| Summary: | The dimensionless velocity field corresponding to the motion of an Oldroyd-B fluid between two infinite coaxial circular cylinders induced by the outer cylinder that rotates around its symmetry axis with an arbitrary time-dependent velocity is determined using the integral transforms technique. The corresponding solution for the motion through an infinite circular cylinder is obtained as a limiting case of the previous solution. It is used to generate exact solutions for the motion due to the cylinder that applies an arbitrary longitudinal shear stress to the fluid. Finally, for a check of results that have been obtained as well as to correct some results from the literature and to get some physical insight for oscillating motions, three special cases are considered and some known results are recovered as limiting cases. The required time after which the fluid moves according to the steady-state solutions is graphically determined for sine and cosine oscillating motions. Keywords: Rate type fluids, Unsteady unidirectional motions, General solutions, Cylindrical domains
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