Slip Effects on Fractional Viscoelastic Fluids

Abstract

Unsteady flow of an incompressible Maxwell fluid with fractional derivative induced by a sudden moved plate has been studied, where the no-slip assumption between the wall and the fluid is no longer valid. The solutions obtained for the velocity field and shear stress, written in terms of Wright generalized hypergeometric functions ${}_p{\Psi }_q$, by using discrete Laplace transform of the sequential fractional derivatives, satisfy all imposed initial and boundary conditions. The no-slip contributions, that appeared in the general solutions, as expected, tend to zero when slip parameter is $\theta \to 0$. Furthermore, the solutions for ordinary Maxwell and Newtonian fluids, performing the same motion, are obtained as special cases of general solutions. The solutions for fractional and ordinary Maxwell fluid for no-slip condition also obtained as limiting cases, and they are equivalent to the previously known results. Finally, the influence of the material, slip, and the fractional parameters on the fluid motion as well as a comparison among fractional Maxwell, ordinary Maxwell, and Newtonian fluids is also discussed by graphical illustrations.