Finite Element Analysis of Biomagnetic Fluid Flow in a Channel with an Overlapping Stenosis


  • Normazni Abdullah Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
  • Zuhaila Ismail Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia



FEM, BFD, Overlapping stenosis, Blood flow


Analysis of biomagnetic fluid (blood) flow (BFD) is important due to the potential biomedical applications that have been proposed such as cell separation for magnetic devices, drug delivery using magnetic particles for the treatment of cancer tumours, hyperthermia, and the reduction of bleeding during surgeries. In this study, the effects of spatially varying magnetic field on a straight channel with an overlapping stenosis is investigated numerically using finite element method (FEM). The mathematical model of biomagnetic fluid is constructed based on the coupled study of Navier-Stokes equations with the principles of ferrohydrodynamic (FHD). While the flow in a constricted artery is considered to be Newtonian, steady, two-dimensional and isothermal. Galerkin finite element method is used to discretize the governing equations and then the source code is developed by using MATLAB software. The source code is validated, and the results is compared with the previous literature. Based on the findings, the introduction of magnetic field alters the behaviour of blood flow in the area near the magnetic source. The increment of magnetic field intensity near stenosis area causes the recirculation area downstream to become smaller. This could be seen from the velocity profile and streamline pattern of constricted artery.


Reddy, K. S., & Yusuf, S. (1998). Emerging epidemic of cardiovascular disease in developing countries. Circulation, 97(6), 596-601.

Hajar, R. (2017). Risk factors for coronary artery disease: historical perspectives. Heart views: The official journal of the Gulf Heart Association, 18(3), 109.

Tegos, T. J., Kalodiki, E., Sabetai, M. M., & Nicolaides, A. N. (2001). The genesis of atherosclerosis and risk factors: A review. Angiology, 52(2), 89-98.

Srivastava, V. P. (1995). Arterial blood flow through a nonsymmetrical stenosis with applications. Japanese Journal of Applied Physics, 34, 6539.

Kasiman, E. H. (2012). Mixed formulations for Navier Stokes equations with magnetic effect in rectangular channel. MEng Thesis, Universiti Teknologi Malaysia, Skudai.

Tzirtzilakis, E. E. (2005). A mathematical model for blood flow in magnetic field. Physics of Fluids, 17, 1-15.

Loukopoulos, V. C., & Tzirtzilakis, E. E. (2004). Biomagnetic channel flow in spatially varying magnetic field. International Journal of Engineering Science, 42(5-6), 571-590.

Reddy, K., Reddy, M., & Reddy, R. (2011). Mathematical model governing magnetic field effect on bio magnetic fluid flow and orientation of red blood cells. Pac.-Asian J. Math, 5, 344-356.

Tzirakis, K., Papaharilaou, Y., Giordano, D., & Ekaterinaris, J. (2014). Numerical investigation of biomagnetic fluids in circular ducts. International Journal for Numerical Methods in Biomedical Engineering, 30(3), 297-317.

Jamalabadi, M. Y. A., Daqiqshirazi, M., Nasiri, H., Safaei, M. R., & Nguyen, T. K. (2018). Modeling and analysis of biomagnetic blood Carreau fluid flow through a stenosis artery with magnetic heat transfer: A transient study. PloS one, 13(2), 42-51.

Higashi, T., Yamagishi, A., & Takeuchi. A. (1993). Orientation of erythrocytes in a strong static magnetic field. Blood, 82(4), 1328-1334.

Haik, Y., Chen, J. C., & Pai, V. M. (1996). Development of bio-magnetic fluid dynamics. In Proceedings of the Ninth International Symposium on Transport Properties in Thermal Fluid Engineering, 25-28.

Pauling, L., & Coryell, C. D. (1936). The magnetic properties and structure of hemoglobin, oxyhemoglobin and carbonmonoxyhemoglobin. Proceedings of the National Academy of Sciences, 22(4), 210-216.

Loukopoulos, V. C., Bourantas, G. C., Labropoulos, D., & and Spa, V. N. (2016). Numerical study of magnetic particles concentration in biofluid (blood) under the influence of high gradient magnetic field in microchannel. In 7th European Congress on Computational Methods in Applied Sciences and Engineering: ECCOMAS Congress, 1084-1092.

Rosensweig, R. E. (1985). Ferrohydrodynamics. Cambridge University Press Cambridge. New York, Melbourne.

Yamada, Y., Yoshimura, N., & Sakurai, T. (1968). Plastic stress-strain matrix and its application for the solution of elastic-plastic problems by the finite element method. International Journal of Mechanical Sciences, 10(5), 343-354.

Babuška, I., Andersson, B., Guo, B., Melenk, J., & Oh, H. (1996). Finite element method for solving problems with singular solutions. Journal of Computational and Applied Mathematics, 74(1-2), 51-70.

Formaggia, L., Lamponi, D., & Quarteroni, A. (2003). One-dimensional models for blood flow in arteries. Journal of Engineering Mathematics, 47(3), 251-276.

de Souza, M. M., & Manica, C. C. (2017). Leray-deconvolution model to Navier–Stokes equations by finite element. Computational and Applied Mathematics, 36(3), 1161-1172.

Wei, F., Westerdale, J., McMahon, E. M., Belohlavek, M., & Heys, J. (2012). Weighted least-squares finite element method for cardiac blood flow simulation with echocardiographic data. Computational and Mathematical Methods in Medicine, 2012.

Zain, N. M., & Ismail, Z. (2017). Modelling of Newtonian blood flow through a bifurcated artery with the presence of an overlapping stenosis. Malaysian Journal of Fundamental Applied Sciences, 13(2017), 304-309.

Achaba, L., Mahfouda, M., & Benhadida, S. (2016). Numerical study of the non-Newtonian blood flow in a stenosed artery using two rheological models. Thermal Science, 20(2), 449-460.

Bazilevs, Y., Zhang, Y., Calo, V. M., Goswami, S., Bajaj, C. L., & Hughes, T. J. (2018). Isogeometric analysis of blood flow: A NURBS-based approach. In Computational Modelling of Objects Represented in Images (pp. 91-96): CRC Press.

Tzirtzilakis, E. E., & Xenos, M. A. (2013). Biomagnetic fluid flow in a driven cavity. Meccanica, 48(1), 187-200.

Abdullah, N., Ismail, Z., Halifi, A. S., Ayob, A. R., Kasiman, E. H., & Amin, N. S. (2020). Numerical computations of biomagnetic fluid flow in a lid driven cavity. CFD Letters, 12(4), 43-53.