A New Approach for the Stability Analysis in Hydromagnetic Couette Flow

Abstract

This paper analyses the effects of small injection/suction Reynolds number, Hartmann parameter, permeability parameter and wave number on a viscous incompressible electrically conducting fluid flow in a parallel porous plates forming a channel. The plates of the channel are parallel with the same constant temperature and subjected to a small injection/suction. The upper plate is allowed to move in flow direction and the lower plate is kept at rest. A uniform magnetic field is applied perpendicularly to the plates. The main objective of the paper is to study the effect of the above parameters on temporal linear stability analysis of the flow with a new approach based on modified Orr-Sommerfeld equation. It is obtained that the permeability parameter, the Hartmann parameter and the wave number contribute to the linear temporal stability while the small injection/suction Reynolds number has a negligible effect on the stability.