Skip Navigation Links
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email:

Peristaltic Flow of Viscoelastic Giesekus Fluid through Concentric Annuli with Heat Transfer

Journal of Applied Nonlinear Dynamics 10(3) (2021) 579--605 | DOI:10.5890/JAND.2021.09.015

Mohamed A. Hassan

Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt

Download Full Text PDF



The flow of non-Newtonian Giesekus fluid through a peristaltic annulus is presented. The interaction between the flow velocity and the heat transfer distributions is obtained due to the viscous dissipation in the energy equation. Due to the slow motion of the Giesekus fluid (Polymer solution), the small value of the Reynolds number is assumed. A modified longwave approximation, due to a series of the wavenumber, is applied to determine the zero as well as the first order distributions for the stress components, the velocity, and temperature. Also, the pressure rise, the radial position of the zero shear rates, and the rate of the heat flux are obtained numerically. The rheological properties of the non-Newtonian Giesekus fluid are discussed due to the mobility parameter and the time relaxation parameter. The graphical results illustrate that the mobility parameter and the time relaxation parameter enhance the flow. Meanwhile, the flow increases due to the peristaltic motion. According to the viscous dissipation effect, the temperature rises with the time relaxation parameter. Also, the contours of the streamlines are presented and the results illustrate that the trapping bolus disappears for the fluids with small-time relaxation and for the flow through a fixed channel without the peristalsis.


