Slip Effects in the Hydromagnetic Flow of a Viscoelastic Fluid Through Porous Medium Over a Porous Oscillatory Stretching Sheet

The hydromagnetic flow of a viscoelastic second-grade fluid through porous medium over a porous oscillatory stretching sheet is considered. It is assumed that the sheet is oscillating back and forth in its own plane and is stretched linearly in the x direction. The similarity of flow is governed by a nonlinear partial differential equation and nonlinear boundary conditions. The solution of the problem is obtained numerically using the finite difference method. The effects of viscoelastic parameter, combined magnetic and porosity parameter, ratio of oscillating frequency to stretching rate parameter, suction parameter, and slip length on velocity and skin-friction coefficient are discussed. The study reveals that an oscillatory sheet embedded in a fluid-saturated porous medium generates oscillatory motion in the fluid. The amplitude and phase of oscillations depend on the rheology of the fluid, as well as on the other parameters coming through imposed boundary conditions, the inclusion of body forces term, and permeability of the porous medium. Moreover, the results also predict a reduction in the amplitude of skin friction by increasing slip at the stretching surface.