Citation :

Sumit Kumar, Surendra Kumar, "Effect of Arrhenius Energy and Variable Thermal Conductivity on Blood Flow through the Stenotic Artery," International Journal of Engineering Trends and Technology (IJETT), vol. 74, no. 5, pp. 411-434, 2026. Crossref, https://doi.org/10.14445/22315381/IJETT-V74I5P127

Abstract

The present research introduces a novel mathematical model that investigates blood flow dynamics in an artery featuring three different types of stenosis, namely irregular, overlapping, and elliptical at the distinct locations, addressing a combination of variable thermal conductivity, Reynolds viscosity model, uniform magnetic field, electrical field, and Arrhenius activation energy effects. After including these concepts in the flow equations, the authors converted them into dimensionless form and finally obtained the numerical solution using the ‘Explicit Finite-Difference Method’. This approach finds the graphical representation of velocity with Darcy number, electrokinetic parameter, radiation parameter, Reynolds number, Hartmann number, and the convection volume fraction of the hybrid nanoparticles. The graphical demonstration of temperature with Eckert number, radiation parameter, Prandtl number, and Reynolds number, while the concentration with the activation energy and Schmidt number. The author observed that when the value of the activation energy increases from 2 to 6 then the percentage increment in the concentration profile as 4.71 % increment for the irregular shape of the stenosis, 4.74 % increment for the overlapping shape of the stenosis, and 4.75 % increment for the elliptical shape of the stenosis at the centre of the artery while 12.91 % increment for the irregular shape of the stenosis, 4.39 % increment for the overlapping shape of the stenosis, and 4.31 % increment for the elliptical shape of the stenosis at the 0.5 radius of the artery. The suspension of silver and titanium oxide nanoparticles is incorporated to intensify heat and mass transfer and optimize drug delivery mechanisms with multiple stenoses in a single straight artery. This approach addresses the physiological complexities of multi-stenosed arteries and opens new avenues for targeted therapies and biomedical applications.

Keywords

Nanoparticles, Non-Newtonian fluid, Stenosed artery, Variable thermal conductivity, Variable viscosity.

References

[1] Ayesha Aktar et al., “Biomagnetic Field Effects on Pulsatile Blood Flow with Gold Nanoparticles through Bifurcated Artery with Stenosis and Aneurysm,” Multidiscipline Modeling in Materials and Structures, vol. 21, no. 5, pp. 1061-1091, 2025.
[CrossRef] [Google Scholar] [Publisher Link]  

[2] Anjali Chauhan, and Chandi Sasmal, “A Comparative Study of Newtonian and Multi-Mode Viscoelastic Models for Blood Flow in Stenosed Arteries at High Physiologic Reynolds and Womersley Numbers,” International Journal of Engineering Science, vol. 221, 2026.
[CrossRef] [Google Scholar] [Publisher Link]

[3] Azad Hussain, Muhammad Naveel Riaz Dar, and Ahmed Arif, “A Computational Investigation using the non-Newtonian Sisko Model and Finite Element Analysis to Determine Blood Flow Characteristics in Trapezoidal Stenosed Arteries,” International Journal of Modern Physics B, vol. 39, no. 15, 2025.
[CrossRef] [Google Scholar] [Publisher Link]

[4] Azad Hussain, Muhammad Naveel Riaz Dar, and Arosha Iftikhar, “Computational Analysis of Blood Flowing through an Artery with Post Stenotic Dilatation by Implying Sisko Model Parametric Approach,” Scientific Reports, vol. 16, no. 1, pp. 1-25, 2026.
[CrossRef] [Google Scholar] [Publisher Link]

[5] Alex J. Barker et al., “Viscous Energy Loss in the Presence of Abnormal Aortic Flow,” Magnetic Resonance in Medicine, vol. 72, no. 3, pp. 620-628, 2014.
[CrossRef] [Google Scholar] [Publisher Link]

[6] Aditya Singh, and Pramod Kumar Yadav, “ANN-based Computational Framework for EMHD Modulated Ternary Hybrid Nanofluid ( /Blood) Flow in a Curved Atherosclerotic Artery,” International Journal of Numerical Methods for Heat and Fluid Flow, vol. 36, no. 1, pp. 188-227, 2026.
[CrossRef] [Google Scholar] [Publisher Link]

