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Fluids 2017, 2(4), 66;

Relative Effects of Asymmetry and Wall Slip on the Stability of Plane Channel Flow

NPCU, Faculty of Sciences, Université Libre de Bruxelles, 1050 Bruxelles, Belgium
Department of Mathematics, SRM Research Institute, SRM University, Tamil Nadu 603203, India
Received: 6 October 2017 / Revised: 10 November 2017 / Accepted: 27 November 2017 / Published: 1 December 2017
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The effect of wall velocity slip on the stability of a pressure-driven two-dimensional asymmetric channel flow is examined by considering Navier slip condition on the channel walls. The two-parameter families of mean velocity profiles are considered to approximate the underlying asymmetric basic flow. Competing effects of skewness and maximum velocity on the stability of the flow are explored for a range of model parameters. The Orr–Sommerfeld system of the asymmetric flow is solved using a Chebyshev spectral collocation method for both symmetric and non-symmetric type slip boundary conditions. Numerical results indicate that moderate asymmetry in the basic flow has a significant role on the stability of the Poiseuille-kind parallel/nearly parallel flows. Wall slip shows a passive control on the instability of the asymmetric flow by increasing or decreasing the critical Reynolds number and the set of unstable wave numbers. The stabilizing/destabilizing effect of slip velocity on the flow instability is weak or strong depending on the presence of velocity slip at the upper or lower wall. Velocity slip has a profound grip on the flow behaviour by changing the shear rate inside the perturbed flow. View Full-Text
Keywords: channel flow; asymmetric flow; linear stability analysis; velocity slip channel flow; asymmetric flow; linear stability analysis; velocity slip

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Ghosh, S. Relative Effects of Asymmetry and Wall Slip on the Stability of Plane Channel Flow. Fluids 2017, 2, 66.

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