Geodesic
Exact solutions for a rotational flow of generalized second grade fluids through a circular cylinder
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2008), pp. 9-17 
Amir Mahmood; Saifullah; Qammar Rubab. Exact solutions for a rotational flow of generalized second grade fluids through a circular cylinder. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2008), pp. 9-17. http://geodesic.mathdoc.fr/item/BASM_2008_3_a1/
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     title = {Exact solutions for a~rotational flow of generalized second grade fluids through a~circular cylinder},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this note the velocity field and the associated tangential stress corresponding to the rotational flow of a generalized second grade fluid within an infinite circular cylinder are determined by means of the Laplace and Hankel transforms. At time $t=0$ the fluid is at rest and the motion is produced by the rotation of the cylinder, around its axis, with the angular velocity $\Omega t$. The velocity field and the adequate shear stress are presented under integral and series forms in terms of the generalized $G$-functions. Furthermore, they are presented as a sum between the Newtonian solutions and the adequate non-Newtonian contributions. The corresponding solutions for the ordinary second grade fluid and Newtonian fluid are obtained as particular cases of our solutions for $\beta=1$, respectively $\alpha=0$ and $\beta=1$.

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