[7] A. Zeeshan et al., “Numerical Evaluation of Blood Flow of MHD Non-Newtonian Bingham Fluid with Heat Transfer in a Vertical Artery with Atherosclerosis,” International Journal of Numerical Methods for Heat and Fluid Flow, vol. 36, no. 1, pp. 275-297, 2026.
[CrossRef] [Google Scholar] [Publisher Link]

[8] Bhupendra Kumar Sharma, and Rishu Gandhi, “Entropy-Driven Optimization of Radiative Jeffrey Tetrahybrid Nanofluid Flow through a Stenosed Bifurcated Artery with Hall Effects,” Physics of Fluids, vol. 35, no. 12, 2023.
[CrossRef] [Google Scholar] [Publisher Link]

[9] Bhavya Tripathi, and Bhupendra Kumar Sharma, “Influence of Heat and Mass Transfer on MHD Two-Phase Blood Flow with Radiation,” AIP Conference Proceedings, vol. 1975, no. 1, 2018. 
[CrossRef] [Google Scholar] [Publisher Link]

[10]  Chandrakanta Parida, Ganeswar Mahanta, and Sachin Shaw, “Nonlinear Hemodynamics Modeling of Fractional Jeffery Ternary Hybrid Nanofluid Flow in Multi-Stenosed Arteries with ANN-based Simulation,” Nonlinear Dynamics, vol. 113, no. 25, pp. 34873-34904, 2025.
[CrossRef] [Google Scholar] [Publisher Link]

[11] D.S. Sankar, and K. Hemalatha, “A Non-Newtonian Fluid Flow Model for Blood Flow through a Catheterized Artery Steady Flow,” Applied Mathematical Modelling, vol. 31, no. 9, pp. 1847-1864, 2007.
[CrossRef] [Google Scholar] [Publisher Link]

[12] Fatima Shafiq Hira et al., “Advanced Computational Modeling of Darcy-Forchheimer Effects and Nanoparticle-Enhanced Blood Flow in Stenosed Arteries,” Engineering Applications of Artificial Intelligence, vol.152, 2025.
[CrossRef] [Google Scholar] [Publisher Link]

[13] Gordon D. Smith, Numerical Solution of Partial Differential Equations: Finite Difference Methods, 3^rd ed., Oxford University Press, 1985.
[Google Scholar] [Publisher Link]

[14] Haris Alam Zuberi et al., “Numerical Simulation of Blood Flow Dynamics in a Stenosed Artery Enhanced by Copper and Alumina Nanoparticles,” Computer Modeling in Engineering and Sciences, vol. 142, no. 2, pp. 1839-1864, 2025.
[CrossRef] [Google Scholar] [Publisher Link]

[15] Issa El Glili et al., “Numerical Simulation of Unsteady Blood based Carreau Nanofluid Flow in an Inclined Porous Saturated Artery having Overlapping Stenosis with Electro-osmosis,” Numerical Heat Transfer, Part A: Applications, vol. 86, no. 21, pp. 7749-7779, 2024.
[CrossRef] [Google Scholar] [Publisher Link]

[16] Jamil Abbas Haider et al., “Multifaceted Simulation: Finite volume and Finite Element Modeling of Blood Flow in Multiple Stenosed Arteries,” Modern Physics Letters B, vol. 39, no. 3, 2025.
[CrossRef] [Google Scholar] [Publisher Link]

[17] Jayati Tripathi, B. Vasu, and O. Anwar Bég, “Computational Simulations of Hybrid Mediated Nano-Hemodynamics (Ag-Au/Blood) through an Irregular Symmetric Stenosis,” Computers in Biology and Medicine, vol. 130, pp. 1-42, 2021.
[CrossRef] [Google Scholar] [Publisher Link]

[18] Jayati Tripathi et al., “Unsteady Hybrid Nanoparticle-Mediated Magneto-Hemodynamics and Heat Transfer through an Overlapped Stenotic Artery: Biomedical Drug Delivery Simulation,” Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, vol. 235, no. 10, pp. 1175-1196, 2021.  
[CrossRef] [Google Scholar] [Publisher Link]

