Skip to main content
Log in

Modeling of unsteady non-Newtonian blood flow through a stenosed artery: with nanoparticles

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

Literature survey related to the nanoparticles reveals that nanofluids are getting popularity in hematological treatment. Development in this direction motivated us to write a theoretical study on unsteady blood motion in stenosed vessel with nanoparticles. Geometry of a stenosed arterial section is being written mathematically by an appropriate geometric expression. The constitutive equation of Carreau fluid model is used to characterize the dynamical behavior of the blood. The rheology of the blood is formulated mathematically by coupled partial differential equations. Similarly, the effects of nanoparticles are incorporated mathematically into governing equations by using Buonjiornio’s formulation. Mild stenotic condition is employed to reduce the two-dimensional differential equations to simple form. Numerical technique is being used to obtain the numerical solution to the existing problem. The obtained simulation reveals that the magnitude of velocity shows an accelerating behavior for Brownian motion parameter and shows deceleration trend on increasing the thermophoresis parameter. Similarly, the instantaneous behavior of blood flow pattern is shown through streamlines.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4: (a)
Fig. 5
Fig. 6: (a)
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Ku DN (1997) Blood flow in arteries. Ann Rev Fluid Mech 29:399–434

    Article  MathSciNet  Google Scholar 

  2. Boyd J, Buick J, Cosgrove JA, Stansell P (2005) Application of the lattice Boltzmann model to simulated stenosis growth in a two-dimensional carotid artery. Phys Med Biol 50(20):4783

    Article  Google Scholar 

  3. Yap C, Dasi LP, Yoganathan AP (2010) Dynamic hemodynamic energy loss in normal and stenosed aortic valves. ASME J Biomech Eng 132(2):021005

    Article  Google Scholar 

  4. Karri S, Vlachos PP (2010) Time-resolved DPIV investigation of pulsatile flow in symmetric stenotic arteries effects of phase angle. ASME J Biomech Eng 132(3):031010

    Article  Google Scholar 

  5. Pinto SIS, Costa ED, Campos JBLM, Miranda JM (2010) Study of blood flow in a bifurcation with a stenosis. In: 15th international conference experimental mechanics, Porto/Portugal, 22–27 July

  6. Daiswamy N, Schoephoerster RT, Moreno MR, Moore JE (2007) Stented artery flow patterns and their effects on the artery wall. Ann Rev Fluid Mech 39:357–382

    Article  MathSciNet  Google Scholar 

  7. Sforza DM, Putman CM, Cebral JR (2009) Hemodynamics of cerebral aneurysms. Ann Rev Fluid Mech 41:91–107

    Article  Google Scholar 

  8. Chakravarty S, Mandal PK (1994) Mathematical modelling of blood flow through an overlapping arterial stenosis. Math Comput Mod 19:59–70

    Article  Google Scholar 

  9. Qiao A, Zhang Z (2014) Numerical simulation of vertebral artery stenosis treated with different stents. ASME J Biomech Eng 136(4):041007

    Article  Google Scholar 

  10. Chakravarty S, Mandal PK (2000) Two-dimensional blood flow through tapered arteries under stenotic conditions. Int J Non-Linear Mech 35:779–793

    Article  Google Scholar 

  11. Riahi DN, Roy R, Cavazos S (2011) On arterial blood flow in the presence of an overlapping stenosis. Math Comput Model 54:2999–30006

    Article  MathSciNet  Google Scholar 

  12. Ikbal MA, Chakravarty S, Sarifuddin, Mandal PK (2012) Unsteady analysis of viscoelastic blood flow through arterial stenosis. Chem Eng Commun 199: 40–62

    Article  Google Scholar 

  13. Zaman Akbar, Ali Nasir, Anwar Bég O, Sajid M (2016) Unsteady two-layer blood flow through a w-shape stenosed artery using the generalized Oldroyd-B fluid model. ANZIAM J 58:96–118

    MathSciNet  MATH  Google Scholar 

  14. Yilmaz F, Gundogdu MY (2008) A critical review on blood flow in large arteries; relevance to blood rheology, viscosity models, and physiologic conditions. Korea-Aust Rheo J 20:197–211

    Google Scholar 

  15. Shaw S, Gorla RSR, Murthy PVSN, Ng CO (2009) Pulsatile Casson fluid flow through a stenosed bifurcated artery. Int J Fluid Mech Res 36(1):43–63

    Article  Google Scholar 

  16. Cho YI, Kensey KR (1991) Effects of non-Newtonian viscosity of blood on flows in a diseased arterial vessel. Part 1: steady flows. Biorheology 28:241–262

    Article  Google Scholar 

  17. Zaman A, Ali N, Anwar Bég O (2015) Unsteady magnetohydrodynamic blood flow in a porous-saturated overlapping stenotic artery: numerical modeling. J Mech Med Biol 16:16. https://doi.org/10.1142/s0219519416500494

