Analytical Solution for the Flow of a Generalized Oldroyd-B Fluid in a Circular Cylinder

The tangential stress and velocity field corresponding to the flow of a generalized Oldroyd-B fluid in an infinite circular cylinder will be determined by mean of Laplace and finite Hankel transform. The motion is produced by the cylinder, that after t = 0 + , begins to rotate about its axis, under the action of oscillating shear stress Ω R sin ( ω t ) given on boundary. The solutions are based on an important remark regarding the governing equation for the non- trivial shear stress. The solutions that have been obtained satisfy all imposed initial and boundary conditions. The obtained solution will be presented under series form in term of generalized G-function. The similar solutions for the ordinary Oldroyd-B fluid, Maxwell, ordinary Maxwell and Newtonian fluids performing the same motion will be obtained as special cases of our general solutions.