Stability Analysis of Plane Couette-Poiseuille Flow With Porous Walls Under Transverse Magnetic Field

Abstract

A linear stability analysis of a plane Couette-Poiseuille flow of an electrically conducting fluid with uniform cross-flow is investigated in the presence of a transverse magnetic field. The Chebyshev spectral collocation method is utilized to obtain eigenvalues of the modified classical Orr-Sommerfeld equation. The effect of cross-flow with its sense and transverse magnetic field on the stability are examined. The results show that crossflow acts to stabilize or destabilize the flow. The cross-flow's sense produces a significant influence on the stability. This effect becomes more important in the presence of a magnetic field. The dependence of the magnetic field's effect on the cross-flow's sense is also presented.

Dominant modes in hydromagnetic stability of channel flow with porous walls

“…In particular, they separated the effects of the velocity distribution from those of the magnitude of the velocity in the basic state, by using the maximal channel velocity of plane Poiseuille flow with the presence of a cross-flow as their characteristic velocity. Recently, Lamine and Hifdi [5] showed that the sense of the cross-flow has no effect on the stability of Poiseuille flow. In this paper, we extend the previous work [4] for an electrically conducting fluid to include the effect of a uniform external transverse magnetic field.…”