Skip to main content
SpringerLink
Log in

Influence of Electromagnetic Field and Thermal Radiation on Pulsatile Blood Flow with Nanoparticles in a Constricted Porous Artery

  • Original Paper
  • Published:
International Journal of Applied and Computational Mathematics Aims and scope Submit manuscript

Abstract

A theoretical model is proposed to investigate the coupled effects of thermal radiation and electromagnetic field on the blood flow in a stenosed tapered artery. Here, blood is treated as a non-Newtonian Jeffrey fluid model which includes magnetic particles. The magneto-hydrodynamic flow is pulsatile, and exhibits slip velocity at the complaint wall. The flow medium consists of a cylindrical rigid tube with porous medium that is subjected to periodic body acceleration, transverse external magnetic field and applied electric field in the axial direction. Assuming the existence of mild stenosis, a set of flow governing equations is solved using integral transform method. Further, exact solutions are computed for non-dimensional temperature and velocity profiles of fluid and particles. Additionally, equations for different flow characteristics such as wall shear stress, volumetric flow rate, and flow resistance are derived and discussed through graphical illustrations. Results demonstrate that the temperature of blood increases with the increase of heat absorption coefficient and time. However, the temperature decreases with the increase of radiation number and Peclet number. While the velocity profile is directly proportional to the Grashof number and heat absorption coefficient, it is inversely proportional to the radiation number and Peclet number. The applied electric field diminishes the magnitude of fluid’s flow resistance, but it increases with the increase of the magnetic field strength. By combining heat radiation with electromagnetic field, this study contributes to new insights to the physical properties of blood.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Data availibility

All the data used for the numerical simulations and comparison purpose have been calculated through MATLAB software and visualized in the graphical illustrations and nothing is left.

References

  1. Young, D.F.: Effect of a time-dependent stenosis on flow through a tube. J. Eng. Ind. 90, 258 (1968)

    Article  Google Scholar 

  2. Young, D.F., Tsai, F.Y.: Flow characteristics in models of arterial stenosis II Unsteady flow. J. Biomech. 6, 547 (1973)

    Article  Google Scholar 

  3. Ahmed, S.A., Giddens, D.P.: Pulsatile poststenotic flow studies with laser Doppler anemometry. J. Biomech. 17, 695 (1984)

  4. Ponalagusamy, R.: Analysis of pulsatile blood flow through stenosed arteries and its applications to cardiovascular diseases. In: Proceedings of 13th National Conference on Fluid Mechanics and Fluid power, p. 463 (1984)

  5. Mehrotra, R., Jayaraman, G., Padmanabhan, N.: Pulsatile blood flow in a stenosed artery-a theoretical model. Med. Biol. Eng. Comput. 23, 55 (1985)

    Article  Google Scholar 

  6. Tu, C., Deville, M., Dheur, L., Vanderschuren, L.: Finite element simulation of pulsatile flow through arterial stenosis. J. Biomech. 25, 1141 (1992)

    Article  Google Scholar 

  7. Casson, N.A.: A flow equation for pigment-oil suspensions of the printing ink type. In: Mill, C.C. (ed.) Rheology of Disperse Systems, p. 84. Pergamon Press, Oxford (1959)

  8. Ponalagusamy, R., Kawahara, M.: A finite element analysis of laminar unsteady flow of viscoelastic fluids through channels with non-uniform cross-sections. Int. J. Numer. Methods Fluids 9, 1487 (1989)

    Article  MATH  Google Scholar 

  9. Luo, X.Y., Kuang, Z.B.: Non-Newtonian flow patterns associated with an arterial stenosis. J. Biomech. Eng. 114, 512 (1992)

    Article  Google Scholar 

  10. Jeong, W.W., Rhee, K.: Effects of surface geometry and non-Newtonian viscosity on the flow field in arterial stenoses. J. Mech. Sci. Technol. 23, 2424 (2009)

    Article  Google Scholar 

  11. Ponalagusamy, R., Tamil Selvi, R., Banerjee, A.K.: Mathematical model of pulsatile flow of non-Newtonian fluid in tube of varying cross-sections and its implications to blood flow. J. Franklin Inst. 349, 1681 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  12. Priyadharshini, S., Ponalagusamy, R.: Biorheological model on flow of Herschel-Bulkley fluid through a tapered arterial stenosis with dilatation. Appl. Bionics Biomech. 406195 (2015)

  13. Haldar, K., Ghosh, S.N.: Effect of a magnetic field on blood flow through an indented tube in the presence of erythrocytes. Indian J. Pure Appl. Math 25, 345 (1994)

