New exact analytical solutions for Stokes' first problem of Maxwell fluid with fractional derivative approach

The unsteady flow of an incompressible Maxwell fluid with fractional derivative induced by a sudden moved plate has been studied using Fourier sine and Laplace transforms. The obtained solutions for the velocity field and shear stress, written in terms of generalized G functions, are presented as sum of the similar Newtonian solutions and the corresponding non-Newtonian contributions. The non-Newtonian contributions, as expected, tend to zero for lambda -> 0. Furthermore, the solutions for ordinary Maxwell fluid, performing the same motion, are obtained as limiting cases of general solutions and verified by comparison with previously known results. Finally, the influence of the material and the fractional parameters on the fluid motion, as well as a comparison among fractional Maxwell, ordinary Maxwell and Newtonian fluids is also analyzed by graphical illustrations. (C) 2011 Elsevier Ltd. All rights reserved.