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Zbl 1167.76311
Wang, Shaowei; Xu, Mingyu
Axial couette flow of two kinds of fractional viscoelastic fluids in an annulus. (English)
[J] Nonlinear Anal., Real World Appl. 10, No. 2, 1087-1096 (2009). ISSN 1468-1218

Summary: This paper deals with the unsteady axial Couette flow of fractional second grade fluid (FSGF) and fractional Maxwell fluid (FMF) between two infinitely long concentric circular cylinders. With the help of integral transforms (Laplace transform and Weber transform), generalized Mittag-Leffler function and H-Fox function, we get the analytical solutions of the models. Then we discuss the exact solutions and find some results which have been known as special cases of our solutions. Finally, we analyze the effects of the fractional derivative on the models by using the numerical results and find that the oscillation exists in the velocity field of FMF.

MSC 2000:: *76A10 Viscoelastic fluids

Keywords: analytical solutions; fractional second grade fluid; fractional Maxwell fluid; fractional calculus

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