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Peristaltic flow of a nanofluid with slip effects

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Abstract

The problem of peristaltic flow of a nanofluid in an asymmetric channel is analyzed by taking into account the slip effects. The relevant equations for the nanofluid are presented and simplified by the long wavelength and small Reynolds number. Closed form solutions for stream function and pressure gradient are developed. However series expressions for temperature and Nanoparticle profiles are constructed. Finally, the influence of several parameters on the physical quantities of interest is discussed.

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References

  1. Latham TW (1966) Fluid motion in a peristaltic pump. MS Thesis, Massachusetts Institute of Technology, Cambridge

  2. Jaffrin MY, Shapiro AH (1971) Peristaltic pumping. Annu Rev Fluid Mech 3:13–16

    Article  ADS  Google Scholar 

  3. Haroun MH (2007) Non-linear peristaltic flow of a fourth grade fluid in an inclined asymmetric channel. Comput Mater Sci 39:324–333

    Article  Google Scholar 

  4. Mekheimer KS (2008) Effect of the induced magnetic field on peristaltic flow of a couple stress fluid. Phys Lett A 372:4271–4278

    Article  ADS  MATH  Google Scholar 

  5. Nadeem S, Akbar NS (2010) Influence of heat transfer on peristaltic transport of a Johnson–Segalman fluid in an inclined asymmetric channel. Commun Nonlinear Sci Numer Simul 15:2860–2877

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Hayat T, Javed M, Asghar S (2008) MHD peristaltic motion of Johnson–Segalman fluid in a channel with compliant walls. Phys Lett A 372:5026–5036

    Article  ADS  MATH  Google Scholar 

  7. Haroun MH (2007) Non-linear peristaltic flow of a fourth grade fluid in an inclined asymmetric channel. Comput Mater Sci 39:324–333

    Article  Google Scholar 

  8. Yıldırım A, Sezer SA (2010) Effects of partial slip on the peristaltic flow of a MHD Newtonian fluid in an asymmetric channel. Math Comput Model 52:618–625

    Article  MATH  Google Scholar 

  9. Sezer SA, Yıldırım A (2010) A numerical treatment for the solution of the hydromagnetic peristaltic flow of a bio-fluid with variable viscosity in a circular cylindrical tube. Int J Numer Methods Biomed Eng 26:1503–1514

    MathSciNet  MATH  Google Scholar 

  10. Yıldırım A, Sezer SA (2010) Non-perturbative solution of three-dimensional Navier–Stokes equations for the flow near an infinite rotating disk. Math Methods Appl Sci 33:1298–1305

    MathSciNet  Google Scholar 

  11. Behrouz R, Mohyud-Din T, Yildirim A (2011) Solution to the MHD flow over a non-linear stretching sheet by homotopy perturbation method. Sci China Ser G, Phys Mech Astron 54:342–345

    Article  ADS  Google Scholar 

  12. Shita GC, Roya M, Ng EYK (2010) Effect of induced magnetic field on peristaltic flow of a micropolar fluid in an asymmetric channel. Int J Numer Methods Biomed Eng 26:1380–1403

    Article  MathSciNet  Google Scholar 

  13. Ng EYK, Tan ST (2007) Study of EDL effect on 3D developing flow in microchannel with Poisson-Boltzmann and Nernst-Planck models. Int J Numer Methods Eng 71:818–836

    Article  MATH  Google Scholar 

  14. Tan ST, Ng EYK (2006) Numerical analysis of EDL effect on heat transfer characteristic of 3-D developing flow in microchannel. Numer Heat Transf, Part A 49:991–1007

    Article  ADS  Google Scholar 

  15. Ng EYK, Tan ST (2004) Computation of 3D developing pressure-driven liquid flow in microchannel with EDL effect. Numer Heat Transf, Part A, Appl 45:1013–1027

    Article  ADS  Google Scholar 

  16. Hayat T, Javed M, Asghar S (2009) Slip effects in peristalsis. Numer Methods Partial Differ Equ. doi:10.1002/num.20564

    Google Scholar 

  17. Srinivas S, Gayathri R, Kothandapani M (2009) The influence of slip conditions, wall properties and heat transfer on MHD peristaltic transport. Comput Phys Commun 180:2115–2122

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. Akbar NS, Hayat T, Nadeem S, Hendi AA (2011) Effects of slip and heat transfer on the peristaltic flow of a third order fluid in an inclined asymmetric channel. Int J Heat Mass Transf 54:1654–1664

    Article  MATH  Google Scholar 

  19. Choi SUS (1995) Enhancing thermal conductivity of fluids with nanoparticles. In: Siginer DA, Wang HP (eds) Developments and applications of non-Newtonian flows, vol 66. ASME, New York, pp 99–105

    Google Scholar 

  20. Khan WA, Pop I (2010) Boundary-layer flow of a nanofluid past a stretching sheet. Int J Heat Mass Transf 53:2477–2483

    Article  MATH  Google Scholar 

  21. Buongiorno J (2006) Convective transport in nanofluids. ASME J Heat Transf 128:240–250

    Article  Google Scholar 

  22. Khanafer K, Vafai K, Lightstone M (2003) Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. Int J Heat Mass Transf 46:3639–3653

    Article  MATH  Google Scholar 

  23. Kuznetsov AV, Nield DA (2010) Natural convective boundary-layer flow of a nanofluid past a vertical plate. Int J Therm Sci 49:243–247

    Article  Google Scholar 

  24. Akbar NS, Nadeem S (2011) Endoscopic effects on the peristaltic flow of a Nano fluid. Commun Theor Phys 56:761–768

    Article  ADS  Google Scholar 

  25. Akbar NS, Nadeem S, Hayat T, Hendi AA (2011) Peristaltic flow of a nanofluid in a non-uniform tube. Heat Mass Transf. doi:10.1007/s00231-011-0892-7

    Google Scholar 

  26. He JH (1998) Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput Methods Appl Mech Eng 167:57–68

    Article  ADS  MATH  Google Scholar 

  27. He JH (2005) Application of homotopy perturbation method to nonlinear wave equations. Chaos Solitons Fractals 26:695–700

    Article  ADS  MATH  Google Scholar 

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Acknowledgement

Third author as a visiting Professor thanks the partial support of Global Research Network for Computational Mathematics and King Saud University for this work.

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Authors and Affiliations

  1. Department of Mathematics, Quaid-i-Azam University 45320, Islamabad, 44000, Pakistan

    Noreen Sher Akbar, S. Nadeem & T. Hayat

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

    T. Hayat & Awatif A. Hendi

Authors
  1. Noreen Sher Akbar
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  2. S. Nadeem
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  3. T. Hayat
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  4. Awatif A. Hendi
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Corresponding author

Correspondence to Noreen Sher Akbar.

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Akbar, N.S., Nadeem, S., Hayat, T. et al. Peristaltic flow of a nanofluid with slip effects. Meccanica 47, 1283–1294 (2012). https://doi.org/10.1007/s11012-011-9512-3

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  • DOI: https://doi.org/10.1007/s11012-011-9512-3

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