Engineering

A comprehensive study of magnetohydrodynamic blood flow in a time-invariant porous artery with multi-irregular stenoses

Authors

  • Muhammad Fahim

    International Islamic Univeristy
    Author

  • Muhammad Sajid

    International Islamic University
    Author

  • Nasir Ali

    International Islamic University
    Author

DOI:

https://doi.org/10.71107/qdgekh21

Keywords:

Magnetohydrodynamic Blood flow, Stenosed vessel, Porous medium, Cross fluid, Heat transfer, Mass diffusion, Numerical investigation

Abstract

This work investigates the impacts of mass and heat transport on blood flow in a time-invariant porous saturated artery with multi-irregular-shaped stenoses in an environment with a magnetic field. A generalized Newtonian cross-fluid model is employed to describe the rheological behavior of blood. Nonlinear momentum, energy, and species concentration equations are normalized using dimensionless variables and then solved numerically by executing a finite difference scheme. Various parameters that arise during the normalization process are examined to determine their effects on flow characteristics, including velocity, temperature, and mass diffusion. Our findings demonstrate that both the altitude of stenosis and the magnetic field parameters inhibit blood flow by reducing blood velocity, volume flow rate, wall shear stress, and heat dissipation while increasing flow resistance and concentration profile, with the effects of stenosis with the effects of the stenosis being more prominent than the magnetic field. In contrast, the permeability of the channel increases wall shear stress, velocity, volume flow rate, and temperature by turning down resistance and concentration profiles. Moreover, the Prandtl and Brinkmann numbers play an important role in controlling the temperature and mass distribution. A higher value of the Prandtl number leads to lower temperature distribution, while a greater value of the Brinkmann number causes higher temperature distribution. Unlike temperature, these quantities have opposite effects on the concentration profile. In addition, a higher Schmidt number indicates a higher concentration distribution, while a higher Soret number points out the opposite behavior.

Downloads

Download data is not yet available.

Author Biographies

  • Muhammad Sajid, International Islamic University

    Professor of Mathematics

  • Nasir Ali, International Islamic University

    Professor of Mathematics

References

[1] Young, D. F. (1979). Fluid mechanics of arterial stenoses. DOI: https://doi.org/10.1115/1.3426241

[2] Misra, J. C., & Chakravarty, S. (1986). Flow in arteries in the presence of stenosis. Journal of Biomechanics, 19(11), 907-918. DOI: https://doi.org/10.1016/0021-9290(86)90186-7

[3] Schirmer, C. M., & Malek, A. M. (2012). Computational fluid dynamic characterization of carotid bifurcation stenosis in patient‐based geometries. Brain and behavior, 2(1), 42-52. DOI: https://doi.org/10.1002/brb3.25

[4] Perktold, K., & Peter, R. (1990). Numerical 3D-simulation of pulsatile wall shear stress in an arterial T-bifurcation model. Journal of biomedical engineering, 12(1), 2-12. DOI: https://doi.org/10.1016/0141-5425(90)90107-X

[5] McGinty, S. (2014). A decade of modelling drug release from arterial stents. Mathematical biosciences, 257, 80-90. DOI: https://doi.org/10.1016/j.mbs.2014.06.016

[6] Yilmaz, F., & Gundogdu, M. Y. (2008). A critical review on blood flow in large arteries; relevance to blood rheology, viscosity models, and physiologic conditions. Korea-Australia Rheology Journal, 20(4), 197-211.

[7] Kumar, S., & Diwakar, C. (2013). A mathematical model of power law fluid with an application of blood flow through an artery with stenosis. Advances in Applied Mathematically Bio-Sciences, 4(2), 51-61.

