Abstract
A linear stability analysis of a plane channel flow with porous walls under a uniform cross-flow and an external transverse magnetic field is explored. The physical problem is governed by a system of combined equations of the hydrodynamic and those of Maxwell. The perturbed problem of base state leads to a modified classical Orr-Sommerfeld equation which is solved numerically using the Chebyshev spectral collocation method. The combined effects of the cross-flow Reynolds number and the Hartmann number on the dangerous mode of hydromagnetic stability are investigated.The study shows that, the magnetic field tends to suppress the instability occurred by cross-flow. This stabilizing effect becomes perceptible when the magnetic field produces a mode transition from walls mode to that of the center.
Highlights
Stability analysis of flows between two porous plates has been considered as an active research area since its deep technological importance in several industrial applications: the biomedical industry, paper making, filtration systems, environmental engineering and aeronautics
An extension of previous works [2, 3], Fransson and Alfredsson [4] have made corrections to the problems discussed in [2, 3]. 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
We extend the previous work [4] for an electrically conducting fluid to include the effect of a uniform external transverse magnetic field
Summary
Stability analysis of flows between two porous plates has been considered as an active research area since its deep technological importance in several industrial applications: the biomedical industry, paper making, filtration systems, environmental engineering and aeronautics. Hains [2] and Sheppard [3] performed a linear stability analysis of the channel flow In these studies, the authors have shown that a modest amount of uniform injection/suction of the same fluid produced a significant increase in critical Reynolds number. We extend the previous work [4] for an electrically conducting fluid to include the effect of a uniform external transverse magnetic field. In this way, several investigations have been devoted to illustrate the effect of external magnetic field on the hydrodynamic stability of the channel.
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