[19] Jayati Tripathi et al., “Computational Simulation of Rheological Blood Flow Containing Hybrid Nanoparticles in an Inclined Catheterized Artery with Stenotic, Aneurysmal and Slip Effects,” Computers in Biology and Medicine, vol. 139, 2021.
[CrossRef] [Google Scholar] [Publisher Link]

[20] Stefan Lecheler, Computational Fluid Dynamics: Getting Started Quickly With ANSYS CFX 18 Through Simple Examples, 1st ed., Springer Wiesbaden, 2022.
[Publisher Link]

[21] K.N. Asha, and Neetu Srivastava, “Analysis of Blood Flow Features in the Curved Artery in the Presence of Differently Shaped Hybrid Nanoparticles,” Partial Differential Equations in Applied Mathematics, vol. 13, pp. 1-7, 2025.
[CrossRef] [Google Scholar] [Publisher Link]

[22] Kannigah Thirunananasambantham et al., “Computational Analysis of Hybrid GPL Blood Nanofluid Flow Over Various Stenosed Arteries in the Presence of a Magnetic Field,” Alexandria Engineering Journal, vol. 129, pp. 598-611, 2025.
[CrossRef] [Google Scholar] [Publisher Link]

[23] Lilibeth P. Coronel, Rey Y. Capangpangan, and Ruji P. Medina, “Engineered Nanoparticles Cytotoxicity Prediction using an Enhanced Convolutional Neural Network,” International Journal of Engineering Trends and Technology, vol. 73, no. 6, pp. 309-317, 2025.
[CrossRef] [Google Scholar] [Publisher Link]

[24] Mohammadamin Bagherkhani, Saeed Dinarvand, and Mohammad Vahabi, “Modeling of Blood Flow in an Irregular Multi-stenosed Vessel in Presence of Iron Oxide and Gold Nanoparticles,” BioNanoScience, vol. 15, no. 1, 2025.
[CrossRef] [Google Scholar] [Publisher Link]

[25] Mallinath Dhange et al., “Hemodynamic Characteristics of Blood Flow in an Inclined Overlapped Stenosed Arterial Section,” Partial Differential Equations in Applied Mathematics, vol. 11, pp. 1-7, 2024.
[CrossRef] [Google Scholar] [Publisher Link]

[26] M. Dhange et al., “Hemodynamic Properties of Blood Flow in an Angled Overlying Stenosed Blood Vessel via Force Field and Gold Nanoparticle Suspension,” Scientific African, vol. 28, pp. 1-13, 2025.  
[CrossRef] [Google Scholar] [Publisher Link]

[27] M.H. Shah et al., “A Caputo Time-Fractional Derivative Approach to Pulsatile Non-Newtonian Sutterby Blood Fluid Flow through a Vertical Stenotic Artery under MHD Influence,” Journal of Computational Applied Mechanics, vol.  57, no. 1, pp. 63-83, 2026.
[Google Scholar]

[28] N. Ameer Ahammad, and Abdulwahab Ali Mohammed Al Talea, “MHD Rotating Flow Over a Semi-Infinite Vertical Moving Plate with Oscillatory Effects,” International Journal of Engineering Trends and Technology, vol. 69, no. 10, pp. 161-167, 2021.
[CrossRef] [Publisher Link]

[29] Noreen Sher Akbar, “Biomathematical Study of Sutterby Fluid Model for Blood Flow in Stenosed Arteries,” International Journal of Biomathematics, vol. 8, no. 6, 2015.
[Google Scholar] [Publisher Link]

[30] Pramod Kumar Yadav, and Aditya Singh, “Biomedical Simulations of Electroosmotic Non-Newtonian Hybrid Nanofluid (Blood) with Hematocrit Viscosity through a Porous Overlapping Irregular Stenosed Artery,” Computers in Biology and Medicine, vol. 196, 2025.
[CrossRef] [Google Scholar] [Publisher Link]

[31] Pooriya Majidi Zar, Zahra Poolaei Moziraji, and Ali Ahmadi Azar, “Mathematical Modeling of Blood Flow with Copper and Graphene Nanoparticles in Inclined Stenotic Arteries,” Scientific Reports, vol. 15, no. 1, pp. 1-26, 2025.
[CrossRef] [Google Scholar] [Publisher Link]