[8] Ali, N., Zaman, A., & Sajid, M. (2014). Unsteady blood flow through a tapered stenotic artery using Sisko model. Computers & Fluids, 101, 42-49. DOI: https://doi.org/10.1016/j.compfluid.2014.05.030

[9] Priyadharshini, S., & Ponalagusamy, R. (2015). Biorheological model on flow of herschel-bulkley fluid through a tapered arterial stenosis with dilatation. Applied Bionics and Biomechanics, 2015. DOI: https://doi.org/10.1155/2015/406195

[10] Akbar, N. S. (2016). Non-Newtonian model study for blood flow through a tapered artery with a stenosis. Alexandria Engineering Journal, 55(1), 321-329. DOI: https://doi.org/10.1016/j.aej.2015.09.010

[11] Subbarayudu, K., Suneetha, S., & Reddy, P. B. A. (2020). The assessment of time dependent flow of Williamson fluid with radiative blood flow against a wedge. Propulsion and Power Research, 9(1), 87-99. DOI: https://doi.org/10.1016/j.jppr.2019.07.001

[12] Rabby, M. G., Razzak, A., & Molla, M. M. (2013). Pulsatile non-Newtonian blood flow through a model of arterial stenosis. Procedia Engineering, 56, 225-231. DOI: https://doi.org/10.1016/j.proeng.2013.03.111

[13] Nadeem, S., & Akbar, N. S. (2010). Simulation of the second grade fluid model for blood flow through a tapered artery with a stenosis. Chinese Physics Letters, 27(6), 068701. DOI: https://doi.org/10.1088/0256-307X/27/6/068701

[14] Ahmad, R., Farooqi, A., Farooqi, R., Hamadneh, N. N., Fayz-Al-Asad, M., Khan, I., ... & Saleem Khan, M. F. (2021). An analytical approach to study the blood flow over a nonlinear tapering stenosed artery in flow of Carreau fluid model. Complexity, 2021, 1-11. DOI: https://doi.org/10.1155/2021/9921642

[15] Adesanya, S. O., Ajala, S. O., & Ayeni, R. O. (2009). A numerical study of the hemodynamics of stenosed artery. Journal of the Nigerian Association of Mathematical Physics, 15.

[16] Kumar, S., Kumar, B. R., Rai, S. K., & Shankar, O. (2023). Effect of rheological models on pulsatile hemodynamics in a multiply afflicted descending human aortic network. Computer Methods in Biomechanics and Biomedical Engineering, 1-28. DOI: https://doi.org/10.1080/10255842.2023.2170714

[17] Barnes, H. A., Hutton, J. F., & Walters, K. (1989). An introduction to rheology (Vol. 3). Elsevier.

[18] Rathod, V. P., & Tanveer, S. (2009). Pulsatile flow of couple stress fluid through a porous medium with periodic body acceleration and magnetic field. Bulletin of the Malaysian Mathematical Sciences Society, 32(2).

[19] Midya, C., Layek, G. C., Gupta, A. S., & Mahapatra, T. R. (2003). Magnetohydrodynamic viscous flow separation in a channel with constrictions. J. Fluids Eng., 125(6), 952-962. DOI: https://doi.org/10.1115/1.1627834

[20] Zaman, A., Ali, N., & Bég, O. A. (2016). Unsteady magnetohydrodynamic blood flow in a porous-saturated overlapping stenotic artery—numerical modeling. Journal of Mechanics in Medicine and Biology, 16(04), 1650049. DOI: https://doi.org/10.1142/S0219519416500494

[21] Awrejcewicz, J., Zafar, A. A., Kudra, G., & Riaz, M. B. (2020). Theoretical study of the blood flow in arteries in the presence of magnetic particles and under periodic body acceleration. Chaos, Solitons & Fractals, 140, 110204. DOI: https://doi.org/10.1016/j.chaos.2020.110204

[22] Mishra, B. K., & Shekhawat, S. S. (2007). Magnetic effect on blood flow through a tapered artery with stenosis. ACTA CIENCIA INDICA MATHEMATICS, 33(2), 295.

[23] Abbas, Z., Shabbir, M. S., & Ali, N. (2018). Numerical study of magnetohydrodynamic pulsatile flow of Sutterby fluid through an inclined overlapping arterial stenosis in the presence of periodic body acceleration. Results in Physics, 9, 753-762. DOI: https://doi.org/10.1016/j.rinp.2018.03.020

[24] Eldesoky, I. M., Kamel, M. H., Hussien, R. M., & Abumandour, R. M. (2013). Numerical study of unsteady MHD pulsatile flow through porous medium in an artery using generalized differential quadrature method (GDQM). International Journal of Materials, Mechanics and Manufacturing, 1(2), 200-206. DOI: https://doi.org/10.7763/IJMMM.2013.V1.43

