Pulsating flow of unsteady immiscible viscous fluid under the combined effects of smooth and corrugated channelwalls

Abstract

This study focuses on finding numerical solutions for the flow of an unsteady immiscible viscous fluid under a general oscillatory time-dependent pressure gradient within a channel that features smooth and corrugated walls. The research investigates how the combination of grooves and flat surfaces in the channel affects fluid flow by examining pulsatile flow between these surfaces. At the interface, the continuity of velocities and shear stresses is assumed. The unsteady flow is influenced by the Reynolds numbers of the fluids involved. The velocity is observed to oscillate at the same frequency as the pressure gradient. The study provides numerical expressions for the mass flow rate and wall shear stresses under the influence of corrugated grooves. The purpose of incorporating grooves is to enhance the efficiency of transport processes compared to a smooth channel.