    MATH  Google Scholar 

  14. Tzirtzilakis, E.E.: A mathematical model for blood flow in a magnetic field. Phys. Fluids 17, 077103 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  15. Bhargava, R., Rawat, S., Takhar, H.S., Beg, O.A.: Pulsatile magneto-biofluid flow and mass transfer in a non-Darcian porous medium channel. Meccanica 42, 247 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  16. Bali, R., Awasthi, U.: Effect of a magnetic field on the resistance to blood flow through stenotic artery. Appl. Math. Comput. 188, 1635 (2007)

    MathSciNet  MATH  Google Scholar 

  17. Bali, R., Awasthi, U.: Mathematical model of blood flow in small vessel in the presence of magnetic field. Appl. Math. 2, 264 (2011)

    Article  MathSciNet  Google Scholar 

  18. Sakamoto, K., Kanai, H.: Electrical characteristics of flowing blood. IEEE Trans. Biomed. Eng. 12, 686 (1979)

    Article  Google Scholar 

  19. Kinouchi, Y., Yamaguchi, H., Tenforde, T.S.: Theoretical analysis of magnetic field interactions with aortic blood flow. Bioelectromagn. J. Bioelectromagn. Soc. Soc. Phys. Regul. Biol. Med. Eur. Bioelectromagn. Assoc. 17, 21 (1996)

    Google Scholar 

  20. Jin, H.K., Hwang, T.Y., Cho, S.H.: Effect of electrical stimulation on blood flow velocity and vessel size. Open Med. 12, 5 (2017)

    Article  Google Scholar 

  21. Hart, F.X., Palisano, J.R.: The application of electric fields in biology and medicine. Electric field 161 (2018)

  22. Mirza, I.A., Abdulhameed, M., Vieru, D., Shafie, S.: Transient electro-magneto-hydrodynamic two-phase blood flow and thermal transport through a capillary vessel. Comput. Methods Prog. Biomed. 137, 149 (2016)

    Article  Google Scholar 

  23. Ponalagusamy, R., Manchi, R.: Particle-fluid two phase modeling of electro-magnetohydrodynamic pulsatile flow of Jeffrey fluid in a constricted tube under periodic body acceleration. Eur. J. Mech. B/Fluids 81, 76 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  24. Sud, V.K., Sekhon, G.S.: Arterial flow under periodic body acceleration. Bull. Math. Biol. 47, 35 (1985)

    Article  MATH  Google Scholar 

  25. Sud, V.K., Sekhon, G.S.: Flow through a stenosed artery subject to periodic body acceleration. Med. Biol. Eng. Comput. 25, 638 (1987)

    Article  Google Scholar 

  26. Mishra, J.C., Sahu, B.K.: Flow through blood vessels under the action of a periodic acceleration field: a mathematical analysis. Comput. Math. Appl. 16, 993 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  27. Majhi, S.N., Nair, V.R.: Pulsatile flow of third grade fluids under body acceleration-modelling blood flow. Int. J. Eng. Sci. 32, 839 (1994)

    Article  MATH  Google Scholar 

  28. Mandal, P.K., Chakravarty, S., Mandal, A., Amin, N.: Effect of body acceleration on unsteady pulsatile flow of non-Newtonian fluid through a stenosed artery. Appl. Math. Comput. 189, 766 (2007)

    MathSciNet  MATH  Google Scholar 

  29. Kumar, A.: Mathematical model of blood flow in arteries with porous effects, 6th World Congress of Biomechanics(WCB 2010). IFMBE Proc. 31, 18 (2010)

    Article  Google Scholar 

  30. Sankar, D.S., Nagar, A.K.: Mathematical analysis of blood flow in porous tubes: a comparative study. Hindawi publishing corporation. Adv. Mech. Eng. 2013, 287954 (2013)

    Article  Google Scholar 

  31. Ponalagusamy, R., Priyadharshini, S.: Numerical modeling on pulsatile flow of Casson nanofluid through an inclined artery with stenosis and tapering under the influence of magnetic field and periodic body acceleration. Korea-Australia Rheol. J. 29, 303 (2017)

    Article  Google Scholar 

  32. El-Shehawey, E.F., Elbarbary, E.M.E., Elsayed, M.E., Afifi, N.A.S., Elshahed, M.: MHD flow of an elastico-viscous fluid under periodic body acceleration. Appl. Math. Comput. 138, 479 (2003)

    MathSciNet  MATH  Google Scholar 

  33. Ponalagusamy, R.: Ph.D. thesis (1986)

  34. Priyadharshini, S., Ponalagusamy, R.: A numerical study on unsteady flow of Herschel-Bulkley Nanofluid through an inclined crater with body acceleration and magnetic field. Int. J. App. Comput. Math. 5, 6 (2019)

