Exact solutions of generalized Oldroyd-B fluid subject to a time-dependent shear stress in a pipe

The velocity field and the shear stress corresponding to the unsteady flow of a generalized Oldroyd-B fluid in an infinite circular cylinder subject to a longitudinal time-dependent shear stress are determined by means of Hankel and Laplace transforms. The exact solutions, written in terms of the generalized \(G\)-functions, satisfy all imposed initial and boundary conditions. The similar solutions for ordinary Oldroyd-B, ordinary and generalized Maxwell, ordinary and generalized second grade as well as for Newtonian fluids are obtained as limiting cases of our general solutions.