  1. [1]  Giesekus, H. (1982), A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility, Journal of Non-Newtonian Fluid Mechanics, 11, 69-109.
  2. [2]  Ravanchi, M.T., Mirzazadeh, M., and Rashidi, F. (2007), Flow of Giesekus viscoelastic fluid in a concentric annulus with inner cylinder rotation, International Journal of Heat and Fluid Flow, 28, 838-845.
  3. [3]  Dapr\`{a}, I. and Scarpi, G. (2015), Analytical solution for a Couette flow of a Giesekus fluid in a concentric Annulus, Journal of Non-Newtonian Fluid Mechanics, 223, 221-227.
  4. [4]  Dapr\`{a}, I. Scarpi, G.(2018), Analytical solution for axial flow of a Giesekus fluid in concentric annuli, Journal of Non-Newtonian Fluid Mechanics, 251, 10-16.
  5. [5]  Lorenzini, M., Dapr\`{a}, I., and Scarpi, G. (2017), Heat transfer for a Giesekus fluid in a rotating concentric annulus, Applied Thermal Engineering, 122, 118-125.
  6. [6]  El-dabe, N.T.M., Moatimid, G.M., Hassan, M.A., and Mostaph, D.R. (2016), Electrohydrodynamic peristaltic flow of a viscoelastic oldroyd fluid with a mild stenosis: application of an endoscope, Journal of applied Mechanics and Technical Physics, 57(1), 38-54.
  7. [7]  El-dabe, N.T.M., Moatimid, G.M., Hassan, M.A., and Mostaph, D.R. (2016), Effect of Partial Slip on Peristaltic Flow of a Sisko Fluid with Mild Stenosis through a Porous Medium, Applied Mathematics and information Science, 10(2), 1-15.
  8. [8]  El-dabe, N.T.M., Moatimid, G.M., Hassan, M.A., Mostaph, D.R. (2015), Analytical solution of the peristaltic flow of a Jeffrey nanofluid in a tapered artery with mild stenosis and slip condition, International Journal of Innovation and Applied Studies, 12(1), 1-32.
  9. [9]  Sheikholeslami, M. (2019), New computational approach for exergy and entropy analysis of nanofluid under the impact of Lorentz force through a porous media, Computer Methods in Applied Mechanics and Engineering, 344, 319-333.
  10. [10]  Li, F., Sheikholeslami, M., Dara, R.N., Jafaryar, M., Shafee, A., Thoi, T.N., and Li, Z. (2020), Numerical study for nanofluid behavior inside a storage finned enclosure involving melting process, Journal of Molecular Liquids, 297, 111939.
  11. [11]  Ma, X., Sheikholeslami, M., Jafaryar, M., Shafee, A., Thoi, T.N., and Li, Z. (2020), Solidification inside a clean energy storage unit utilizing phase change material with copper oxide nanoparticles, Journal of Cleaner Production, 245, 118888.
  12. [12]  Narla, V.K., Tripathi, D., and Beg, O.A. (2020), Analysis of entropy generation in biomimetic electroosmotic nanofluid pumping through a curved channel with joule dissipation, Thermal Science and Engineering Progress , 15, 100424.
  13. [13]  Prakash, J., Tripathi, D., and B\{e}g, D. (2020), Comparative study of hybrid nanofluids in microchannel slip flow induced by electroosmosis and peristalsis, Applied Nanoscience,
  14. [14]  Prakash, J., Siva, E.P., Tripathi, D., and B\{e}g, O.A.(2019), Thermal slip and radiative heat transfer effects on electro-osmotic magnetonanoliquid peristaltic propulsion through a microchannel, Heat Transfer Asian Research, 48, 2882-2908.
  15. [15]  Wikipedia, Peristaltic pump, accessed October, 2018, from:{\_}pump, 2001.
  16. [16]  Shapiro, A.H., Jaffrin, M.Y., and Weinberg, S.L. (1969), Peristaltic pumping with long wavelengths at lowReynolds number, Journal of Fluid Mechanics, 37(4), 799-825.
  17. [17]  Hayat, T., Alvi, N., and Ali, N. (2008), Peristaltic mechanism of a Maxwell fluid in an asymmetric channel, Nonlinear Analysis: Real World Applications, 9, 1474-1490.
  18. [18]  Vajravelu, K., Radhakrishnamacharya, G., and Radhakrishnamurty, V. (2007), Peristaltic flow and heat transfer in a vertical porous annulus, with long wave approximation, International Journal of Non-Linear Mechanics, 42, 754-759.
  19. [19]  Mekheimer, Kh.S., Hasona, W.M., Abo-Elkhair, R.E., and Zaher, A.Z. (2018), Peristaltic blood flow with gold nanoparticles as a third grade nanofluid in catheter: Application of cancer therapy, Physics Letters A, 382, 85-93.
  20. [20]  Mekheimer, Kh.S. and Abd elmaboud, Y. (2008), Peristaltic flow of a couple stress fluid in an annulus: Application of an endoscope, Physica A, 387, 2403-2415.
  21. [21]  Moatimid, G.M., Mohamed, M.A.A., Hassan, M.A., and El-Dakdoky, E.M.M. (2018), Influence of Wall Properties on the Peristaltic Flow of an Electromagnetic Nanofluid, Journal of engineering Mechanics, 144, 8.
  22. [22]  Eldabe, N.T.M., Hassan, M.A., and Abou-Zeid, M.Y. (2016), Wall Properties Effect on the Peristaltic Motion of a Coupled Stress Fluid with Heat and Mass Transfer through a Porous Medium, Journal of engineering Mechanics, 142(3), 1-9.
  23. [23]  El-dabe, N.T.M., Moatimid, G.M., Hassan, M.A., and Godh, W.A.(2018), Wall properties of peristaltic MHD Nanofluid flow through porous channel, Fluid Mechanics Research International Journal, 2(1), 42-53.
  24. [24]  Hassan, M.A. (2019), Slow motion of a slip spherical particle through a viscoelastic Giesekus fluid in a peristaltic tube, Physica Scripta, 94, 105011 (17pp),
  25. [25]  Narla, V.K. and Tripathi, D. (2019), Electroosmosis modulated transient blood flow in curved microvessels: Study of a mathematical model, Microvascular Research, 123, 25-34.
  26. [26]  Prakash, J., Ravinder, J., and Tripathi, D. (2019), Electroosmotic flow of pseudoplastic nanoliquids via peristaltic pumping, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 41, 61, {}.
  27. [27]  Narla, V.K., Tripathi, D., and Sekhar, G.P.R. (2019), Time-dependent analysis of electroosmotic fluid flow in a microchannel, Journal of Engineering Mathematics, 114, 177-196, {}.
  28. [28]  Tripathi, D., Bhushan, S., B\{e}g, O.A., and Akbar, N.S. (2018), Transient peristaltic diffusion of nanofluids: A model of micropumps in medical engineering, Journal of Hydrodynamics, 30(6), 1001-1011, {}.
  29. [29]  Calin, A., Wilhelm, M., and Balan, C. (2010), Determination of the non-linear parameter (mobility factor) of the Giesekus constitutive model using LAOS procedure, Journal of Non- Newtonian Fluid Mechanics, 165, 1564-1577.
  30. [30]  Figura, L.O. and Teixeira, A.A. (2007), Food Physics Physical Properties --Measurement and Applications, Springer-Verlag, Berlin Heidelberg.
  31. [31]  Wikipedia, adverse pressure pumping, accessed October, 2018, from : Adverse{\_}pressure{\_}gradient, 2001.
  32. [32]  Akbar, N.S., Huda, A.B., Habib, M.B., and Tripathi, D. (2019), Nanoparticles shape effects on peristaltic transport of nanofluids in presence of magnetohydrodynamics, Microsystem Technologies, 25, 283-294.
  33. [33]  Noreen, S. and Tripathi, D. (2019), Heat transfer analysis on electroosmotic flow via peristaltic pumping in non Darcy porous medium, Thermal Science and Engineering Progress, 11, 254--262.
  34. [34]  Prakash, J., Sharma, A., and Tripathi, D. (2020), Convective heat transfer and double diffusive convection in ionic nanofluids flow driven by peristalsis and electromagnetohydrodynamics, Pramana Journal of Physics, 94(4), {}.
  35. [35]  Crane (1988), Flow of fluids through valves, fittings and pipe, Crane CO., London.
  36. [36]  Website: Engineered Software Knowledge Base, Relationship Between Pressure Drop and Flow Rate in a Pipeline, { pressure-drop-and-flow-rate-in-a-pipeline}, , accessed May, 2020.
  37. [37]  Ucar, E., Mobedi, M., Ozerdem, B., and Pop, I. (2013), A comment on change of nusselt number sign in a channel flow filled by a fluid-saturated porous medium with constant heat flux boundary conditions, Transport in Porous Media, 96, 97-103.
  38. [38]  Narla, V.K., Tripathi, D., and Beg, O.A. (2018), Electro-osmosis Modulated Viscoelastic Embryo Transport in Uterine Hydrodynamics: Mathematical Modelling, Journal of Biomechanical Engineering, 1. doi: 10.1115/1.4041904.