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Applied Mathematics and Mechanics

, Volume 33, Issue 6, pp 717–730 | Cite as

Flow on oscillating rectangular duct for Maxwell fluid

  • M. NazarEmail author
  • F. Shahid
  • M. Saeed Akram
  • Q. Sultan
Article

Abstract

This paper presents an analysis for the unsteady flow of an incompressible Maxwell fluid in an oscillating rectangular cross section. By using the Fourier and Laplace transforms as mathematical tools, the solutions are presented as a sum of the steady-state and transient solutions. For large time, when the transients disappear, the solution is represented by the steady-state solution. The solutions for the Newtonian fluids appear as limiting cases of the solutions obtained here. In the absence of the frequency of oscillations, we obtain the problem for the flow of the Maxwell fluid in a duct of a rectangular cross-section moving parallel to its length. Finally, the required time to reach the steady-state for sine oscillations of the rectangular duct is obtained by graphical illustrations for different parameters. Moreover, the graphs are sketched for the velocity.

Key words

Maxwell fluid oscillating rectangular duct velocity field 

Chinese Library Classification

O357.2 

2010 Mathematics Subject Classification

76A02 76D08 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • M. Nazar
    • 1
    Email author
  • F. Shahid
    • 1
  • M. Saeed Akram
    • 1
  • Q. Sultan
    • 1
  1. 1.Centre for Advanced Studies in Pure and Applied MathematicsBahauddin Zakariya UniversityMultanPakistan

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