[32] Rahmat Ellahi, Mohsin Raza, and Kambiz Vafai, “Series Solutions of Non-Newtonian Nanofluids with Reynolds’ Model and Vogel’s Model by Means of the Homotopy Analysis Method,” Mathematical and Computer Modelling, vol. 55, no. 7-8, pp. 1876-1891, 2012.
[CrossRef] [Google Scholar] [Publisher Link]

[33] Rishu Gandhi et al., “Modeling and Analysis of Magnetic Hybrid Nanoparticle ( /blood) based Drug Delivery through a Bell-Shaped Occluded Artery with Joule Heating, Viscous Dissipation and Variable Viscosity Effects,” Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, vol. 236, no. 5, pp. 2024-2043, 2022.
[CrossRef] [Google Scholar] [Publisher Link]

[34] Rishu Gandhi et al., “Entropy Generation and Shape Effects Analysis of Hybrid Nanoparticles ( /blood) Mediated Blood Flow through a Time-Variant Multi-Stenotic Artery,” International Journal of Thermofluids, vol. 18, pp. 1-13, 2023.
[CrossRef] [Google Scholar] [Publisher Link]

[35] Ramakrishna Manchi, and R. Ponalagusamy, “Pulsatile Flow of EMHD Micropolar Hybrid Nanofluid in a Porous Bifurcated Artery with an Overlapping Stenosis in the Presence of Body Acceleration and Joule Heating,” Brazilian Journal of Physics, vol. 52, no. 2, 2022.
[CrossRef] [Google Scholar] [Publisher Link]

[36] Sara I. Abdelsalam, and M.M. Bhatti, “Synergistic Progression of Nanoparticle Dynamics in Stenosed Arteries,” Qualitative Theory of Dynamical Systems, vol. 24, no. 1, 2025.
[CrossRef] [Google Scholar] [Publisher Link]

[37] Saiful Islam et al., “Electroosmotic Flow in Ternary ( ) Blood-based Sutterby Nanomaterials with Bio-Active Mixers,” International Journal of Thermofluids, vol. 18, pp. 1-15, 2023.
[CrossRef] [Google Scholar] [Publisher Link]

[38] Syed M. Hussain, “Irreversibility Analysis of Time-Dependent Magnetically Driven Flow of Sutterby Hybrid Nanofluid: A Thermal Mathematical Model,” Waves in Random and Complex Media, vol. 35, no. 4, pp. 7628-7660, 2025.
[CrossRef] [Google Scholar] [Publisher Link]

[39] Suneetha Sangapatnam, “Casson Flow of Blood Containing  and  Nanoparticles Over a Stenotic Artery,” East European Journal of Physics, no. 1, pp. 309-317, 2025.
[CrossRef] [Google Scholar] [Publisher Link]

[40] Souhail Souai et al., “Assessment of Heat and Mass Transfer in a Porous N-Shaped Heat Exchanger using Hybrid Nanofluid under Cross-Diffusion and Magnetic Effects,” European Journal of Mechanics-B/Fluids, vol. 114, 2025.
[CrossRef] [Google Scholar] [Publisher Link]

[41] Suneetha Sangapatnam, and Ramasekhar Gunisetty, “Computational Role of Blood-based Casson Fluid Flow through a Stenotic Artery: An Application to Cardiovascular Issues,” Thermal Science, vol. 29, no. 2, pp. 3267-3277, 2025.
[CrossRef] [Google Scholar] [Publisher Link]

[42] Taimoor Salahuddin et al., “Blood Flow Study in Stenotic Arteries through Porous Medium with Heat Generation,” International Communications in Heat and Mass Transfer, vol. 164, 2025.
[CrossRef] [Google Scholar] [Publisher Link]

[43]Yasir Ul Umair Bin Turabi et al., “FEM Simulation to Predict Thermal Enhancement Mechanism in Nanoparticles Laden blood Flow through an Inflamed Stenosis Artery with Magnetohydrodynamics Effect,” Multiscale and Multidisciplinary Modeling, Experiments and Design, vol. 8, no. 5, 2025.
        [CrossRef] [Google Scholar] [Publisher Link]