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The Orr-Sommerfeld equation, modified to include viscoelastic effects, is solved asymptotically. The method of inner and outer expansions is used to determine the characteristic equation. The present results are found to be in fairly good agreement with the results obtained numerically by Chun and Schwarz. However, the present results do not agree with those obtained in an earlier asymptotic solution by Chan Man Fong and Walters. It is shown that the effect of the viscoelasticity is stabilizing.

journal of hydronautics

Stability of plane Poiseuille flows of viscoelastic liquids - An asymptotic solution (Plane Poiseuille viscoelastic liquids flow stability, using method of inner and outer expansions based on Chun and Schwarz asymptotic solution of Orr-Sommerfeld equation)