New Exact Solutions for Stokes First Problem of a Generalized Jeffreys Fluid in a Porous Half Space

Abstract

The fractional calculus approach has been taken into account in the Darcys law and the constitutive relationship of fluid model. Based on a modified Darcys law for a viscoelastic fluid, Stokes first problem is considered for a generalized Jeffreys fluid in a porous half space. By using the Fourier sine transform and the Laplace transform, two forms of exact solutions of Stokes first problem for a generalized Jeffreys fluid in the porous half space are obtained in term of generalized Mittag-Leffler function, and one of them is presented as the sum of the similar Newtonian solution and the corresponding non-Newtonian contributions. As the limiting cases, solutions of the Stokes first problem for the generalized second fluid, the fractional Maxwell fluid and the Newtonian fluid in the porous half space are also obtained.