Theoretical Study of the Laminar Flow in a Channel With Moving Bars

This paper presents a study of the laminar flow in a channel with longitudinal moving bars arrayed along the channel width. The governing equations describing the fluid, which flows along the direction of the bar’s length, are expressed with double Poisson equations and are solved by eigenfunction-expansion and point-match method. The result shows that when the solid bars move forward, the fluid flow will move in the same direction, and the $fRe$ decreases as the positive velocity of bars increases. However, when the bars move backward, a reverse flow will occur in the channel, and the $fRe$ is higher at larger negative velocity of bars. For a channel flow with moving bars, the $fRe$ value is not a constant, such as a classical one without moving bars, in which the $fRe$ value is a constant. Furthermore, when the area of the cross section of the bar is fixed, both the mean velocities and the $fRe$ values of the fluid can be obtained under different velocities and aspect ratios of the bars.