SpringerLink
Log in

Heat transfer analysis in peristaltic flow of MHD Jeffrey fluid with variable thermal conductivity

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

The effect of an inclined magnetic field in the peristaltic flow of a Jeffrey fluid with variable thermal conductivity is discussed. The temperature dependent thermal conductivity of fluid in an asymmetric channel is taken into account. A dimensionless nonlinear system subject to a long wavelength and a low Reynolds number is solved. The explicit expressions of the stream function, the axial velocity, the pressure gradient, and the temperature are obtained. The effects of all physical parameters on peristaltic transport and heat transfer characteristics are observed from graphical illustrations. The behaviors of θ ∈ [0, π/2] and θ ∈ [π/2, π] on fluid flow and heat transfer are found to be opposite. Further, the size of trapped bolus is greater for the case of the inclined magnetic field (θ ≠ π/2) than that for the case of the transverse magnetic field (θ = π/2). The heat transfer coefficient decreases when the constant thermal conductivity (Newtonian) fluid is changed to the variable thermal conductivity (Jeffrey) fluid.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Shapiro, A. H., Jaffrin, M. Y., and Weinberg, S. L. Peristaltic pum** with long wavelength at low Reynolds numbers. Journal of Fluid Mechanics, 37, 799–825 (1969)

    Article  Google Scholar 

  2. Mishra, M. and Rao, A. R. Peristaltic transport of a Newtonian fluid in an asymmetric channel. Zeitschrift für Angewandte Mathematik und Physik, 54, 532–550 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  3. Kothandapani, M. and Srinivas, S. Non-linear peristaltic transport of a Newtonian fluid in an inclined asymmetric channel through a porous medium. Physics Letters A, 372, 1265–1276 (2008)

    Article  MATH  Google Scholar 

  4. Tripathi, D. A mathematical model for the movement of food bolus of varying viscosities through the esophagus. Acta Astronautica, 69, 429–439 (2011)

    Article  Google Scholar 

  5. Mekheimer, K. S., Abd Elmaboud, Y., and Abdellateef, A. I. Peristaltic transport through eccentric cylinders: mathematical model. Applied Bionics and Biomechanics, 10, 19–27 (2013)

    Article  Google Scholar 

  6. Eytan, O. and Elad, D. Analysis of intra-uterine fluid motion induced by uterine contractions. Bulletin of Mathematical Biology, 61, 221–238 (1999)

    Article  Google Scholar 

  7. Radhakrishnamacharya, G. Long wavelength approximation to peristaltic motion of power law fluid. Rheologica Acta, 21, 30–35 (1982)

    Article  MATH  Google Scholar 

  8. Siddiqui, A. M. and Schwarz, W. H. Peristaltic flow of a second order fluid in tubes. Journal of Non-Newtonian Fluid Mechanics, 53, 257–284 (1994)

    Article  Google Scholar 

  9. Tsiklauri, D. and Beresnev, I. Non-Newtonian effects in the peristaltic flow of a Maxwell fluid. Physical Review E, 64, 036303 (2001)

    Article  Google Scholar 

  10. Mekheimer, K. S. Peristaltic transport of a couple-stress fluid in a uniform and non-uniform channels. Biorheology, 39, 755–765 (2002)

    Google Scholar 

  11. Hayat, T., Wang, Y., Siddiqui, A. M., and Hutter, K. Peristaltic motion of a Johnson-Segalman fluid in a plannar channel. Mathematical Problems in Engineering, 1, 1–23 (2003)

    Article  MathSciNet  Google Scholar 

  12. Srinivasacharya, D., Mishra, M., and Ramachandra, A. R. Peristaltic pum** of a micropolar fluid. Acta Mechanica, 161, 165–178 (2003)

    MATH  Google Scholar 

  13. Vajravelu, K., Sreenadh, S., and Babu, V. R. Peristaltic transport of a Hershel-Bulkley fluid in an inclined tube. International Journal of Non-Linear Mechanics, 40, 83–90 (2005)

    Article  MATH  Google Scholar 

  14. Tripathi, D. A mathematical model for the peristaltic flow of chyme movement in small intestine. Mathematical Biosciences, 233, 90–97 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  15. Ellahi, R., Riaz, A., Nadeem, S., and Ali, M. Peristaltic flow of Carreau fluid in a rectangular duct through a porous medium. Mathematical Problems in Engineering, 2012, 329639 (2012)

    Article  MathSciNet  Google Scholar 

  16. Mekheimer, K. S. and El-Kot, M. A. Influence of magnetic field and Hall currents on blood flow through a stenotic artery. Applied Mathematics and Mechanics (English Edition), 29 (8), 1093–1104 (2008) DOI 10.1007/s10483-008-0813-x

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  18. Hayat, T. and Ali, N. Peristaltically induced motion of a MHD third grade fluid in a deformable tube. Physica A, 370, 225–239 (2006)

    Article  Google Scholar 

  19. Hayat, T. and Ali, N. A mathematical description of peristaltic hydromagnetic flow in a tube. Applied Mathematics and Computation, 188, 1491–1502 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  20. Hayat, T., Saleem, N., and Ali, N. Effect of induced magnetic field on peristaltic transport of a Carreau fluid. Communications in Nonlinear Science and Numerical Simulation, 15, 2407–2423 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  21. Mekheimer, K. S., Komy, S. R., and Abdelsalam, S. I. Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a microchannel. Chinese Physics B, 22, 124702 (2013)

