Microsystem Technologies

, Volume 25, Issue 4, pp 1267–1296 | Cite as

Physiological analysis of streamline topologies and their bifurcations for a peristaltic flow of nano fluid

  • Sadia Waheed
  • Anber Saleem
  • S. NadeemEmail author
Technical Paper


In the present article, the techniques of dynamical systems are utilized to investigate the streamline patterns along their bifurcations for peristaltic flow under mixed convection effect. Here the peristaltic flow is discussed in a vertical channel. The flow is considered in a two-dimensional symmetric channel as well as an axisymmetric tube. We have evaluated the peristaltic flow of blood base nanofluid. The momentum equations are reduced by employing approximation of low Reynolds number and long wavelength. For the discourse of the path of particle in the wave frame, an arrangement of nonlinear independent differential equations are built up and the strategies for dynamical frameworks are utilized to examine the local bifurcations and their topological changes. Critical points classifications were made by scrutiny of the eigenvalues of the Jacobian matrix. This principle are utilized to divulge the local bifurcation of the critical points encountered for different flow situations. Flow situations marked as: backward flow, trapping or augmented flow. The analysis is disclosed that the number and size of trapped bolus increases in planner channel and decline in axisymmetric channel by increasing Grashof number. Moreover, the decreasing behaviour of temperature is depicted, which clarify the nanofluid as a cooling agent. Graphically, a wide range of topological changes of bifurcations are examined. At long last, to outline the bifurcation the diagram of global bifurcation is utilized.



