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Heat Transfer on MHD Peristaltic Rotating Flow of a Jeffrey Fluid in an Asymmetric Channel

Abstract

This paper addresses heat transfer and rotation effects on MHD peristaltic flow of a Jeffrey fluid in an asymmetric channel with partial slip. Mathematical modeling is carried out by utilizing long wavelength and small Reynolds number assumptions. The analytical solution has been computed for the stream function, velocity and temperature distribution. The expression for pressure rise is carried out using numerical integration. The effects of various emerging parameters on the flow characteristics are shown and discussed with the help of graphs. The pumping characteristics, axial pressure gradient and trapping phenomenon have been studied. The axial velocity depresses with increasing of Hartmann number, Jeffrey fluid parameter and slip parameter. The size of trapping bolus enhances when an increase in Hartmann number, Jeffrey fluid parameter and rotation parameter. The temperature diminishes as the larger values of slip parameter. A comparison of a special case of our results with the one previously reported in the literature shows a very good agreement.

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References

  1. Latham, T.W.: Fluid Motion in a Peristaltic Pump. MIT Press, Cambridge (1966)

    Google Scholar 

  2. Shapiro, A.H., Jaffrin, M.Y., Weinberg, S.L.: Peristaltic pumping with long wavelengths at low Reynolds numbers. J. Fluid Mech. 37, 799–825 (1969)

    Article  Google Scholar 

  3. Mekheimer, KhS, Elmaboud, Y.A.: Peristaltic flow of a couple stress fluid in an annulus application of an endoscope. Phys. A 387, 2403–2415 (2008)

    Article  MATH  Google Scholar 

  4. Haroun, M.H.: Effect of Deborah number and phase difference on peristaltic transport of a third grade fluid in an asymmetric channel. Commun. Nonlinear Sci. Numer. Simul. 12, 1464–1480 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. Hayat, T., Ali, N.: Effects of an endoscope on the peristaltic flow of a micropolar fluid. Math. Comput. Model. 48, 721–733 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  6. Srinivas, S., Kothandapani, M.: Peristaltic transport in an asymmetric channel with heat transfer—a note. Int. Commun. Heat Mass Trans. 35, 514–522 (2008)

    Article  MATH  Google Scholar 

  7. Nadeem, S., Akram, S.: Peristaltic flow of a Williamson fluid in an asymmetric channel. Commun. Nonlinear Sci. Numer. Simul. 15, 1705–1716 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  8. Hayat, T., Javed, M., Hendi, A.A.: Peristaltic transport of viscous fluid in a curved channel with compliant walls. Int. J. Heat Mass Transf. 54, 1615–1621 (2011)

    Article  MATH  Google Scholar 

  9. Nadeem, S., Akbar, N.S.: Influence of radially varying MHD on the peristaltic flow in an annulus with heat and mass transfer. J. Taiwan Inst. Chem. Eng. 41, 286–294 (2010)

    Article  Google Scholar 

  10. Ali, N., Hayat, T., Asghar, S.: Peristaltic flow of a Maxwell fluid in a channel with compliant walls. Chaos Solut. Fractals 39, 407–416 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  11. Vajravelu, K., Sreenadh, S., Lakshminarayana, P.: The influence of heat transfer on peristaltic transport of a Jeffrey fluid in a vertical porous stratum. Commun. Nonlinear Sci. Numer. Simul. 16, 3107–3125 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  12. Kothandapani, M., Srinivas, S.: On the influence of wall properties in the MHD peristaltic transport with heat transfer and porous medium. Phys. A 372, 4586–4591 (2008)

    MATH  Google Scholar 

  13. Akbar, N.S., Nadeem, S., Lee, C.: Characteristics of Jeffrey fluid model for peristaltic flow of chime in small intestine with magnetic field. Results Phys. 3, 152–160 (2013)

    Article  Google Scholar 

  14. Gnaneswara Reddy, M., Makinde, O.D.: Magnetohydrodynamic peristaltic transport of Jeffrey nanofluid in an asymmetric channel. J. Mol. Liq. 223(2016), 1242–1248 (2016)

    Article  Google Scholar 

  15. Abd-Alla, A.M., Abo-Dahaba, S.M., El-Shahrany, H.D.: Effects of rotation and magnetic field on nonlinear peristaltic flow of second-order fluid in an asymmetric channel through a porous medium. Chin. Phys. B 22, 325–352 (2013)

    Article  Google Scholar 

  16. Mahmoud, S.R., Abd-Alla, A.M., El-Sheikh, M.A.: Effect of the rotation on wave motion through cylindrical bore in a micropolar porous medium. Int. Mod. Phys. B 25, 2713–2728 (2011)

    Article  MATH  Google Scholar 

  17. Abd-Alla, A.M., Yahya, G.A., Mahmoud, S.R., Alosaimi, H.S.: Effect of the rotation, magnetic field and initial stress on peristaltic motion of micropolar fluid. Meccanica 47, 1455–1465 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  18. Hayat, T., Rafiq, M., Ahmad, B.: Influences of rotation and thermophoresis on MHD peristaltic transport of Jeffrey fluid with convective conditions and wall properties. J. Magn. Magn. Mater. 410, 89–99 (2016)

