Starting flows for a fractional Oldroyd-B fluid between two coaxial cylinders

Abstract

In In this article we have discussed some starting flows for fractional Oldroyd-B fluid between two coaxial cylinders. Firstly we have model the governing equation for unsteady rotational flow of the incompressible fluid of a generalized Oldroyd-B fluid in an annular pipe. And then we have formulate the two physical fluid flow problem between two coaxial cylinders namely; (i) the outer cylinder generates the effective oscillation in terms of harmony (ii) an the abrupt rotation of the outer cylinder with consistent speed. While the inner cylinder kept fixed for both the situation. Exact analytical solutions for these two types of flows are obtained in term of Mittag-Leffler function by using Webers’ and Laplace transforms for sequential fractional derivative. Moreover, the limiting cases of our solution correspond to the same solutions for Maxwell, Second grade and Newtonian fluid models performing the same motion.