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Exact solution for the rotational flow of a generalized second-grade fluid in a circular cylinder. (English) Zbl 1269.76014
Summary: This paper deals with the rotational flow of a generalized second grade fluid, within a circular cylinder, due to a torsional shear stress. The fractional calculus approach in the constitutive relationship model of a second grade fluid is introduced. The velocity field and the resulting shear stress are determined by means of the Laplace and finite Hankel transforms to satisfy all imposed initial and boundary conditions. The solutions corresponding to second grade fluids as well as those for Newtonian fluids are obtained as limiting cases of our general solutions. The influence of the fractional coefficient on the velocity of the fluid is also analyzed by graphical illustrations.

MSC:
76A05 Non-Newtonian fluids
76U05 General theory of rotating fluids
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