    Article  Google Scholar 

  22. Kothandapani, M. and Srinivas, S. Peristaltic transport of a Jeffrey fluid under the effect of magnetic field in an asymmetric channel. International Journal of Non-Linear Mechanics, 43, 915–924 (2008)

    Article  Google Scholar 

  23. Pandey, S. K. and Chaube, M. K. Peristaltic flow of a micropolar fluid through a porous medium in the presence of an external magnetic field. Communications in Nonlinear Science and Numerical Simulation, 16, 3591–3601 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  24. Tripathi, D. and Bég, O. A. Transient magneto-peristaltic flow of couple stress biofluids: a magneto-hydro-dynamical study on digestive transport phenomena. Mathematical Biosciences, 246, 72–83 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  25. Ogulu, A. Effect of heat generation on low Reynolds number fluid and mass transport in a single lymphatic blood vessel with uniform magnetic field. International Communications in Heat and Mass Transfer, 33, 790–799 (2006)

    Article  Google Scholar 

  26. Eldabe, N. T. M., El-Sayed, M. F., Ghaly, A. Y., and Sayed, M. H. Mixed convective heat and mass transfer in a non-Newtonian fluid at a peristaltic surface with temperature dependent viscosity. Archive of Applied Mechanics, 78, 599–624 (2007)

    Article  Google Scholar 

  27. Hayat, T. and Hina, S. The influence of wall properties on the MHD peristaltic flow of a Maxwell fluid with heat and mass transfer. Nonlinear Analysis: Real World Applications, 11, 3155–3169 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  28. Abd Elmaboud, Y., Mekheimer, K. S., and Abdellateef, A. I. Thermal properties of couple-stress fluid flow in an asymmetric channel with peristalsis. Journal of Heat Transfer, 135, 044502 (2013)

    Article  Google Scholar 

  29. Seth, G. S. and Ghosh, S. K. Unsteady hydromagnetic flow in a rotating channel in the presence of inclined magnetic field. International Journal of Engineering Science, 24, 1183–1193 (1986)

    Article  MATH  Google Scholar 

  30. Ghosh, S. K. A note on steady and unsteady hydromagnetic flow in a rotating channel in the presence of inclined magnetic field. International Journal of Engineering Science, 29, 1013–1016 (1991)

    Article  MATH  Google Scholar 

  31. Elshehawey, E. F., Elbarbary, E. M. E., and Elgazery, N. S. Effect of inclined magnetic field on magneto fluid flow through a porous medium between two inclined wavy porous plates (numerical study). Applied Mathematics and Computation, 135, 85–103 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  32. Guria, M., Das, S., Jana, R. N., and Ghosh, S. K. Oscillatory Couette flow in the presence of an inclined magnetic field. Meccanica, 44, 555–564 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  33. Bég, O. A., Sim, L., Zueco, J., and Bhargava, R. Numerical study of magnetohydrodynamic viscous plasma flow in rotating porous media with Hall currents and inclined magnetic field influence. Communications in Nonlinear Science and Numerical Simulation, 15, 345–359 (2010)

    Article  MATH  Google Scholar 

  34. Nadeem, S. and Akram, S. Influence of inclined magnetic field on peristaltic flow of a Williamson fluid model in an inclined symmetric or asymmetric channel. Mathematical and Computer Modelling, 52, 107–119 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  35. Noreen, S., Hayat, T., Alsaedi, A., and Qasim, M. Mixed convection heat and mass transfer in peristaltic flow with chemical reaction and inclined magnetic field. Indian Journal of Physics, 87, 889–896 (2013)

    Article  Google Scholar 

  36. Kumari, A. V. R. and Radhakrishnamacharya, G. Effect of slip and mangetic field on peristaltic flow in an inclined channel with wall effects. International Journal of Biomathematics, 5, 1250015 (2012)

    Article  MathSciNet  Google Scholar 

  37. Nadeem, S. and Akram, S. Heat transfer in a peristaltic flow of MHD fluid with partial slip. Communications in Nonlinear Science and Numerical Simulation, 15, 312–321 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  38. Chiam, T. C. Heat transfer in a fluid with variable thermal conductivity over a linear stretching sheet. Acta Mechanica, 129, 63–72 (1998)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, 44000, Pakistan

    Q. Hussain & S. Asghar

  2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdul Aziz University, Jeddah, 21589, Saudi Arabia

    S. Asghar, T. Hayat & A. Alsaedi

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

    T. Hayat

Authors
  1. Q. Hussain
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Asghar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. Hayat
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Alsaedi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Q. Hussain.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hussain, Q., Asghar, S., Hayat, T. et al. Heat transfer analysis in peristaltic flow of MHD Jeffrey fluid with variable thermal conductivity. Appl. Math. Mech.-Engl. Ed. 36, 499–516 (2015). https://doi.org/10.1007/s10483-015-1926-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-015-1926-9

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation