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Peristaltically induced motion of a MHD third grade fluid in a deformable tube

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  • Hayat, T.
  • Ali, N.

Abstract

We consider incompressible, magnetohydrodynamic (MHD) third grade fluid confined in a circular cylindrical tube. The tube surfaces are electrically non-conducting. Travelling sinusoidal wave is imposed on the tube which induces peristaltic motion in the fluid. The stream function, axial velocity and pressure gradient are determined analytically for small Deborah number (Γ). The analysis consists of a perturbation expansion in terms of the Deborah number up to O(Γ). Solutions for pressure rise and frictional force per wavelength are given through the use of numerical integration. The general solution of highly non-linear equation for the hydrodynamic third grade fluid is developed. The results are finally compared with the third grade hydrodynamic and Newtonian fluid cases. It is found that the axial velocity increases by increasing Deborah number but decreases for large values of Hartmann number.

Suggested Citation

  • Hayat, T. & Ali, N., 2006. "Peristaltically induced motion of a MHD third grade fluid in a deformable tube," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 225-239.
    • Handle: RePEc:eee:phsmap:v:370:y:2006:i:2:p:225-239
    DOI: 10.1016/j.physa.2006.02.029
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    References listed on IDEAS

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    1. El Hakeem Abd El Naby, Abd & El Misery, A.E.M. & Abd El Kareem, M.F., 2004. "Separation in the flow through peristaltic motion of a carreau fluid in uniform tube," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 1-14.
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    Cited by:

    1. Wang, Yongqi & Hayat, Tasawar & Ali, Nasir & Oberlack, Martin, 2008. "Magnetohydrodynamic peristaltic motion of a Sisko fluid in a symmetric or asymmetric channel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 347-362.
    2. Hayat, T. & Hussain, Q. & Ali, N., 2008. "Influence of partial slip on the peristaltic flow in a porous medium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3399-3409.
    3. Ali, Nasir & Hayat, Tasawar & Asghar, Saleem, 2009. "Peristaltic flow of a Maxwell fluid in a channel with compliant walls," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 407-416.

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    1. El Naby, Abd El Hakeem Abd & El Misery, A.E.M. & Abd El Kareem, M.F., 2006. "Effects of a magnetic field on trapping through peristaltic motion for generalized Newtonian fluid in channel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 79-92.

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