Abstract
The goal of this work is to study the oscillating flow of Jeffreys fluids through a semicircular channel. Here, the oscillating flow is perceived to be driven by a periodically oscillating pressure gradient. The analytical solutions for velocity and volumetric flow rate are derived by using the separation of variables method, and the influence of some related variables such as Reynolds numberRe, pressure gradient amplitudeA¯, and relaxation timeλ¯1and retardation timeλ¯2on them is analyzed by plotting. The effects of the above-mentioned parameters on the velocity amplitude oscillation and the variation of the volumetric flow rate with the Reynolds numberReand pressure gradient amplitudeA¯, respectively, are mainly discussed. Results indicate that the phenomenon of velocity amplitude oscillation is always found in the oscillating flow. The larger the Reynolds numberReand relaxation timeλ¯1, the smaller the retardation timeλ¯2, and the stronger the velocity amplitude oscillation. For the pressure gradient amplitudeA¯, it generally only determines the direction of oscillating flow and the magnitude of velocity amplitude, and has little effect on this oscillation. The volumetric flow rate amplitude increases sharply with the oscillation Reynolds numberReto reach the peak, and then decays rapidly to a rather small value. Furthermore, the volumetric flow rate amplitude exhibits a linear increasing behavior with the pressure gradient amplitudeA¯. Considering the similar properties of Jeffreys fluids and blood, the results presented in this paper are of the great implications for the investigation of human physiological systems.
Published Version
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