Unsteady Magnetohydrodynamic Flow of Second Grade Fluid due to Uniform Accelerating Plate

Abstract

New exact solutions for unsteady magnetohydrodynamic (MHD) flows of a generalized second-grade fluid due to uniform accelerating plate are derived. The generalized second-grade fluid saturates the porous space. Fractional derivative is used in the governing equation. The analytical expressions for velocity and shear stress fields are obtained by using Laplace transform technique for the fractional calculus. The obtained solutions are expressed in series form in terms of Fox H-functions. Similar solutions for ordinary second-grade fluid passing through a porous space are also recovered. Moreover, several figures are sketched for the pertinent parameters to analyze the characteristics of velocity field and shear stress.

Keywords

• MHD flow; Generalized second-grade fluid; Fractional derivatives; Fox H-functions; Discrete Laplace transform.