  1. Ahmad S, Pop I (2010) Mixed convection boundary layer flow from a vertical flat plate embedded in a porous medium filled with nanofluids. Int Commun Heat Mass Transf 37(8):987–991CrossRefGoogle Scholar
  2. Akbari M, Behzadmehr A, Shahraki F (2008) Fully developed mixed convection in horizontal and inclined tubes with uniform heat flux using nanofluid. Int J Heat Fluid Flow 29(2):545–556CrossRefGoogle Scholar
  3. Bakker PG (1991) Bifurcations in flow patterns. Kluwer Academic Publishers, DordrechtCrossRefzbMATHGoogle Scholar
  4. Brøns M (2007) Streamline topology: patterns in fluid flows and their bifurcations. Adv Appl Mech 41:1–42CrossRefGoogle Scholar
  5. Chen CH (2009) Magneto-hydrodynamic mixed convection of a power-law fluid past a stretching surface in the presence of thermal radiation and internal heat generation/absorption. Int J NonLinear Mech 44(6):596–603CrossRefzbMATHGoogle Scholar
  6. Chiu HC, Jang JH, Yan WM (2007) Mixed convection heat transfer in horizontal rectangular ducts with radiation effects. Int J Heat Mass Transf 50(15):2874–2882CrossRefzbMATHGoogle Scholar
  7. Hammou ZA, Benhamou B, Galanis N, Orfi J (2004) Laminar mixed convection of humid air in a vertical channel with evaporation or condensation at the wall. Int J Therm Sci 43(6):531–539CrossRefGoogle Scholar
  8. Ijaz S, Nadeem S (2016) Slip examination on the wall of tapered stenosed artery with emerging application of nanoparticles. Int J Therm Sci 109:401–412CrossRefGoogle Scholar
  9. Jiménez-Lozano J, Sen M (2010) Streamline topologies of two-dimensional peristaltic flow and their bifurcations. Chem Eng Process Process Intensif 49(7):704–715CrossRefGoogle Scholar
  10. Makinde OD, Aziz A (2010) MHD mixed convection from a vertical plate embedded in a porous medium with a convective boundary condition. Int J Therm Sci 49(9):1813–1820CrossRefGoogle Scholar
  11. Mansour RB, Galanis N, Nguyen CT (2011) Experimental study of mixed convection with water-\(\text{ Al }_{2}\text{ O }_{3}\) nanofluid in inclined tube with uniform wall heat flux. Int J Therm Sci 50(3):403–410CrossRefGoogle Scholar
  12. Manton MJ (1975) Long-wavelength peristaltic pumping at low Reynolds number. J Fluid Mech 68(03):681–693CrossRefzbMATHGoogle Scholar
  13. Maraj EN, Sher Akbar Noreen, Nadeem S (2015) Mathematical study for peristaltic flow of Williamson fluid in a curved channel. Int J Biomath 08:1550005MathSciNetCrossRefzbMATHGoogle Scholar
  14. Moallemi MK, Jang KS (1992) Prandtl number effects on laminar mixed convection heat transfer in a lid-driven cavity. Int J Heat Mass Transf 35(8):1881–1892CrossRefzbMATHGoogle Scholar
  15. Nadeem S, Sadaf H (2017) Exploration of single wall carbon nanotubes for the peristaltic motion in a curved channel with variable viscosity. J Braz Soc Mech Sci Eng 39(1):117–125CrossRefGoogle Scholar
  16. Nadeem S, Shahzadi I (2015) Mathematical analysis for peristaltic flow of two phase nanofluid in a curved channel. Commun Theor Phys 64(5):547MathSciNetCrossRefzbMATHGoogle Scholar
  17. Nadeem S, Hayat T, Akbar NS, Malik MY (2009) On the influence of heat transfer in peristalsis with variable viscosity. Int J Heat Mass Transf 52(21):4722–4730CrossRefzbMATHGoogle Scholar
  18. Nadeem S, Ahmed Z, Saleem S (2016a) The effect of variable viscosities on micropolar flow of two nanofluids. Zeitschriftfür Naturforschung A 71(12):1121–1129Google Scholar
  19. Nadeem S, Khan AU, Saleem S (2016b) A comparative analysis on different nanofluid models for the oscillatory stagnation point flow. Eur Phys J Plus 131(8):261CrossRefGoogle Scholar
  20. Pal D, Talukdar B (2010) Buoyancy and chemical reaction effects on MHD mixed convection heat and mass transfer in a porous medium with thermal radiation and Ohmic heating. Commun Nonlinear Sci Numer Simul 15(10):2878–2893CrossRefzbMATHGoogle Scholar
  21. Partha MK, Murthy PVSN, Rajasekhar GP (2005) Effect of viscous dissipation on the mixed convection heat transfer from an exponentially stretching surface. Heat Mass Transf 41(4):360–366CrossRefGoogle Scholar
  22. Perk L (2013) Differential equations and dynamical systems, vol 7. Springer Science & Business Media, BerlinGoogle Scholar
  23. Perry AE, Chong MS (1987) A description of eddying motions and flow patterns using critical-point concepts. Annu Rev Fluid Mech 19(1):125–155CrossRefGoogle Scholar
  24. Rathod VP, Laxmi D (2014) Effects of heat transfer on the peristaltic MHD flow of a Bingham fluid through a porous medium in a channel. Int J Biomath 07:1450060MathSciNetCrossRefzbMATHGoogle Scholar
  25. Rehman AU, Mehmood R, Nadeem S (2017) Entropy analysis of radioactive rotating nanofluid with thermal slip. Appl Therm Eng 112:832–840CrossRefGoogle Scholar
  26. Sadaf H, Nadeem S (2017) Analysis of combined convective and viscous dissipation effects for peristaltic flow of Rabinowitsch fluid model. J Bionic Eng 14(1):182–190CrossRefGoogle Scholar
  27. Scherer JR, Kwiatek MA, Soper NJ, Pandolfino JE, Kahrilas PJ (2009) Functional esophagogastric junction obstruction with intact peristalsis: a heterogeneous syndrome sometimes akin to achalasia. J Gastrointest Surg 13(12):2219–2225CrossRefGoogle Scholar
  28. Seeger MA, Diederichs K, Eicher T, Brandstatter L, Schiefner A, Verrey F, Pos KM, The KM (2008) AcrB efflux pump: conformational cycling and peristalsis lead to multidrug resistance. Curr Drug Targets 9(9):729–749CrossRefGoogle Scholar
  29. Seydel R (1988) From equilibrium to chaos: practical bifurcation and stability analysis. Elsevier, New YorkzbMATHGoogle Scholar
  30. Shahzadi I, Nadeem S (2016a) Stimulation of metallic nanoparticles under the impact of radial magnetic field through eccentric cylinders: a useful application in biomedicine. J Mol Liq 225:365–381CrossRefGoogle Scholar
  31. Shahzadi I, Nadeem S (2016b) Impact of curvature on the mixed convective peristaltic flow of shear thinning fluid with nanoparticles. Can J Phys 94(12):1319–1330CrossRefGoogle Scholar
  32. Shapiro AH, Jaffrin MY, Weinberg SL (1969) Peristaltic pumping with long wavelengths at low Reynolds number. J Fluid Mech 37(04):799–825CrossRefGoogle Scholar
  33. Srinivas S, Gayathri R, Kothandapani M (2011) Mixed convective heat and mass transfer in an asymmetric channel with peristalsis. Commun Nonlinear Sci Numer Simul 16(4):1845–1862MathSciNetCrossRefzbMATHGoogle Scholar
  34. Zien TF, Ostrach S (1970) A long wave approximation to peristaltic motion. J Biomech 3(1):63–75CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsQuaid-I-Azam UniversityIslamabadPakistan
  2. 2.Department of AnatomyIslamabad Medical and Dental CollegeIslamabadPakistan

Personalised recommendations