[25] Caro, C. G., Fitz-Gerald, J. M., & Schroter, R. C. (1971). Atheroma and arterial wall shear-observation, correlation and proposal of a shear dependent mass transfer mechanism for atherogenesis. Proceedings of the Royal Society of London. Series B. Biological Sciences, 177(1046), 109-133. DOI: https://doi.org/10.1098/rspb.1971.0019

[26] Ethier, C. R. (2002). Computational modeling of mass transfer and links to atherosclerosis. Annals of biomedical engineering, 30, 461-471. DOI: https://doi.org/10.1114/1.1468890

[27] Back, L. H., Radbill, J. R., & Crawford, D. W. (1977). Analysis of oxygen transport from pulsatile, viscous blood flow to diseased coronary arteries of man. Journal of biomechanics, 10(11-12), 763-774. DOI: https://doi.org/10.1016/0021-9290(77)90090-2

[28] Charm, S., Paltiel, B., & Kurland, G. S. (1968). Heat transfer coefficients in blood flow. Biorheology, 5(2), 133-145. DOI: https://doi.org/10.3233/BIR-1968-5205

[29] Sharma, P. R., Ali, S., & Katiyar, V. K. (2011). Mathematical modeling of heat transfer in blood flow through stenosed artery. Journal of Applied Sciences Research, 7(1), 68-78.

[30] Sinha, A., Misra, J. C., & Shit, G. C. (2016). Effect of heat transfer on unsteady MHD flow of blood in a permeable vessel in the presence of non-uniform heat source. Alexandria Engineering Journal, 55(3), 2023-2033. DOI: https://doi.org/10.1016/j.aej.2016.07.010

[31] Zaman, A., Ali, N., Bég, O. A., & Sajid, M. (2016). Heat and mass transfer to blood flowing through a tapered overlapping stenosed artery. International Journal of Heat and Mass Transfer, 95, 1084-1095. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2015.12.073

[32] Abd-Alla, A. M., Abo-Dahab, S. M., Thabet, E. N., Bayones, F. S., & Abdelhafez, M. A. (2023). Heat and mass transfer in a peristaltic rotating frame Jeffrey fluid via porous medium with chemical reaction and wall properties. Alexandria Engineering Journal, 66, 405-420. DOI: https://doi.org/10.1016/j.aej.2022.11.016

[33] Dada, M. S., & Alamu-Awoniran, F. (2020). Heat and mass transfer in micropolar model for blood flow through a stenotic tapered artery. Applications and Applied Mathematics: An International Journal (AAM), 15(2), 24.

[34] Nakayama, A., & Kuwahara, F. (2008). A general bioheat transfer model based on the theory of porous media. International Journal of Heat and Mass Transfer, 51(11-12), 3190-3199. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2007.05.030

[35] Nasha, V., & Kumar, S. (2021). MHD Two-layered blood flow under effect of heat and mass transfer in stenosed artery with porous medium.

[36] Kumawat, C., Sharma, B. K., Al-Mdallal, Q. M., & Rahimi-Gorji, M. (2022). Entropy generation for MHD two phase blood flow through a curved permeable artery having variable viscosity with heat and mass transfer. International Communications in Heat and Mass Transfer, 133, 105954. DOI: https://doi.org/10.1016/j.icheatmasstransfer.2022.105954

[37] Wang, X., Qiao, Y., Qi, H., & Xu, H. (2022). Numerical study of pulsatile non-Newtonian blood flow and heat transfer in small vessels under a magnetic field. International Communications in Heat and Mass Transfer, 133, 105930. DOI: https://doi.org/10.1016/j.icheatmasstransfer.2022.105930

Downloads

Published

2026-05-08

Data Availability Statement

All relevant data supporting the findings of this study are included in the manuscript.

Issue

Vol. 2 No. 1 (2026): Conclusions in Engineering

Section

Articles

License

Copyright (c) 2026 Muhammad Fahim, Muhammad Sajid, Nasir Ali (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

A comprehensive study of magnetohydrodynamic blood flow in a time-invariant porous artery with multi-irregular stenoses. (2026). Conclusions in Engineering, 2(1), 63-76. https://doi.org/10.71107/qdgekh21

Similar Articles

You may also start an advanced similarity search for this article.