    Article  Google Scholar 

  19. Hayat, T., Farooq, S., Ahmad, B., Alsaedi, A.: Homogeneous-heterogeneous reactions and heat source/sink effects in MHD peristaltic flow of micropolar fluid with Newtonian heating in a curved channel. J. Mol. Liq. 223, 469–488 (2016)

    Article  Google Scholar 

  20. Ebaid, A.: Effects of magnetic field and wall slip conditions on the peristaltic transport of a Newtonian fluid in an asymmetric channel. Phys. Lett. A 372, 4493–4499 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  21. Akbar, N.S., Hayat, T., Nadeem, S., Hendi, A.A.: 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 (2011)

    Article  MATH  Google Scholar 

  22. Hayat, T., Hussain, Q., Umar Qureshi, M., Awatif, NAli, Hendi, A.: Influence of slip condition on the peristaltic transport in an asymmetric channel with heat transfer: an exact solution. Int. J. Numer. Methods Fluids 67, 1944–1959 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  23. Abd-Alla, A.M., Abo-Dahab, S.M.: Magnetic field and rotation effects on peristaltic transport of a Jeffrey fluid in an asymmetric channel. J. Magn. Magn. Mater. 374, 680–689 (2015)

    Article  Google Scholar 

  24. Gnaneswara Reddy, M., Venugopal Reddy, K.: Impact of velocity slip and joule heating on MHD peristaltic flow through a porous medium with chemical reaction. J. Niger. Math. Soc. 35, 227–244 (2016)

    Article  MATH  MathSciNet  Google Scholar 

  25. Gnaneswara Reddy, M., Venugopal Reddy, K., Makinde, O.D.: Hydromagnetic peristaltic motion of a reacting and radiating couple stress fluid in an inclined asymmetric channel filled with a porous medium. Alex. Eng. J. 55, 1841–1853 (2016)

    Article  Google Scholar 

  26. Mishra, M., Rao, A.R.: Peristaltic transport of a Newtonian fluid in an asymmetric channel. Z. Angew. Math. Phys. 53, 532–550 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  27. Kothandapani, M., Srinivas, S.: Peristatltic transport of a Jeffrey fluid under the effect of magnetic field in an asymmetric channel. Int. J. Nonlinear Mech. 43, 915–924 (2008)

    Article  Google Scholar 

  28. Hayat, T., Iqbal, Rija, Tanveer, Anum, Alsaedi, A.: Influence of convective conditions in radiative peristaltic flow of pseudoplastic nanofluid in a tapered asymmetric channel. J. Magn. Magn. Mater. 408, 168–176 (2016)

    Article  Google Scholar 

  29. Javed, M., Hayat, T., Mustafa, M., Ahmad, B.: Velocity and thermal slip effects on peristaltic motion of Walters-B fluid. Int. J. Heat Mass Transf. 96, 210–217 (2016)

    Article  Google Scholar 

  30. Hina, S., Mustafa, M., Hayat, T., Alsaedi, A.: Peristaltic transport of Powell–Eyring fluid in a curved channel with heat/mass transfer and wall properties. Int. J. Heat Mass Transf. 101, 156–165 (2016)

    Article  Google Scholar 

  31. Shehzad, S.A., Abbasi, F.M., Hayat, T., Alsaadi, Fuad: Model and comparative study for peristaltic transport of water based nanofluids. J. Mol. Liq. 209, 723–728 (2015)

    Article  Google Scholar 

  32. Hina, S., Mustafa, M., Hayat, T., Alotaibi, NaifD: On peristaltic motion of pseudoplastic fluid in a curved channel with heat/mass transfer and wall properties. Appl. Math. Comput. 263, 378–391 (2015)

    MathSciNet  Google Scholar 

  33. Hina, S., Mustafa, M., Hayat, T., Alsaedi, A.: Peristaltic flow of Powell–Eyring fluid in curved channel with heat transfer: a useful application in biomedicine. Comput. Methods Progr. Biomed. 135, 89–100 (2016)

    Article  Google Scholar 

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Correspondence to M. Gnaneswara Reddy.

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Gnaneswara Reddy, M., Venugopal Reddy, K. & Makinde, O.D. Heat Transfer on MHD Peristaltic Rotating Flow of a Jeffrey Fluid in an Asymmetric Channel. Int. J. Appl. Comput. Math 3, 3201–3227 (2017). https://doi.org/10.1007/s40819-016-0293-1

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  • DOI: https://doi.org/10.1007/s40819-016-0293-1

Keywords

  • Peristaltic flow
  • Rotation
  • Magnetic field
  • Heat transfer
  • Jeffrey fluid
  • Partial slip
  • Asymmetric channel