    Article  Google Scholar 

  35. Priyadharshini, S., Ponalagusamy, R.: An unsteady flow of magnetic nanoparticles as drug carrier suspended in micropolar fluid through a porous tapered arterial stenosis under non-uniform magnetic field and periodic body acceleration. Comput. Appl. Math. 37, 4259 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  36. Ponalagusamy, R., Priyadharshini, S.: Couple stress fluid model for pulsatile flow of blood in a porous tapered arterial stenosis under magnetic field and periodic body acceleration. J. Mech. Med. Biol. 17, 1750109 (2017)

    Article  MATH  Google Scholar 

  37. Ponalagusamy, R., Priyadharshini, S.: Pulsatile MHD flow of a Casson fluid through a porous bifurcated arterial stenosis under periodic body acceleration. App. Math. Comput. 333, 325 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  38. Chato, J.C.: Heat transfer to blood vessels. J. Biomech Eng. 102, 110 (1980)

    Article  Google Scholar 

  39. Ogulu, A., Abbey, T.M.: Simulation of heat transfer on an oscillatory blood flow in an indented porous artery. Int. Commun. Heat Mass Transf. 32, 983 (2005)

    Article  Google Scholar 

  40. Prakash, J., Makinde, O.D.: Radiative heat transfer to blood flow through a stenotic artery in the presence of magnetic field. Latin Am. Appl. Res. 41, 273 (2011)

    Google Scholar 

  41. Shit, G.C., Roy, M.: Pulsatile flow and heat transfer of a magneto-micropolar fluid through a stenosed artery under the influence of body acceleration. J. Mech. Med. Biol. 11, 643 (2011)

    Article  Google Scholar 

  42. Haik, Y., Pai, V., Chen, C.J.: Development of magnetic device for cell separation. J. Magn. Magn. Mater. 194, 254 (1999)

    Article  Google Scholar 

  43. Sharma, S., Singh, U., Katiyar, V.K.: Magnetic field effect on flow parameters of blood along with Magnetic particles in a cylindrical tube. J. Magn. Magn. Mater. 377, 395 (2015)

  44. Ghasemi, S.E., Hatami, M., Sarokolaie, A.K., Ganji, D.D.: Study on blood flow containing nanoparticles through porous arteries in presence of magnetic field using analytical methods. Phys. E Low-Dimens. Syst. Nanostruct. 70, 146 (2015)

    Article  Google Scholar 

  45. Ellahi, R., Rahman, S.U., Nadeem, S., Vafai, K.: The blood flow of Prandtl fluid through a tapered stenosed arteries in permeable walls with magnetic field. Commun. Theor. Phys. 63, 353 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  46. Bhatti, M.M., Zeeshan, A., Ellahi, R.: Endoscope analysis on peristaltic blood flow of Sisko fluid with Titanium magneto-nanoparticles. Comput. Biolo. Med. 78, 29 (2016)

    Article  Google Scholar 

  47. Bhatti, M.M., Zeeshan, A., Ijaz, N.: Slip effects and endoscopy analysis on blood flow of particle-fluid suspension induced by peristaltic wave. J. Mol. Liquids 218, 240 (2016)

    Article  Google Scholar 

  48. Sinha, A., Shit, G.C.: Electromagnetohydrodynamic flow of blood and heat transfer in a capillary with thermal radiation. J. Magn. Magn. Mater. 378, 143 (2015)

    Article  Google Scholar 

  49. Nubar, Y.: Blood flow, slip and viscometry. Biophys. J. 11, 252 (1971)

    Article  Google Scholar 

  50. Brunn, P.: The velocity slip of polar fluids. Rheologica Acta 14, 1039 (1975)

    Article  MATH  Google Scholar 

  51. Ponalagusamy, R.: Blood flow through an artery with mild stenosis: a two-layered model different shapes of stenoses and slip velocity at the wall. J. Appl. Sci. 7, 1071 (2007)

    Article  Google Scholar 

  52. Manjunatha, G., Rajashekhar, C., Vaidya, H., Prasad, K.V., Makinde, O.D., Viharika, J.U.: Impact of variable transport properties and slip effects on MHD Jeffrey fluid flow through channel. Arab. J. Sci. Eng. 45, 417 (2020)

    Article  Google Scholar 

  53. Prasad, K.V., Vaidya, H., Rajashekhar, C., Khan, S.U., Manjunatha, G., Viharika, J.U.: Slip flow of MHD Casson fluid in an inclined channel with variable transport properties. Commun. Theor. Phys. 72, 095004 (2020)

