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Self-Similar Unsteady Flow of a Sisko Fluid in a Cylindrical Tube Undergoing Translation

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  • M. Khan
  • S. Abelman
  • D. P. Mason
  • F. M. Mahomed

Abstract

The governing nonlinear equation for unidirectional flow of a Sisko fluid in a cylindrical tube due to translation of the tube wall is modelled in cylindrical polar coordinates. The exact steady-state solution for the nonlinear problem is obtained. The reduction of the nonlinear initial value problem is carried out by using a similarity transformation. The partial differential equation is transformed into an ordinary differential equation, which is integrated numerically taking into account the influence of the exponent n and the material parameter b of the Sisko fluid. The initial approximation for the fluid velocity on the axis of the cylinder is obtained by matching inner and outer expansions for the fluid velocity. A comparison of the velocity, vorticity, and shear stress of Newtonian and Sisko fluids is presented.

Suggested Citation

  • M. Khan & S. Abelman & D. P. Mason & F. M. Mahomed, 2015. "Self-Similar Unsteady Flow of a Sisko Fluid in a Cylindrical Tube Undergoing Translation," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-14, September.
    • Handle: RePEc:hin:jnlmpe:135424
    DOI: 10.1155/2015/135424
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