Effect of sinusoidal pressure gradient on MHD flow of viscoelastic fluid in a channel

Unsteady Hydro Magnetic oscillatory flow of incompressible viscoelastic fluid in a channel packed with porous material is investigated under the influence of oscillatory pressure gradient. Moreover, the applied magnetic field of moderate strength interacts with electrically conducting fluid, to generate a resistive volumetric body force. In addition to it, viscoelastic fluidity, characterizing the non-Newtonian behavior in conjunction with permeability of the medium as well as sinusoidal sheared flow due to imposed favorable pressure gradient, contribute to the novelty of the study. The previous work was confined to constant motion of the lower plate but the present work includes the sinusoidal motion of the lower plate in addition to the constant motion. The importance lies with the fact that the coupling effect of sinusoidal fluctuation and viscoelastic fluidity go hard in industrial applications, particularly in process industry. The governing equations characterizing the flow are solved analytically. The striking results of this study are: the formation of inverted boundary layer in case of oscillatory lower plate with moderately escalated time span but such instability leading to flow reversal, does not appear in case of constant motion of the lower plate. Hence, it is recommended that for stability of flow and to avoid flow reversal, higher frequency of oscillation as well as larger time span is not desirable. The elastico-viscosity property reduces the volume flow rate which may be useful to control the efflux and differentiates the state of motion (resulting low skin friction) and state of rest (resulting high skin friction) in respect shearing effects at the bounding surfaces.