Unsteady unidirectional flow of an Oldroyd-B fluid in a circular duct with different given volume flow rate conditions

In this paper, the velocity profile and pressure gradient of the unsteady state unidirectional flow of an Oldroyd-B fluid in a circular duct are considered. The flow motion in the duct 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 suddenly started, and a constant acceleration, flow respectively. These two results are applied 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, oscillatory flow is also considered.