, Volume 9, Issue 1, pp 117–130 | Cite as

Peristaltic Transport of Nanofluid in a Vertical Porous Stratum with Heat Transfer Effects

  • A. N. S. SrinivasEmail author
  • C. Haseena
  • S. Sreenadh


The heat transfer effects on peristaltic motion of nanofluid in a vertical porous stratum under long wavelength and low Reynolds number approximations are studied in this paper. The fluid motion is governed by non-linear coupled partial differential equations which are solved using perturbation expansion by taking N as a perturbation parameter. The expressions for velocity, temperature, concentration, and pressure rise per wavelength are obtained. The influence of different pertinent parameters on fluid velocity, temperature, concentration, and pressure rise over one wavelength is analyzed through graphs. The trapping phenomenon is presented graphically. The result shows that the velocity decreases with growing values of permeability parameter. The significant effects of the Grashof number, thermophoresis parameter, and Brownian motion parameter on the nanoparticle concentration and temperature distribution are observed. The influence of physical parameters on size of the tapered bolus is discussed. The results obtained for the present flow description reveal several interesting behaviors that warrant advance study on the non-Newtonian fluid phenomenon.


Peristaltic transport Heat transfer Nanofluid Porous stratum 



Half width of the channel


Amplitude of wave


Wave length of the peristaltic wave


Wave speed

\( \overline{t} \)


\( \left(\overline{X},\overline{Y}\right) \)

Stationary coordinates

\( \left(\overline{x},\overline{y}\right) \)

Moving coordinates

\( \left(\overline{U},\overline{V}\right) \)

Velocity components in fixed frame

\( \left(\overline{u},\overline{v}\right) \)

