On the Unsteady Linearly Accelerating Flow of a Fractional Second Grade Fluid Through a Circular Cylinder

In this paper we obtain the velocity field and the adequate shear stress corresponding to the un- steady flow of a second grade fluid with fractional calculus due to a linearly accelerating circular cylinder, by means of the finite Hankel and Laplace transforms. The solutions that have been obtained satisfy both the governing equations and all imposed initial and boundary conditions. For �� → 1 and for �� → 1 and �� 1 → 0, the corresponding solutions for a second grade fluid, respectively, for the Newtonian fluid, performing the same motion, are obtained from our general solutions. Finally, the influences of the pertinent parameters on the fluid motion, as well as a comparison between models, is underlined by graphical illustrations.