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Peristaltic flow of Walter’s B fluid in endoscope

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Abstract

The peristaltic flow of a Walter’s B fluid in an endoscope is studied. The problem is modeled in a cylindrical coordinate system. The main theme of the present analysis is to study the endoscopic effects on the peristaltic flow of the Walter’s B fluid. To the best of the authors’ knowledge, no investigation has been made so far in the literatures to study the Walter’s B fluid in an endoscope. Analytical solutions are obtained using the regular perturbation method by taking δ as a perturbation parameter. The approximate analytical solutions for the pressure rise and friction forces are evaluated using numerical integration. The effects of emerging parameters of the Walter’s B fluid are presented graphically.

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References

  1. Nadeem, S. and Akbar, N. S. Influence of heat transfer on a peristaltic transport of Herschel Bulkley fluid in a non-uniform inclined tube. Communications in Nonlinear Science and Numerical Simulation, 14, 4100–4113 (2009) DOI 10.1016/j.cnsns.2009.02.032

    Article  MathSciNet  Google Scholar 

  2. Hakeem, A. E., Naby, A. E., Misery, A. E. M. E., and Shamy, I. I. E. Separation in the flow through peristaltic motion of a Carreau fluid in uniform tube. Physica A, 343, 1–14 (2004)

    MathSciNet  Google Scholar 

  3. Ealshahed, M. and Haroun, M. H. Peristaltic transport of Johnson-Segalman fluid under effect of a magnetic field, Mathematical. Problems in Engineering, 6, 663–677 (2005)

    Article  Google Scholar 

  4. Nadeem, S. and Akbar, N. S. Effects of heat transfer on the peristaltic transport of MHD Newtonian fluid with variable viscosity: application of a domain decomposition method. Communications in Nonlinear Science and Numerical Simulation, 14, 3844–3855 (2009)

    Article  MathSciNet  Google Scholar 

  5. Nadeem, S. and Akbar, N. S. Influence of radially varying MHD to the peristaltic flow in an annulus with heat and mass transfer. Taiwan Institute of Chemical Engineers, 41, 286–294 (2010)

    Article  Google Scholar 

  6. Hakeem, A. E., Naby, A. E., Misery, A. E. M. E., and Shamy, I. I. E. Hydromagnetic flow of fluid with variable viscosity in a uniform tube with peristalsis. Physica A, 36, 8535–8547 (2003)

    MATH  Google Scholar 

  7. Haroun, M. H. Effect of Deborah number and phase difference on peristaltic transport of a third order fluid in an asymmetric channel. Communications in Nonlinear Science and Numerical Simulation, 4, 463–477 (2007)

    MathSciNet  Google Scholar 

  8. Mekheimer, K. S. and Elmaboud, Y. A. Peristaltic flow of a couple stress fluid in an annulus: application of an endoscope. Physica A, 387, 2403–2415 (2008)

    Google Scholar 

  9. Hakeem, A. E., Naby, A. E., Misery, A. E. M. E., and Shamy, I. I. E. Effects of an endoscope and generalized Newtonian fluid on peristaltic motion. Applied Mathematics and Computation, 128, 19–35 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  10. Mekheimer, K. S. and Elmaboud, Y. A. The influence of heat transfer and magnetic field on peristaltic transport of a Newtonian fluid in a vertical annulus: an application of an endoscope. Physics Letters A, 372, 1657–1665 (2008)

    Article  Google Scholar 

  11. Hayat, T., Momoniat, E., and Mahmood, F. M. Peristaltic MHD flow of a third grade fluid with an endoscope and variable viscosity. Journal of Nonlinear Mathematical Physics., 15, 91–104 (2008)

    Article  Google Scholar 

  12. Hayat, T., Ahmed, N., and Ali, N. Effects of an endoscope and the magnetic field on the peristalsis involving Jeffrey fluid. Communications in Nonlinear Science and Numerical Simulation, 13, 1581–1591 (2008)

    Article  MathSciNet  Google Scholar 

  13. Hakeem, A. M., Naby, A. E., Misery, A. E. M. E., and Shamy, I. I. E. Effects of an endoscope and fluid with variable viscosity on peristaltic motion. Applied Mathematics and Computation, 158, 497–511 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  14. Misery, A. M. E., Hakeem, A. E., Naby, A. E., and Nagar, A. H. E. Effects of a fluid with variable viscosity and an endoscope on peristaltic motion. Journal of the Physical Society of Japan, 72, 89–93 (2001)

    Article  Google Scholar 

  15. Hayat, T. and Ali, N. Effects of an endoscope on peristaltic flow of a micropolar fluid. Mathematical and Computer Modelling, 48, 721–733 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Hayat, T., Ali, N., Asghar, S., and Siddiqui, A. M. Exact peristaltic flow in tubes with an endoscope. Applied Mathematics and Computation, 182, 359–368 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  17. Hayat, T., Momoniat, E., and Mahomed, F. M. Endoscope effects on MHD peristaltic flow of a power-law fluid. Mathematical Problems in Engineering, 6, 1–19 (2006)

    Article  MathSciNet  Google Scholar 

  18. Baris, S. Steady three-dimensional flow of a Walter’s B fluid in a vertical channel. Turkish Journal of Engineering and Environmental Sciences, 26, 385–394 (2002)

    Google Scholar 

  19. Ariel, P. D. Flow of viscoelastic fluids through a porous channel — I. International Journal for Numerical Methods in Fluids, 17, 605–633 (1993)

    Article  MATH  Google Scholar 

  20. Ariel, P. D. A new finite-difference algorithm for computing the boundary layer flow of viscoelastic fluids in hydromagnetics. Computer Methods in Applied Mechanics and Engineering, 124, 1–13 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  21. Ariel, P. D. On extra boundary condition in the stagnation point flow of a second grade fluid. International Journal of Engineering Science, 40, 145–162 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  22. Sadeghy, K. and Sharifi, M. Local similarity solution for the flow of a second grade viscoelastic fluid above a moving plate. International Journal of Non-Linear Mechanics, 39, 1265–1273 (2004)

    Article  MATH  Google Scholar 

  23. Nadeem, S. and Akbar, N. S. Peristaltic flow of Walter’s B fluid in a uniform inclined tube. Journal of Biorheology, 24, 22–28 (2010)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Quaid-i-Azam University, Islamabad, 45320, Pakistan

    S. Nadeem, N. S. Akbar & T. Hayat

  2. Department of Physics, Faculty of Science, King Saud University, P.O. Box 1846, Riyadh, 11321, Saudi Arabia

    T. Hayat & A. A. Hendi

Authors
  1. S. Nadeem
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  2. N. S. Akbar
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  3. T. Hayat
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  4. A. A. Hendi
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Corresponding author

Correspondence to S. Nadeem.

Additional information

Project supported by the Visiting Professor Programming of King Saud University (No. KSU-VPP-117)

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Nadeem, S., Akbar, N.S., Hayat, T. et al. Peristaltic flow of Walter’s B fluid in endoscope. Appl. Math. Mech.-Engl. Ed. 32, 689–700 (2011). https://doi.org/10.1007/s10483-011-1449-7

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  • DOI: https://doi.org/10.1007/s10483-011-1449-7

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