Analytical solutions of oscillating Couette–Poiseuille flows for the viscoelastic Oldroyd B fluid

This paper deals with the analytical investigation of oscillatory Couette–Poiseuille flows with regard to the viscoelastic Oldroyd B fluid, taking the inertial force into account. The fluid is confined by two infinite horizontal plates under the exertion of a periodic pressure gradient. The upper plate is fixed at rest, and the below plate oscillates in its own plane. The velocity distributions and the stress responses are analytically obtained and graphically presented. The oscillating flow behaviors of the Oldroyd B fluid and its two limiting cases, the Newtonian fluid and the upper-convected Maxwell fluid, are investigated and compared. The inertial, viscous, and elastic effects on the flow behaviors, stress responses, the relation between the shear stress and the shear rate, and the emerging resonance are extensively discussed by reference to the dimensionless parameters, i.e., Reynolds number, Deborah number, and the ratio of the relaxation time to the retardation time.