The Rayleigh–Stokes problem for an edge in a viscoelastic fluid with a fractional derivative model

Abstract

This paper investigates the exact analytic solutions for the Rayleigh–Stokes problem for an edge in a generalized Oldroyd-B fluid. This paper employs the fractional calculus approach to study the flows in an Oldroyd-B fluid. The velocity field corresponding to an incompressible generalized Oldroyd-B fluid with a fractional derivative model within an infinite edge is determined using Fourier sine and Laplace transforms. Two characteristic examples: (i) flow due to an impulsive motion of edge, and (ii) flow due to a uniformly accelerated edge are considered. The solutions that have been obtained reduce to the known solutions of an Oldroyd-B fluid by setting α = β = 1 . Moreover, the similar solutions for Maxwell and second grade fluids with fractional derivative models and those for the ordinary models appear as the limiting cases of the presented solutions.