Starting solutions for the motion of a second grade fluid due to longitudinal and torsional oscillations of a circular cylinder

The starting solutions corresponding to the motions of a second grade fluid due to the longitudinal and torsional oscillations of a circular cylinder are determined by means of the finite Hankel transforms. These solutions, presented as sum of the steady-state and transient solutions tend to those for a Navier–Stokes fluid as a limiting case. The steady-state solutions are also presented in simpler forms, in terms of the modified Bessel functions of the first and second kind.