Viscoelastic hydromagnetic oscillatory flow in a channel in the presence of sinusoidal pressure gradient and linear motion of the plate

The surge of interest to explain the effect of sinusoidal pressure gradient on an unsteady two-dimensional viscoelastic hydromagnetic flow in a channel backed with porous material is the focus of discussion in the present problem. The channel walls are subjected to constant motion. The presence of a transverse magnetic field at a distance acts as an additional body force, a controlling device, as well an input of the system. The elasticity of the liquid in motion and porosity of the medium characterize the flow field. The analytical solution ends in an important conclusion: the degree of the elastic property of the liquid (addition of polymeric substance) acts to accelerate the flow, and the magnetic intensity of the transversal magnetic field acts as an input to decelerate the motion as well as regulate the oscillatory time to avoid flow reversal.