Study of steady viscous flow through a wavy channel: non-orthogonal coordinates

Abstract

In this paper we consider the steady flow of a viscous fluid through a channel bounded by two sinusoidally varying plates differing in phase by π and separated by a mean distance 2h. For the non-varying channel, the classical parabolic velocity profile for the fully developed flow is well known. An attempt here is made to analyze the flow in a generalized non-orthogonal coordinate system that renders the wavy channels as plane walls. Continuity equation and Navier-Stokes equations are presented in the generalized coordinate system and simplified through use of small perturbation under small Reynolds number approximation. Flow characteristics such as centerline velocity and drag force have been evaluated and discussed.