Low Reynolds number flow in a channel with oscillating wavy-walls: An analytical study

An analytical study using perturbation methods has been investigated on the flow profiles and power requirements in an oscillating flow field with a wavy-walled boundary. The velocity field is found for a fluid in between two wavy-walled plates that oscillate in phase. The wavy-walled boundary causes the flow to produce regions of recirculations within the recesses of the boundary. Once the velocity profiles are identified, the power required to drive the oscillatory fluid motion is then calculated and compared to a flat plate geometry without recesses. As expected, the analytical results show that more power is needed to drive a wavy-walled system than a flat plate configuration.