Exact solutions for the flow of a generalized second grade fluid due to a longitudinal quadratic time-dependent shear stress

The velocity ¯eld and the adequate shear stress, corresponding to the °ow of a generalized second grade °uid in an annular region, due to a quadratic time-dependent shear stress, are determined by means of the Laplace and the ¯nite Hankel transforms. The solutions that have been obtained satisfy both the governing equations and all imposed initial and boundary conditions. For b ! 1 or ¯ ! 1 and ®1 ! 0, the cor- responding solutions for a second grade °uid, respectively, for the Newtonian °uid, performing the same motion, are obtained from general solutions. Finally, the in°uence of the material and fractional parameters on the shear stress as well as a comparison between models is drawn by graphical illustrations