  In this note the velocity field and the associated tangential stress
corresponding to the rotational flows 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 $\beta =
1$.