    Article  MathSciNet  Google Scholar 

  54. Vaidya, H., Rajashekhar, C., Prasad, K.V., Khan, S.U., Riaz, A., Viharika, J.U.: MHD peristaltic flow of nanofluid in a vertical channel with multiple slip features: an application cyme movement. Biomech. Model. Mechanobiol. 1, 1047–1067 (2021)

    Article  Google Scholar 

  55. Hayat, T., Ahmad, N., Ali, N.: Effects of an endoscope and magnetic field on the peristalsis involving Jeffrey fluid. Commun. Nonlinear Sci. Numer. Simul. 13, 1581 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  56. Akbar, N.S., Nadeem, S., Ali, M.: Jeffrey fluid model for blood flow through a tapered artery with a stenosis. J. Mech. Med. Biol. 11, 529 (2011)

    Article  Google Scholar 

  57. Akbar, N.S., Nadeem, S., Hayat,T., Hendi, A.A.: Effects of heat and chemical reaction on Jeffrey fluid model with stenosis. Appl. Anal. 91, 1631 (2012)

  58. Ellahi, R., Rahman, S.U., Nadeem, S.: Blood flow of Jeffrey fluid in a catherized tapered artery with the suspension of nanoparticles. Phys. Lett. A 378, 2973 (2014)

    Article  MATH  Google Scholar 

  59. Hussain, Q., Asghar, S., Hayat, T., Alsaedi, A.: Heat transfer analysis in peristaltic flow of MHD Jeffrey fluid with variable thermal conductivity. Appl. Math. Mech.-Engl. Ed. 36, 499 (2016)

    Article  MathSciNet  Google Scholar 

  60. Shit, G.C., Majee, S.: Pulsatile flow of blood and heat transfer with variable viscosity under magnetic and vibration environment. J. Magn. Magn. Mater. 388, 106 (2015)

    Article  Google Scholar 

  61. Ponalagusamy, R.: Particulate suspension Jeffrey fluid flow in a stenosed artery with a particle-free plasma near the wall. Korea-Australia Rheol. J. 28, 217 (2016)

    Article  Google Scholar 

  62. Priyadharshii, S., Ponalagusamy, R.: Computational model on pulsatile flow of blood through a tapered arterial stenosis with radially variable viscosity and magnetic field. Sadhana 42, 1901 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  63. Ratan Shah, S., Kumar, R.: Performance of blood flow with suspension of nanoparticles through tapered stenosed artery for Jeffrey fluid model. Int. J. Nanosci. 17, 1850004 (2018)

    Article  Google Scholar 

  64. Ponalagusamy, R., Tamil Selvi, R.: Influence of magnetic field and heat transfer on two-phase fluid model for oscillatory blood flow in an arterial stenosis. Mecanica 50, 927 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  65. Priyadharshini, S., Ponalagusamy, R.: Mathematical modelling for pulsatile flow of Casson fluid along with magnetic nanoparticles in a stenosed artery under external magnetic field and body acceleration. Neural Comput. Appl. 31, 813 (2019)

    Article  Google Scholar 

  66. Chen, M.M., Holmes, K.R.: Microvascular contributions in tissue heat transfer. Ann. New York Acad. Sci. 335, 137 (1980)

    Article  Google Scholar 

  67. Srinivas, S., Kothandapani, M.: Peristaltic transport in an asymmetric channel with heat transfer: a note. Int. Commun. Heat Mass Transf. 35, 514 (2008)

    Article  MATH  Google Scholar 

Download references

Funding

Not Applicable.

Author information

Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Tiruchirappalli, Tiruchirappalli, India

    R. Tamil Selvi, R. Ponalagusamy & R. Padma

Authors
  1. R. Tamil Selvi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Ponalagusamy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. Padma
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed equally in developing the whole article and granted all the obtained results and revisions. Specifically, Conceptualization and Methodology, RPS, Software and Validation, RT and RP, Writing-Original Draft Preparation, RP, Review and Editing, RT and RPS.

Corresponding author

Correspondence to R. Tamil Selvi.

Ethics declarations

Conflict of interest

The authors declare that they have no conflicts of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Selvi, R.T., Ponalagusamy, R. & Padma, R. Influence of Electromagnetic Field and Thermal Radiation on Pulsatile Blood Flow with Nanoparticles in a Constricted Porous Artery. Int. J. Appl. Comput. Math 7, 216 (2021). https://doi.org/10.1007/s40819-021-01143-x

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40819-021-01143-x

Keywords

Mathematics Subject Classification

Search

Navigation