Exact solution for the rotational flow of a generalized second grade fluid in a circular cylinder

This paper deals with the rotational flow of a generalizedsecond grade fluid, within a circular cylinder, due toa torsional shear stress. The fractional calculus approach inthe constitutive relationship model of a second grade fluid isintroduced. The velocity field and the resulting shear stressare determined by means of the Laplace and finite Hankeltransforms to satisfy all imposed initial and boundary conditions.The solutions corresponding to second grade fluids aswell as those for Newtonian fluids are obtained as limitingcases of our general solutions. The influence of the fractionalcoefficient on the velocity of the fluid is also analyzed bygraphical illustrations.