Exact Solutions For the Flow of A Generalized Second Grade Fluid Due To A Longitudinalquadratic Time-Dependent Shear Stress

The velocity field and the adequate shear stress, corresponding to the flow of a generalized second grade fluid in an annular region, due to a quadratic time-dependent shear stress,are determined by means of the laplace and the finite hankel transforms. the solutions that have been obtained satisfy both the governing equations and all imposed initial and boundary conditions. for (3 —>• 1 or (3 —>• 1 and a 0, the corresponding solutions fora second grade fluid, respectively, for the newtonian fluid, performing the same motion,are obtained from general solutions. finally, the influence of the material and fractional parameters on the shear stress as well as a comparison between models is drawn by graphicalillustrations.