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Numerical solution of oscillatory flow of Maxwell fluid in a rectangular straight duct

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Abstract

A numerical analysis is presented for the oscillatory flow of Maxwell fluid in a rectangular straight duct subjected to a simple harmonic periodic pressure gradient. The numerical solutions are obtained by a finite difference scheme method. The stability of this finite difference scheme method is discussed. The distributions of the velocity and phase difference are given numerically and graphically. The effects of the Reynolds number, relaxation time, and aspect ratio of the cross section on the oscillatory flow are investigated. The results show that when the relaxation time of the Maxwell model and the Reynolds number increase, the resonance phenomena for the distributions of the velocity and phase difference enhance.

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Authors and Affiliations

  1. Department of Engineering Mechanics, School of Civil Engineering, Shandong University, Jinan, 250061, China

    Xuyang Sun, Shaowei Wang, Moli Zhao & Qiangyong Zhang

Authors
  1. Xuyang Sun
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  2. Shaowei Wang
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  3. Moli Zhao
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  4. Qiangyong Zhang
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Correspondence to Shaowei Wang.

Additional information

Citation: SUN, X. Y., WANG, S. W., ZHAO, M. L., and ZHANG, Q. Y. Numerical solution of oscillatory flow of Maxwell fluid in a rectangular straight duct. Applied Mathematics and Mechanics (English Edition), 40(11), 1647–1656 (2019) https://doi.org/10.1007/s10483-019-2535-6

Project supported by the National Natural Science Foundation of China (Nos. 11672164 and 41831278) and the Taishan Scholars Project Foundation of Shandong Province of China

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Sun, X., Wang, S., Zhao, M. et al. Numerical solution of oscillatory flow of Maxwell fluid in a rectangular straight duct. Appl. Math. Mech.-Engl. Ed. 40, 1647–1656 (2019). https://doi.org/10.1007/s10483-019-2535-6

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  • DOI: https://doi.org/10.1007/s10483-019-2535-6

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2010 Mathematics Subject Classification

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