Unsteady flow of a generalized Maxwell fluid with fractional derivative due to a constantly accelerating plate

Abstract

The velocity field and the adequate shear stress corresponding to the unsteady flow of a generalized Maxwell fluid are determined using Fourier sine and Laplace transforms. They are presented as a sum of the Newtonian solutions and the corresponding non-Newtonian contributions. The similar solutions for Maxwell and Newtonian fluids, performing the same motion, are obtained as limiting cases of our general results. Graphical illustrations show that the velocity profiles corresponding to a generalized Maxwell fluid are going to that for an ordinary Maxwell fluid if α → 1 .