On hydromagnetic flow of an Oldroyd-B fluid near a pulsating plate

An initial value investigation is made of the motion of an incompressible, viscoelastic, conducting Oldroyd-B fluid bounded by an infinite rigid non-conducting plate. The unsteady flow is generated from rest in the fluid due to velocity tooth pulses subjected on the plate in presence of an external magnetic field. It is assumed that no external electric field is acting on the system and the magnetic Reynolds number is very small. The operational method is used to obtain exact solutions for the fluid velocity and the shear stress on the plate. Quantitative analysis of the results are presented with a view to disclose the simultaneous effects of the magnetic field and the fluid elasticity on the flow and the wall shear stress for different periods of pulsation of the plate. It is shown that the classical and hydromagnetic Rayleigh solutions are limiting cases of the present analysis.