Velocity components in moving frame


Amplitude ratio




Dimensionless nanoparticle concentration


Dimensionless temperature distribution


Dimensional nanoparticle concentration


Dimensional temperature distribution


Reference temperature


Temperature at the plates


Reference concentration


Concentration at the plates




Kinematic viscosity


Thermal conductivity




Permeability parameter


Darcy’s number


Thermophoresis parameter


Brownian motion parameter


Local temperature Grashof number


Nanoparticle Grashof number


Reynolds number


Prandtl number


Eckert number


Wave number


Perturbation parameter


Acceleration due to gravity


Brownian diffusion coefficient


Thermophoretic diffusion coefficient


Coefficient of expansion with concentration


Volume flow rate in fixed frame


Volume flow rate in wave frame


Dimensionless mean flow in fixed frame


Dimensionless mean flow in wave frame


Pressure rise


  1. 1.
    Aly, E. H., & Ebaid, A. (2014). Exact analytical solution for the peristaltic flow of nanofluids in an asymmetric channel with slip effect of the velocity, temperature and concentration. Journal of Mechanics, 30, 411–422.CrossRefzbMATHGoogle Scholar
  2. 2.
    Akbar, N. S., Nadeem, S., Hayat, T., & Hendi, A. A. (2012a). Peristaltic transport of a nanofluid in non-uniform tube. Heat and Mass Transfer, 48, 451–459.CrossRefGoogle Scholar
  3. 3.
    Akbar, N. S., & Nadeem, S. (2011). Endoscopic effects on peristaltic flow of a nanofluid. Communications in Theoretical Physics, 56, 761–768.CrossRefzbMATHGoogle Scholar
  4. 4.
    Akbar, N. S., Nadeem, S., Lee, C., Khan, Z. H., & Haq, R. U. I. (2013). Numerical study of Williamson nanofluid in an asymmetric channel. Results in Physics, 3, 161–166.CrossRefGoogle Scholar
  5. 5.
    Akbar, N. S., Nadeem, S., Hayat, T., & Hendi, A. A. (2012b). Peristaltic transport of a nanofluid with slip effects. Maccanica, 47, 1283–1294.CrossRefzbMATHGoogle Scholar
  6. 6.
    Akram, S., Nadeem, S., Ghafoor, A., & Lee, C. (2013). Consequences of nanofluid on peristaltic flow in an asymmetric channel. International Journal of Basic Applied Sciences, 12, 75–96.Google Scholar
  7. 7.
    Buongiorno, J. (2005). Connective transport in nanofluids. ASME, Journal of Heat Transfer, 128, 240–250.CrossRefGoogle Scholar
  8. 8.
    Choi, S. U. S., & Eastman, J. A. (1995). Enhancing thermal conductivity of fluids with nanoparticles. New York: ASME Publications.Google Scholar
  9. 9.
    Grosan, T & Pop, I. (2012) Fully developed mixed convection in a vertical channel filled by a nanofluid. Journal of Heat Transfer, 134(8):082501. (5 pages).CrossRefGoogle Scholar
  10. 10.
    Kothandapani, M., & Prakash, J. (2013). Effect of radiation and magnetic field on peristaltic transport of nanofluids through a porous space in a tapered asymmetric channel. Journal of Magnetism and Magnetic Materials, 378, 152–163.CrossRefGoogle Scholar
  11. 11.
    Kothandapani, M., & Prakash, J. (2015). Effects of thermal radiation parameter and magnetic field on the peristaltic motion of Williamson nanofluids in a tapered asymmetric channel. International Journal of Heat Mass Transfer, 51, 234–245.CrossRefGoogle Scholar
  12. 12.
    Latham TW (1966) Fluid motions in a peristaltic pump. M.S. Thesis, MIT.Google Scholar
  13. 13.
    Mekheimer, K. S., & Abd Elmaboud, Y. (2008). The influence of heat transfer and magnetic field on peristaltic transport of Newtonian fluid in a vertical annulus: application of an endoscope. Physics Letters A, 372, 1657–1665.CrossRefzbMATHGoogle Scholar
  14. 14.
    Mustafa, M., Hina, S., Hayat, T., & Alsaedi, A. (2012). Influence of wall properties on the peristaltic flow of a nanofluid: analytic and numerical solutions. International Journal of Heat and Mass Transfer, 55, 4871–4877.CrossRefGoogle Scholar
  15. 15.
    Sacheti, N.C., Chandran, P., Singh, A.K., & Bhadauria, B.S. (2014). Devoloping buoyancy driven flow of a nanofluid in a vertical channel subject to heat flux. International Journal of Engineering Mathematics.
  16. 16.
    Prasad, K. V., Vaidya, H. M., & Vajravelu, K. (2015). MHD mixed convection heat transfer in a vertical channel with temperature dependent transport properties. Journal of Applied Fluid Mechanics, 8, 693–701.CrossRefGoogle Scholar
  17. 17.
    Rudraiah, N., & Nagaraj, S. T. (1977). Natural convection through vertical porous stratum. International Journal of Engineering Science, 15, 589–600.CrossRefzbMATHGoogle Scholar
  18. 18.
    Shapiro, A. H., Jaffrin, M. Y., & Weinberg, S. L. (1969). Peristaltic pumping with long wavelengths and low Reynolds number. Journal of Fluid Mechanics, 37, 799–825.CrossRefGoogle Scholar
  19. 19.
    Sreenadh, S., Rashidi, M. M., Kumara Swamy Naidu, K., & Parandhama, A. (2016). Free convection flow of a Jeffrey fluid through a vertical deformable porous stratum. Journal of Applied Fluid Mechanics, 9, 2391–2401.CrossRefGoogle Scholar
  20. 20.
    Sreenadh, S., Sudhakara, E., Krishnamurthy, M., & Gopi Krishna, G. (2015). MHD convection flow of a couple stress fluid through a vertical porous stratum. World Applied Sciences Journal., 33, 918–930.Google Scholar
  21. 21.
    Vajravelu, K., Radhakrishnamacharya, G., & Radhakrishnamurthy, V. (2007). Peristaltic transport and heat transfer in a vertical porous annulus with long wavelength approximations. International Journal of Non-Linear Mechanics, 42, 754–759.CrossRefzbMATHGoogle Scholar
  22. 22.
    Vajravelu, K., Sreenadh, S., & Lakshminarayana, P. (2011). The influence of heat transfer on peristaltic transport of Jeffrey fluid in a vertical porous stratum. Communications in Nonlinear Science and Numerical Simulation., 16, 3107–3125.MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Vajravelu, K., Sreenadh, S., Rajinikanth, K., & Lee, C. (2012). Peristaltic transport of a Williamson fluid in asymmetric channel with permeable walls. Nonlinear Analysis: Real World Applications, 13, 2804–2822.MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Rahimi-Gorji, M., Pourmeharan, O., Gorji-Bandpy, M., & Ganji, D. D. (2016). Unsteady squeezing nanofluid simulation and investigation of its effect on important heat transfer parameters in presence of magnetic field. Journal of Taiwan Institute of Chemical Engineers, 67, 267–475.CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.School of Advanced SciencesVITVelloreIndia
  2. 2.Department of MathematicsSri Venkateswara UniversityTirupatiIndia

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