Experimental Validation of Fractionalized Maxwell Fluid Model of MHD Blood Flow through Bifurcated Arteries for Tumor Treatments
Article Sidebar
Page Numbers:
756-776
Digital Object Identifier:
10.58578/mjms.v3i3.7338
Viewed: 152 times
Downloaded: 84 times
LYAS Publisher cordially invites qualified professionals to serve as Editors or Reviewers. Your expertise will make an important contribution to maintaining and strengthening the academic quality of our publications. Interested applicants are kindly requested to complete the application form at the following link: Editors & Reviewers
Please feel free to contact us if you need any further information about the submission process or if you have any additional questions.
Authors:
Mohammed Gazali Abdulhamid1, Abubakar Mohammed2, Isah Abdullahi3*, Nafisatu Usman4 
Copyright :
Authors retain copyright and grant the journal right of first publication.
Main Article Content
Abstract
This study provides an experimental validation of a fractionalized Maxwell fluid model to describe magnetohydrodynamic (MHD) blood flow in bifurcated arteries, with targeted applications in tumor therapy. By incorporating fractional calculus, the model captures viscoelastic memory effects that account for key non-Newtonian properties of blood, including shear-thinning behavior, elastic recovery, and time-dependent stress relaxation under combined electromagnetic and thermal influences. The Homotopy Perturbation Method (HPM) was employed to derive approximate analytical solutions for the governing equations, and the model’s predictions were benchmarked against existing theoretical and experimental data. Numerical simulations indicate that the fractional Maxwell model outperforms classical models in predicting velocity profiles, thermal distributions during hyperthermia treatment, and nanoparticle concentration relevant to drug delivery. The model consistently yields lower mean square errors, demonstrating enhanced accuracy and robustness. These results validate the efficacy of fractional-order modeling in hemodynamic simulations and underscore its clinical potential in improving hyperthermia-based cancer therapies and nanoparticle-mediated drug delivery strategies in complex arterial geometries.
Citation Metrics:
Downloads
Article Details
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
References
Y. Zhang, Y. Peng, J. Gao, Y. Bai, D. Sun, X. Sun, and B. Lv, “Analysis of periodic pulsating blood flow of fractional Maxwell power-law fluid in carotid artery with elastic vessel wall,” Comput. Methods Biomech. Biomed. Engin., vol. 27, no. 13, pp. 1845–1857, Oct. 2024. DOI available via PubMed record.
P. Perdikaris and G. E. Karniadakis, “Fractional-order viscoelasticity in one-dimensional blood flow models,”Ann. Biomed. Eng., vol. 42, no. 5, pp. 1012–1023, May 2014. DOI: 10.1007/s10439-014-0970-3.
H. Ali, A. M. Megahed, and A. Alzahrani, “Study of non-Newtonian biomagnetic blood flow in a stenosed bifurcated artery having elastic walls,” Sci. Rep., vol. 11, Art. no. 22648, Dec. 2021. DOI not found.
R. Ellahi, M. Ayaz, M. Raza, and T. Hayat, “Effect of heat and mass transfer and magnetic field on peristaltic flow of a fractional Maxwell fluid in a tube,” Math. Probl. Eng., vol. 2021, Art. no. 9911820, pp. 1–12, 2021. DOI: 10.1155/2021/9911820.
J. Jain, M. Sharma, and R. Singh, “Mathematical modelling of blood flow in a stenosed artery under MHD effect through porous medium” Int. J. Eng. Trans. B: Appl., vol. 23, 2010..
E. E. Tzirtzilakis, “A mathematical model for blood flow in magnetic field,” Phys. Fluids, vol. 17, no. 7, 2005. DOI not available.
T. Hayat, M. Qasim, and Z. Abbas, “Peristaltic motion of a Burger’s fluid in a porous medium with heat and mass transfer,”Int. J. Heat Mass Transf., vol. 54, 2011. DOI not available.
