Two-Phase Inclined MHD Blood Flow in Porous Tumor Region with Concentration and Volume Fraction
Abstract
There are different approaches for treating invasive and non-invasive tumors. The flowing fluid (blood) provides the required nutrients to the tumors and absorbs the suspensions. Drug delivery systems are dependent on the medium (flowing fluid) that carries the drugs. The blood vessels usually carry drugs to the targeted regions that treat the affected region. This situation varies the concentration of the tumor surrounding the medium. The system is monitored under a magnetic field that is applied at an angle ( The system of the blood flow surrounding a tumor is governed by partial differential equations (PDEs). The Governing equations are solved using the mathematical function PDEPE in MATLAB. The effects of different parameters, concentration parameters, inclined magnetic field, porosity, on fluid (blood) velocity, and medication (drug) velocity in the presence of volume fraction. Flow patterns so obtained show significant effects that help to treat the deceased regions clinically. The numerical results are interpreted through the graphs drawn.
Downloads
References
World Health Organization News 01-02-2024. https://www.who.int/news/item/01-02-2024-global-cancer-burden-growing--amidst-mounting-need-for-services.
N.P. Singh and A.K. Singh, “MHD Effects on heat and mass transfer in the flow of a dusty viscous fluid with volume fraction,” Indian Journal of Pure and Applied Physics, 39, 496-509 (2001).
H.M. Byrne and J.R. King, “A Two-Phase Model of Solid Tumour Growth,” Applied Mathematics Letters, 16, 567 573 (2003). https://doi.org/10.1016/S0893-9659(03)00038-7
I.I Bogdanov, V.V. Mourzenko, J.F. Thovert and P.M. Adler, “Two-phase flow through fractured porous media,” Physical Review E, 68, 767-782 (2003). https://doi.org/10.1103/PhysRevE.68.026703
O. Prakash, S.P. Singh, D. Kumar and Y. Dwivedi, “A study of effects of heat source on MHD blood flow through a bifurcated artery,” AIP Advances, 1, 042128 (2011). https://doi.org/10.1063/1.3658616
A. Chaudhuri, C.F. Osterhoudtand and D. Sinha, “Determination of Volume Fractions in Two-Phase Flows from Sound Speed Measurement,” in: ASME 2012 Noise Control and Acoustics Division Conference, (New York, USA, 2012), pp. 559-567. https://doi.org/10.1115/NCAD2012-1381
Z. Abbas, J. Hasnain and M. Sajid, “MHD two-phase fluid flow and heat transfer with partial slip in an inclined channel,” Thermal Science, 20(5), 1435-1446 (2016). https://doi.org/10.2298/TSCI130327049A
K.R. Madhura and D.S. Swetha, “Influence of Volume Fraction of Dust Particles on Dusty Fluid Flow through Porous Rectangular Channel,” International Journal of Mathematics Trends and Technology (IJMTT), 50(5), 261-275 (2017). https://doi.org/10.14445/22315373/IJMTT-V50P543
H. Chen, X. Tong, L. Lang, O. Jacobson, B. C. Yung, X. Yang, R. Bai, et al., “Quantification of Tumor Vascular Permeability and Blood Volume by Positron Emission Tomography,” Theranostics, 7(9), 2363–2376 (2017). https://doi.org/10.7150/thno.19898
K.R. Thulborn, A. Lu, I.C. Atkinson, M. Pauliah, K. Beal, T.A. Chan, A. Omuro, et al., “Residual Tumor Volume, Cell Volume Fraction, and Tumor Cell Kill During Fractionated Chemoradiation Therapy of Human Glioblastoma using Quantitative Sodium MR Imaging,” Clinical cancer research: an official journal of the American Association for Cancer Research, 25(4), 1226–1232 (2019). https://doi.org/10.1158/1078-0432.CCR-18-2079
B. Wirthl, J. Kremheller, B.A. Schrefler and W.A. Wall, “Extension of a multiphase tumor growth model to study nanoparticle delivery to solid tumors,” PLoS One, 15(2), e0228443 (2020). https://doi.org/10.1371/journal.pone.0228443
A. Bera, S. Dutta, J.C. Misra and G.C. Shit, “Computational modeling of the effect of blood flow and dual phase lag on tissue temperature during tumor treatment by magnetic hyperthermia,” Mathematics and Computers in Simulation, 188, 389-403 (2021). https://doi.org/10.1016/j.matcom.2021.04.020
D. Kumar, B. Satyanarayana, R. Kumar, S. Kumar and N. Deo, “Application of heat source and chemical reaction in MHD blood flow through permeable bifurcated arteries with inclined magnetic field in tumor treatments,” Results in Applied Mathematics, 10, 100151 (2021). https://doi.org/10.1016/j.rinam.2021.100151
V. Darvishi, M. Navidbakhsh and S. Amanpour, “Heat and mass transfer in the hyperthermia cancer treatment by magnetic nanoparticles,” Heat and Mass Transfer, 58(6), 1029-1039 (2022). https://doi.org/10.1007/s00231-021-03161-3
H. Wang, A.A. Alizadeh, A.M. Abed, A. Piranfar, G.F. Smaisim, S. K. Hadrawi and M. Hekmatifar, “Investigation of the effects of porosity and volume fraction on the atomic behavior of cancer cells and microvascular cells of 3DN5 and 5OTF macromolecular structures during hematogenous metastasis using the molecular dynamics method,” Computers in Biology and Medicine, 158, 106832 (2023). https://doi.org/10.1016/j.compbiomed.2023.106832
N. Yadav, S. Jaiswal and P.K. Yadav, “Two-phase magnetohydrodynamic blood flow through the curved porous artery,” Physics of Fluids, 36, 091924 (2024). https://doi.org/10.1063/5.0225245
M.Y. Maslov, E.R. Edelman, A.E. Wei, M.J. Pezone and M.A. Lovich, “High concentrations of drug in target tissues following local controlled release are utilized for both drug distribution and biological effect: An example with epicardial inotropic drug delivery,” Journal of Controlled Release, 171(2), 201–207 (2013). https://doi.org/10.1016/j.jconrel.2013.06.038
B. Shakya, “The Role of Chemistry in Cancer Chemotherapy: A Mini Review,” Amrit Journal, 3, 49-56 (2023). https://doi.org/10.3126/amritj. v3i1.61541
T.C. Ezike, U.S. Okpala, U.L. Onoja, C.P. Nwike, E.C. Ezeako, O.J. Okpara, C.C. Okoroafor, et al., “Advances in drug delivery systems, challenges, and future directions,” Heliyon, 9(6), e17488 (2023). https://doi.org/10.1016/j.heliyon.2023.e17488
R.K. Jain, “Transport Phenomena in Tumors,” Advances in Chemical Engineering, 19, 129–200 (1994). https://doi.org/10.1016/s0065-2377(08)60214-8
Copyright (c) 2025 D. Kumar, M. Garvandha, S. Kumar, N. Deo

This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).



