Applied Mathematics and Mechanics

, Volume 40, Issue 11, pp 1647–1656 | Cite as

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

  • Xuyang Sun
  • Shaowei WangEmail author
  • Moli Zhao
  • Qiangyong Zhang


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.

Key words

Maxwell fluid oscillatory flow finite difference method rectangular duct 

Chinese Library Classification


2010 Mathematics Subject Classification

76A05 76M20 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    FUN, C. and CHAO, B. T. Unsteady, laminar, incompressible flow through rectangular ducts. Zeitschrift für Angewandte Mathematik und Physik, 16, 351–360 (1965)CrossRefGoogle Scholar
  2. [2]
    RAMKISSOON, H., EASWARAN, C. V., and MAJUMDAR, S. R. Unsteady flow of an elasticoviscous fluid in tubes of uniform cross-section. International Journal of Non-Linear Mechanics, 24, 585–597 (1989)CrossRefGoogle Scholar
  3. [3]
    SPIGA, M. and MORINI, G. L. A symmetric solution for vecolity profile in laminar flow through rectangular ducts. International Communications in Heat and Mass Transfer, 21, 469–475 (1994)CrossRefGoogle Scholar
  4. [4]
    LIN, T. C. and PU, Q. Oscillatory flow through a rectangular tube. Acta Mechanica Sinica, 110, 423–436 (1986)Google Scholar
  5. [5]
    TALLARICO, A. and DRAGONI, M. Viscous Newtonian laminar flow in a rectangular channel: application to Etna lava flows. Bulletin of Volcanology, 61, 40–47 (1999)CrossRefGoogle Scholar
  6. [6]
    FETECAU, C. and FETECAU, C. Decay of a potential vortex in a Maxwell fluid. International Journal of Non-Linear Mechanics, 38, 985–990 (2003)CrossRefGoogle Scholar
  7. [7]
    FETECAU, C. A new exact solution for the flow of a Maxwell fluid past an infinite plate. International Journal of Non-Linear Mechanics, 38, 423–427 (2003)MathSciNetCrossRefGoogle Scholar
  8. [8]
    FETECAU, C. and FETECAU, C. The Rayleigh-Stokes-problem for a fluid of Maxwellian type. International Journal of Non-Linear Mechanics, 38, 603–607 (2003)CrossRefGoogle Scholar
  9. [9]
    NADEEM, S., ASGHAR, S., HAYAT, T., and HUSSAIN, M. The Rayleigh Stokes problem for rectangular pipe in Maxwell and second grade fluid. Meccanica, 43, 495–504 (2008)MathSciNetCrossRefGoogle Scholar
  10. [10]
    ZHENG, L., ZHAO, F., and ZHANG, X. Exact solutions for generalized Maxwell fluid flow due to oscillatory and constantly accelerating plate. Nonlinear Analysis Real World Applications, 11, 3744–3751 (2010)MathSciNetCrossRefGoogle Scholar
  11. [11]
    QI, H. T. and LIU, J. G. Some duct flow of a fractional Maxwell fluid. European Physical Journal Special Topics, 193, 71–79 (2011)CrossRefGoogle Scholar
  12. [12]
    NAZAR, M., ZULQARNAIN, M., AKRAM, M. S., and ASIF, M. Flow through an oscillating rectangular duct for generalized Maxwell fluid with fractional derivatives. Communications in Nonlinear Science and Numerical Simulation, 17, 3219–3234 (2012)MathSciNetCrossRefGoogle Scholar
  13. [13]
    NAZAR, M., SHAHID, F., AKRAM, M. S., and SULTAN, Q. Flow on oscillating rectangular duct for Maxwell fluid. Applied Mathematics and Mechanics (English Edition), 33, 717–730 (2012) MathSciNetCrossRefGoogle Scholar
  14. [14]
    YIN, Y. and ZHU, K. Q. Oscillating flow of a viscoelastic fluid in a pipe with the fractional Maxwell model. Applied Mathematics and Computation, 173, 231–242 (2006)MathSciNetCrossRefGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Xuyang Sun
    • 1
  • Shaowei Wang
    • 1
    Email author
  • Moli Zhao
    • 1
  • Qiangyong Zhang
    • 1
  1. 1.Department of Engineering Mechanics, School of Civil EngineeringShandong UniversityJinanChina

Personalised recommendations