Boundary layer flow due to the vibration of a sphere. (English) Zbl 1449.76002

Sadiq, Muhammad Adil

J. Appl. Math. 2014, Article ID 191606, 14 p. (2014).

Summary: Boundary layer flow of the Newtonian fluid that is caused by the vibration of inner sphere while the outer sphere is at rest is calculated. Vishik-Lyusternik (Nayfeh refers to this method as the method of composite expansions) method is employed to construct an asymptotic expansion of the solution of the Navier-Stokes equations in the limit of high-frequency vibrations for Reynolds number of \(O(1)\). The effect of the Stokes drift of fluid particles is also considered.

MSC:

76A05	Non-Newtonian fluids
76D05	Navier-Stokes equations for incompressible viscous fluids
76D10	Boundary-layer theory, separation and reattachment, higher-order effects
76B99	Incompressible inviscid fluids

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