MATEC Web Conf.
Volume 286, 201914th Congress of Mechanics (CMM2019)
|Number of page(s)||3|
|Section||Fluid Mechanics, Rheology, Modeling, Instabilities and Transition|
|Published online||14 August 2019|
Dominant modes in hydromagnetic stability of channel flow with porous walls
Laboratory of Mechanics, Faculty of Sciences Aïn-Chock, University Hassan II , Casablanca, Morocco
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.
Key words: Dominant modes / cross-flow / magnetic field / porous walls / hydromagnetic stability / Spectral method.
© The Authors, published by EDP Sciences, 2019
This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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