On exact solutions for some oscillating motions of a generalized Oldroyd-B fluid |
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Authors: | M Khan Asia Anjum Haitao Qi and C Fetecau |
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Abstract: | This paper deals with exact solutions for some oscillating motions of a generalized Oldroyd-B fluid. The fractional calculus
approach is used in the constitutive relationship of fluid model. Analytical expressions for the velocity field and the corresponding
shear stress for flows due to oscillations of an infinite flat plate as well as those induced by an oscillating pressure gradient
are determined using Fourier sine and Laplace transforms. The obtained solutions are presented under integral and series forms
in terms of the Mittag–Leffler functions. For α = β = 1, our solutions tend to the similar solutions for ordinary Oldroyd-B fluid. A comparison between generalized and ordinary
Oldroyd-B fluids is shown by means of graphical illustrations. |
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