    Article  Google Scholar 

  18. Haghighi AR, Asl MS, Kiyasatfar M (2015) Mathematical modeling of unsteady blood flow through elastic tapered artery with overlapping stenosis. J Braz Soc Mech Sci Eng 37:571–578

    Article  Google Scholar 

  19. Branes HA, Hutton JF, Walter K (1989) An introduction to rheology. Elsevier, Amsterdam

    Google Scholar 

  20. Choi SUS (1995) Enhancing thermal conductivity of fluid with nanoparticles. In: Siginer DA, Wang HP (eds) Developments and application of non-Newtonian flows, 66. ASME, New York, pp 99–105

    Google Scholar 

  21. Yoo JW, Chambers E, Mitragotri S (2010) Factors that control the circulation time of nanoparticles in blood: challenges, solutions and future prospects. Curr Pharm Des 16(21):2298–2307

    Article  Google Scholar 

  22. Tripathi D, Anwar Bég O (2014) A study on peristaltic flow of nanofluids: application in drug delivery systems. Int J Heat Mass Trans 70:61–70

    Article  Google Scholar 

  23. Nadeem S, Ijaz S (2015) Theoretical analysis of metallic nanoparticles on blood flow through stenosed artery with permeable walls. Phys Lett A 379:542–554

    Article  Google Scholar 

  24. Harris DL, Graffagnini MJ (2007) Nanomaterials in medical devices: a snapshot of markets, technologies and companies. Nanotechnol Law Bus Winter 4:415–422

    Google Scholar 

  25. Fullstone G, Wood J, Holcombe M, Battaglia G (2015) Modelling the transport of nanoparticles under blood flow using an agent-based approach. Nat Sci Rep 5(10649):1–13

    Google Scholar 

  26. Tan J, Thomas A, Liu Y (2012) Influence of red blood cells on nanoparticle targeted delivery in microcirculation. Soft Matter 8:1934–1946

    Article  Google Scholar 

  27. Gentile F, Ferrari M, Decuzzi P (2008) The transport of nanoparticles in blood vessels: the effect of vessel permeability and blood rheology. Ann Biomed Eng 36(2):254–261

    Article  Google Scholar 

  28. Ali N, Zaman A, Sajid M, Nietoc JJ, Torres A (2015) Unsteady non-Newtonian blood flow through a tapered overlapping stenosed catheterized vessel. Math Bio sci 269:94–103

    Article  MathSciNet  Google Scholar 

  29. Burton AC (1966) Physiology and biophysics of the circulation, Introductory text. Year Book Medical Publisher, Chicago

    Google Scholar 

  30. Ling SC, Atabek HB (1972) A nonlinear analysis of pulsatile flow in arteries. J Fluid Mech 55:493–511

    Article  Google Scholar 

  31. Hoffmann KA, Chiang ST (2000) Computational Fluid Dynamics. Engineering Edition System, Wichita

    Google Scholar 

  32. Rana P, Bhargava R, Anwar Beg O (2013) Finite element simulation of unsteady MHD transport phenomena on a stretching sheet in a rotating nanofluid. Proc. IMECHE- Part N. J Nanoeng Nanosyst 227:77–99

    Google Scholar 

  33. Bhargava R, Sharma S, Anwar Bég O, Zueco J (2010) Finite element study of nonlinear two-dimensional deoxygenated biomagnetic micropolar flow. Commun Nonlinear Sci Numer Simul 15:1210–1233

    Article  MathSciNet  Google Scholar 

  34. Anwar Bég O, Bég Tasveer A, Bhargava R, Rawat S, Tripathi D (2012) Finite element study of pulsatile magneto-hemodynamic non-Newtonian flow and drug diffusion in a porous medium channel. J Mech Med Biol 12:1250081.1–1250081.26

    Google Scholar 

  35. Zaman Akbar, Ali Nasir, Anwar Bég O (2015) Numerical simulation of unsteady micropolar hemodynamics in a tapered catheterized artery with a combination of stenosis and aneurysm. Med Biol Eng Comput. https://doi.org/10.1007/s11517-015-1415-3

    Article  Google Scholar 

  36. Zaman A, Ali N, Sajid M, Hayat T (2016) Numerical and analytical study of two-layered unsteady blood flow through catheterized artery. PLoS ONE 11(8):e0161377. https://doi.org/10.1371/journal.pone.0161377

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. Zaman.

Additional information

Technical Editor: Cezar Negrao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zaman, A., Khan, A.A. & Ali, N. Modeling of unsteady non-Newtonian blood flow through a stenosed artery: with nanoparticles. J Braz. Soc. Mech. Sci. Eng. 40, 307 (2018). https://doi.org/10.1007/s40430-018-1230-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40430-018-1230-5

Keywords

Navigation