Unsteady unidirectional flow of second grade fluid between the parallel plates with different given volume flow rate conditions

Abstract

In this paper, the velocity profile and pressure gradient of the unsteady state unidirectional flow of second grade fluids between the parallel plates are considered. The flow motion in the plates is induced by a given but arbitrary inlet volume flow rate which varies with time. Based on the flow conditions described, two basic flow situations are solved, which are a sudden started and a constant acceleration flow, respectively. Then we apply these two results to a practical case that is a trapezoidal piston motion which contains three phases of piston motion, the constant acceleration from the rest to a fixed velocity, then keeping at this velocity, following with the constant deceleration to a stop. In addition, the oscillatory flow is also considered.