Some accelerated flows for a generalized Oldroyd-B fluid

Abstract

In this paper, we construct the exact solutions for the accelerated flows of a generalized Oldroyd-B fluid. The fractional calculus approach is used in the constitutive relationship of a viscoelastic fluid. The velocity field and the adequate tangential stress that is induced by the flow due to constantly accelerating plate and flow due to variable accelerating plate are determined by means of discrete Laplace transform. In the special cases when α = β = 1 , as it was to be expected, our solutions tend to the similar solutions for an Oldroyd-B fluid. Moreover, the corresponding solutions for a Maxwell, second grade and Newtonian fluids appear as the limiting cases of the presented results.