J. H. He, “Homotopy perturbation technique,” Comput. Methods Appl. Mech. Eng., vol. 178, 1999.
I. A. Mirza, M. Abdulhameed, and S. Shafie, “Magnetohydrodynamic approach of non-Newtonian blood flow with magnetic particles in stenosed artery,” Appl. Math. Mech., vol. 38, no. 3, 2017.
R. Rodrigues, F. J. Galindo-Rosales, and L. Campo-Deaño, "Magnetorheological characterization of blood analogues seeded with paramagnetic particles," arXiv preprint arXiv:2504.09194, Apr. 2025.
J. Escandon “Transient electroosmotic flow of Maxwell fluids in a slit microchannel with asymmetric zeta potentials,” Eur. J. Mech. B/Fluids, vol. 53, pp. 180–189, 2015.
S. Kumari, R. Rathee, and J. Nandal, “Unsteady peristaltic transport of MHD fluid through an inclined stenosed artery with slip effect,” Int. J. Appl. Eng. Res., vol. 14, no. 8, pp. 1881–1891, 2019.
E. Omamoke and E. Amos, “Treatment and slip effect on MHD blood flow through a stenotic artery: A mathematical model,” Asian Res. J. Math., vol. 19, no. 6, pp. 61–76, 2023.
D. Kumar, Satyanarayana, B., Rajesh K, Narendra, D., & Sanjeev, K. (2021). Application of heat source and chemical reaction in magnetohydrodynamic blood flow through permeable bifurcated arteries with inclined magnetic field in tumor treatments. Journal of result in applied Mathematics.10(2021)100151,1-13.
D. G. Yakubu, I. Abdullahi, and A. Musa, "The dynamic flow of ternary nanofluids with magnetic nanoparticles in an inclined artery exposed to thermal radiation and magnetic fields," Alexandria Engineering Journal, Jan. 2025, doi: 10.1016/j.aej.2025.01.056
M. Marcinkowska-Gapińska, A. Libura, S. Hołda, and D. Baran, "Analysis of the magnetic field influence on the rheological properties of healthy persons’ blood," BioMed Research International, vol. 2013, Art. ID 490410, pp. 1–7, 2013. doi: [10.1155/2013/490410](https://doi.org/10.1155/2013/490410)
A. Atangana and D. Baleanu, “New fractional derivative with non-local and non-singular kernel: Theory and application to heat transfer model,” Thermal Sci., vol. 21, no. 2, pp. 761–766, 2016.
A. Isah, A. Musa, G. Yakubu, G. T. Adamu, A. Mohammed, A. Baba, S. Kadas, and A. Mahmood, “The impact of heat source and chemical reaction on MHD blood flow through permeable bifurcated arteries with tilted magnetic field in tumor treatments,” Comput. Methods Biomech. Biomed. Eng., 2023.
I. Abdullahi, D. G. Yakubu, M. Y. Adamu, M. Ali, and A. M. Kwami, inclined magnetic fields, heat transfer and thermal radiation on fractionalized EMHD Burgers’ fluid flow via bifurcated artery for tumor treatments,” Partial Differential Equations in Applied Mathematics, vol. 13, p. 101093, 2025, doi: 10.1016/j.padiff.2025.101093.
Majidi P, Shateri A, Jalili P, Al-Yarimi FAM, Jalili B, Ganji DD, Ben Khedher N. Radiative effects on 2d unsteady mhd al₂o₃-water nanofluid flow between squeezing plates: a comparative study using agm and hpm in python[J]. ZAMM-Zeitschrift für Angewandte Mathematik und Mechanik, 2025, 105(2). DOI: 10.1002/zamm.202400546.
Wikipedia, Fractional calculus, 2023, 02/08/2023
Moussa B, Youssouf M, Abdoul Wassiha N, Youssouf P. Homotopy perturbation method to solve Duffing-Van der Pol equation. Advances in Differential Equations and Control Processes. 2024;31(3).
He, J.-H.; He, C.-H.; Alsolami, A. A. A good initial guess for approximating nonlinear oscillators by the homotopy perturbation method. Facta Universitatis-Series Mechanical Engineering. 2023, 21(1), 21-29.