Study of magnetic blood flow through a curved vessel with a stenosis and aneurysm: An explicit finite difference approach

Document Type : Original Paper


1 Department of Mathematics, Faculty of Basic Science, Shahid Shamsipour Technical College, Technical and Vocational University, Tehran, Iran

2 Department of Mathematics, Faculty of Basic Science, Central branch of Islamic Azad University, Tehran, Iran


We carried out an analysis to investigate the effect of magnetic field on the pulsatile blood flow characteristics in a tapered artery. The main reason for considering the magnetic field in the presented model is that the blood flow conducts electricity and it is experimentally proved that the streaming of the blood flow can be affected significantly in the presence of the magnetic field. To simulate the realistic conditions of the human body, the artery wall has been assumed to be tapered and elastic with a combination of stenosis and aneurysm. The considered non-Newtonian model is characterized by the Cross fluid to describe the rheology of the blood flow. The governing PDE is solved numerically by utilizing the finite difference method. The effects of distinct parameters including aneurysm, stenosis, pulsatile nature of the blood flow and magnetic field on the blood flow velocity, volumetric flow rate and resistance impedance are presented by their representation graphs.


Main Subjects

[1] Antiga, L. and D.A. Steinman, Rethinking turbulence in blood, Biorheology, 46(2) (2009) 77–81.
[2] Chakravarty, S. and P.K. Mandal, Two-dimensional blood flow through tapered arteries under stenotic conditions, International Journal of Non-Linear Mechanics, 35(5) (2000) 779–793.
[3] Chen, P., van Sloun, R.J., Turco, S., Wijkstra, H., Filomena, D., Agati, L., Houthuizen, P. and Mischi, M., Blood flow patterns estimation in the left ventricle with low-rate 2D and 3D dynamic contrast-enhanced ultrasound, Computer Methods
and Programs in Biomedicine, 198 (2021) 105810.
[4] Dutra, R.F., Zinani, F.S.F., Rocha, L.A.O. and Biserni, C., Effect of non-Newtonian fluid rheology on an arterial bypass graft: A numerical investigation guided by constructal design, Computer Methods and Programs in Biomedicine, 201 (2021) 105944.
[5] Foong, L.K., Zarringhalam, M., Toghraie, D., Izadpanahi, N., Yan, S.R. and Rostami, S., Numerical study for blood rheology inside an artery: The effects of stenosis and radius on the flow behavior, Computer methods and programs in biomedicine, 193 (2020) 105457.
[6] Haghighi, A., N. Aliashrafi, and M. Kiyasatfar, Mathematical Modeling of Micropolar Blood Flow in a Stenosed Artery Under the Body Acceleration and Magnetic Field, International Journal of Industrial Mathematics, 11(1) (2019) 1–10.
[7] Haghighi, A.R., and M.S. Asl, A Mathematical modeling of a two layered blood flow through constricted vesselsof. Journal of Advanced Mathematical Modeling, 3(1) (2013) 79–99.
[8] Haghighi, A.R. and N. Aliashrafi, A mathematical modeling of pulsatile blood flow through a stenosed artery under effect of a magnetic field, Journal of Mathematical Modeling, 6(2) (2018) 149–164.
[9] Haghighi, A.R. and N. Pirhadi, A numerical study of heat transfer and flow characteristics of pulsatile blood flow in a tapered artery with a combination of stenosis and aneurysm, International Journal of Heat and Technology, 37(1) (2019) 11–21.
[10] Haghighi, A.R., N. Aliashrafi, and M.S. Asl, An implicit approach to the micropolar fluid model of blood flow under the effect of body acceleration, Mathematical Sciences, 14(3) (2020) 269–277.
[11] Hasan, M., B.P. Patel, and S. Pradyumna, Influence of cross‐sectional velocity profile on flow characteristics of arterial wall modeled as elastic and viscoelastic material, International Journal for Numerical Methods in Biomedical Engineering,
37 (2021) e3454.
[12] Hatami, M., J. Hatami, and D.D. Ganji, Computer simulation of MHD blood conveying gold nanoparticles as a third grade non-Newtonian nanofluid in a hollow porous vessel, Computer methods and programs in biomedicine, 113(2) (2014) 632–641.
[13] Ichioka, S., Minegishi, M., Iwasaka, M., Shibata, M., Nakatsuka, T., Harii, K., Kamiya, A. and Ueno, S., High‐intensity static magnetic fields modulate skin microcirculation and temperature in vivo, Bioelectromagnetics: Journal of the Bioelectromagnetics Society, The Society for Physical Regulation in Biology and Medicine, The European Bioelectromagnetics Association, 21(3) (2000) 183–188.
[14] Ikbal, M.A., Chakravarty, S., Wong, K.K., Mazumdar, J. and Mandal, P.K., Unsteady response of non-Newtonian blood flow through a stenosed artery in magnetic field, Journal of Computational and Applied Mathematics, 230(1) (2009) 243–259.
[15] Jafari, A., Zamankhan, P., Mousavi, S.M. and Kolari, P., Numerical investigation of blood flow. Part II: In capillaries, Communications in Nonlinear Science and Numerical Simulation, 14(4) (2009) 1396–1402.
