Exact solutions for the unsteady rotational flow of non-Newtonian fluid in an annular pipe

This paper deals with some unsteady transient rotational flows of an Oldroyd-B fluid in an annular pipe. The fractional calculus approach in the constitutive relationship model of an Oldroyd-B fluid is introduced. A generalized Jeffreys model with the fractional calculus is built. Exact solutions for some unsteady rotational flows of an Oldroyd-B fluid in an annular pipe are obtained by using Hankel transform and the theory of Laplace transform for fractional calculus. The well known solutions for a Navier-Stokes fluid, as well as those corresponding to a Maxwell fluid and a second grade one, appear as limiting cases of our solutions.