Tangential Shear Stress in an Oscillatory Flow of a Viscoelastic Fluid in a Flat Channel

Abstract

The problems of the oscillatory flow of a viscoelastic incompressible fluid in a flat channel are solved for a given harmonic oscillation of the fluid flow rate. The transfer function of the amplitude-phase frequency response is determined. This function is used to determine the influence of the oscillation frequency, acceleration, and relaxation properties of the liquid on the ratio of shear stress on the channel wall to the average velocity over the channel section. Changes in the amplitude and phase of the shear stress on the channel wall in an unsteady flow are also determined depending on the dimensionless oscillation frequency and the relaxation properties of the liquid. It is shown that the viscoelastic properties of the fluid, as well as its acceleration, are the limiting factors for using the quasi-stationary approach. The found formulas for determining the transfer function during the flow of a viscoelastic fluid in a non-stationary flow allow, to determine the dissipation of mechanical energy in a non-stationary flow of the medium, which are of no small importance when calculating the regulation of hydraulic and pneumatic systems.