Analytic Solution for Oscillatory Flow in a Channel for Jeffrey Fluid

Abstract

AbstractThis paper describes the study of two-dimensional oscillatory flow inside a rectangular channel for Jeffrey fluid with small suction. The main objective is to investigate the viscoelastic behavior of non-Newtonian fluids subject to time harmonic oscillations. The fluid flow in the channel is generated by suction at the porous walls while time harmonic pressure waves give rise to oscillations in the velocity field. Analytical solution of the time-independent axial velocity and time-dependent oscillatory axial velocity in the channel is obtained. To understand the characteristics of non-Newtonian fluids, the effects of retardation time, and Deborah number on the oscillatory velocity, its amplitude and penetration depth are analyzed. The methodologies adopted to solve this physically complex problem are perturbation, Wentzel-Kramers-Brillouin, and variation-of-parameter. The paper will help in understanding the characteristics of non-Newtonian fluids that are subject to applied oscillatory harmonic s...