[16] Jamil, D.F., Saleem, S., Roslan, R., Al-Mubaddel, F.S., Rahimi-Gorji, M., Issakhov, A. and Din, S.U., Analysis of non-Newtonian Magnetic Casson Blood Flow in an Inclined Stenosed Artery using Caputo-Fabrizio Fractional Derivatives, Computer Methods and Programs in Biomedicine, 203 (2021) 106044.
[17] Kamangar, S., Badruddin, I.A., Ahamad, N.A., Govindaraju, K., Nik-Ghazali, N., Ahmed, N.J., Badarudin, A. and Khan, T.M. The influence of geometrical shapes of stenosis on the blood flow in stenosed artery, Sains Malaysiana, 46(10) (2017)
[18] Long, Q., Xu, X.Y., Ramnarine, K.V. and Hoskins, P., Numerical investigation of physiologically realistic pulsatile flow through arterial stenosis, Journal of Biomechanics, 34(10) (2001) 1229–1242.
[19] Lopes, D., Puga, H., Teixeira, J. and Lima, R., Blood flow simulations in patientspecific geometries of the carotid artery: A systematic review, Journal of Biomechanics, 111 (2020) 110019.
[20] Maiti, S., S. Shaw, and G. Shit, Fractional order model for thermochemical flow of blood with Dufour and Soret effects under magnetic and vibration environment, Colloids and Surfaces B: Biointerfaces, 197 (2021) 111395.
[21] Mandal, P.K., An unsteady analysis of non-Newtonian blood flow through tapered arteries with a stenosis, International Journal of Non-Linear Mechanics, 40(1) (2005) 151–164.
[22] Mehmood, O.U., N. Mustapha, and S. Shafie, Unsteady two-dimensional blood flow in porous artery with multi-irregular stenoses, Transport in porous media, 92(2) (2012) 259–275.
[23] Mekheimer, K.S. and M. El Kot, Influence of magnetic field and Hall currents on blood flow through a stenotic artery, Applied Mathematics and Mechanics, 29(8)(2008) 1093.
[24] Mojarab, A. and R. Kamali, Design, optimization and numerical simulation of a MicroFlow sensor in the realistic model of human aorta, Flow Measurement and Instrumentation, 74 (2020) 101791.
[25] Pincombe, B. and J. Mazumdar, The effects of post-stenotic dilatations on the flow of a blood analogue through stenosed coronary arteries, Mathematical and Computer Modelling, 25(6) (1997) 57–70.
[26] Pincombe, B., J. Mazumdar, and I. Hamilton-Craig, Effects of multiple stenoses and post-stenotic dilatation on non-Newtonian blood flow in small arteries, Medical & biological engineering & computing, 37(5) (1999) 595–599.
[27] Shah, N.A., D. Vieru, and C. Fetecau, Effects of the fractional order and magnetic field on the blood flow in cylindrical domains, Journal of Magnetism and Magnetic Materials, 409 (2016) 10–19.
[28] Shit, G. and M. Roy, Pulsatile flow and heat transfer of a magneto-micropolar fluid through a stenosed artery under the influence of body acceleration, Journal of Mechanics in Medicine and Biology, 11(03) (2011) 643–661.
[29] Sun, P., S. Bozkurt, and E. Sorguven, Computational analyses of aortic blood flow under varying speed CF-LVAD support, Computers in Biology and Medicine, 127 (2020) 104058.
[30] Tzirtzilakis, E., A mathematical model for blood flow in magnetic field, Physics of fluids, 17(7) (2005) 077103.
[31] Varshney, G., V. Katiyar, and S. Kumar, Effect of magnetic field on the blood flow in artery having multiple stenosis: a numerical study, International Journal of Engineering, Science and Technology, 2(2) (2010) 967–82.
[32] Wong, K.K.L., Tu, J., Mazumdar, J. and Abbott, D., Modelling of blood flow resistance for an atherosclerotic artery with multiple stenoses and poststenotic dilatations, ANZIAM Journal, 51 (2009) 66–82.
[33] Yan, S.R., Zarringhalam, M., Toghraie, D., Foong, L.K. and Talebizadehsardari, P., Numerical investigation of non-Newtonian blood flow within an artery with cone shape of stenosis in various stenosis angles, Computer methods and programs in biomedicine, 192 (2020) 105434.
[34] Zaman, A. and A.A. Khan, Time dependent non-Newtonian nano-fluid (blood) flow in w-shape stenosed channel; with curvature effects, Mathematics and Computers in Simulation, 181 (2021) 82–97.
[35] Zaman, A., Ali, N., Bég, O.A. and Sajid, M., Heat and mass transfer to blood flowing through a tapered overlapping stenosed artery, International Journal of Heat and Mass Transfer, 95 (2016) 1084–1095.
[36] Zaman, A., N. Ali, and M. Sajid, Numerical simulation of pulsatile flow of blood in a porous-saturated overlapping stenosed artery, Mathematics and Computers insimulation, 134 (2017) 1–16.
[37] Zaman, A., N. Ali, and O.A. Beg, Numerical simulation of unsteady micropolar hemodynamics in a tapered catheterized artery with a combination of stenosis and aneurysm, Medical & biological engineering & computing, 54(9) (2016) 1423–1436.
Volume 11, Issue 4 - Serial Number 4
December 2021
Pages 712-726
  • Receive Date: 12 June 2021
  • Revise Date: 27 September 2021
  • Accept Date: 30 November 2021
  • First Publish Date: 15 December 2021