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Stokes Flows of a Newtonian Fluid with Fractional Derivatives and Slip at the Wall
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Abstract
Stokes flows of a Newtonian fluid with fractional derivatives produced by the motion of a flat plate are analyzed under the slip condition at boundary. The plate motion is assumed to have a translation in its plane with a given velocity and the relative velocity between the velocity of the fluid at the wall and the speed of the wall is assumed to be proportional to the shear rate at the wall. The exact expressions for the velocity and the shear stress are determined by means of the Laplace transform. The velocity fields corresponding to both cases with slip and non-slip conditions, for fractional Newtonian and Newtonian fluids are obtained. The particular case, namely sine oscillations of the wall is studied. Results for fractional Newtonian fluids are compared with those of viscous Newtonian fluids in both cases of the flow with slip and non-slip conditions. In addition the influence of the slip coefficient on the relative velocity is studied.
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