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Zbl 1202.76017
Qi, Haitao; Xu, Mingyu
Stokes' first problem for a viscoelastic fluid with the generalized Oldroyd-B model. (English)
[J] Acta Mech. Sin. 23, No. 5, 463-469 (2007). ISSN 0567-7718; ISSN 1614-3116/e

Summary: The flow near a wall suddenly set in motion for a viscoelastic fluid with the generalized Oldroyd-B model is studied. The fractional calculus approach is used in the constitutive relationship of fluid model. Exact analytical solutions of velocity and stress are obtained by using the discrete Laplace transform of the sequential fractional derivative and the Fox $H$-function. The obtained results indicate that some well known solutions for the Newtonian fluid, the generalized second grade fluid as well as the ordinary Oldroyd-B fluid, as limiting cases, are included in our solutions.

MSC 2000:: *76A10 Viscoelastic fluids

Keywords: generalized Oldroyd-B fluid; Stokes' first problem; fractional calculus; exact solution; fox $H$-function

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