how small injection/suction, magnetic field, permeability, and wave number influence the linear stability of viscous, electrically conducting fluid flow in a porous channel using a modified Orr-Sommerfeld equation.

Contribution

It introduces a novel analysis of flow stability considering multiple parameters through a modified Orr-Sommerfeld equation.

Findings

Small injection/suction affects flow stability.

Magnetic field influences the stability thresholds.

Permeability and wave number alter flow behavior.

Abstract

This paper analyses the effects of small injection/suction Reynolds number, Hartmann number, permeability parameter and wave number on a viscous incompressilbe electrically conduction fluid flow in a parallel porous channel. The plates of the channel with small constant injection/suction, have constant temperature. The upper plate is allowed to mouve in flow direction and the lower plate is kept at rest. A magnetic field of uniform strength is also applied normally to the plates what are parallel. The originality of the paper is to study the effect of the above parameter in temporal linear stabilty analysis of the flow throught the modified Orr-Sommerfeld equation.