Gold Nanoparticles' Effect on MHD Blood Flow via a Stenosed Artery
Abstract
This work employs a rheological model for a theoretical investigation of stress on the walls of the artery and how the enhanced MHD flow of blood circulation through an oblique artery is affected by flow impedance resistance in gold nanoparticles. Blood is designed as a viscous fluid containing a mixture of gold nanoparticles to enhance its thermal and flow characteristics. Analytical solutions are made possible by simplification under low Reynolds number and mild stenosis circumstances. The temperature, velocity profiles, wall shear stress (WSS), and stream resistivity (FR) can all be determined using the current analytical method. In the discussion section, the results are displayed graphically. The analysis indicates that gold nanoparticles significantly reduce resistance and alter wall shear profiles, while an increasing magnetic field tends to elevate flow resistance. These findings can assist in optimizing the use of nanofluids in biomedical applications involving stenosed arteries and catheter-based therapies.
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References
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[10] D. A. Macdonald, On Steady flow through modelled vascular stenosis. J. Biomech. 12 (1979), 13-30.
[11] N. Verma, R. S. Parihar, Effect of magneto-hydrodynamics and haematocrit on blood flow in an artery with multiple mild stenosis. Int. J. Appl. Math. Comput., 1 (2009), no.1, 30-46.
[12] K. M. Prasad, G. Radhakrishnamacharya, Flow of Herschel-Bulkley fluid through an inclined tube of non-uniform cross-section with multiple stenoses. Arch. Mech., 60 (2008), 161-172.
[13] J. H. Forrester, D. F. Young, Flow through a conversing diverging tube and its implications in occlusive vascular disease. J. Biomech., 3 (1970), 297-316.
[14] J. Perkkio, R. Keskinen, the effect of the concentration profile of red cells on blood flow in the artery with stenosis. Bull. Math. Biol., 45 (1983), no.2, 259-267.
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[19] A. K. Gupta, G. D. Gupta, Unsteady blood flow in an artery through a non-symmetrical stenosis. Acta Ciencia Indica. XXVII M, 2 (2001), 137-142.
[20] R. N. Pralhad, D. H. Schultz, Modelling of arterial stenosis and its applications to Blood diseases. Math. Biosci., 190 (2004), 203-220.
[21] R. Ponalagusamy, Two-fluid model for blood flow through a tapered arterial stenosis: Effect of non-zero couple stress boundary condition at the Interface. Int. J. Comput. Math. 3 (2017), no. D, 807- 824.
[22] S. U. S. Choi, J. A. Eastman, Enhancing thermal conductivity of fluids with nanofluids. ASME Fluids Engg. Div. 231 (1995), 99-105.
[23] B. Godin, J. H. Sakamoto, R. E. Serda, A. Grattoni, A. Bouamrani, A. M. Ferrari, Emerging of nano-medicine for the diagnosis and treatment of cardio-vascular diseases. Trends. Pharmacological Sci., 31 (2010), 199-205.
[24] J. Buongiorno, Convective transport in nanofluids. J. Heat Trans. 128 (2006), no.3, 240-250. http://dx.doi.org/10.1115/1.2150834
[25] N. S. Akbar, Z. , Metachronal beating of cilia under the influence of Casson fluid and magnetic field. J. Magn. Magn. Mater., 378 (2015), 320-326.
[26] K. M. Prasad, N. Subadra, S. K. Reddy, Peristaltic transport of a couple stress fluid with nanoparticles having permeable walls. J. Nanofluids., 6 (2017), 751-760.
[27] A. Rahbari, M. Fakour, A. Hamzehnezhad, M. A. Vakilabadi, D. D. Ganji , Heat transfer and fluid flow of blood with nanoparticles through porous vessels in a magnetic field: A quasi-one-dimensional analytical approach. Math. Biosc.,283 (2017), 38-47.
[28] M. D. Hatami, D. D. Ganji, Computer simulation of MHD blood conveying gold nanoparticles as a third grade non-Newtonian nanofluid in a hollow porous vessel. Comput. Meth. Prog. Bio., 113 (2014), no.2, 632-641.
[29] K. S. Mekheimer, E. L. Elnaqeeb, M. A. Kot, F. Alghamdi, Simultaneous effect of magnetic field and metallic nanoparticles on a micropolar fluid through an overlapping stenotic artery: Blood flow model. Phys. Essays., 29 (2016), no. 2, .272-283. https://doi.org/10.4006/0836-1398-29.2.272
[30] K. Vajravelu, K. V. Prasad, J. Lee, C. Lee, I. Pop, R. A. V. Gorder, Convective heat transfer in the flow of viscous Ag-water and Cu-water nanofluids over a stretching surface. Int. J. Therm. Sci., 50 (2011), 843.
[31] N. S. Akbar, M. Raza, M. R. Ellahi, Influence of heat generation and heat flux in peristalsis with interaction of nanoparticles. European Phys. J. Plus., 129 (2014), 185.
[32] N. S. Akbar, Endoscope effects on the peristaltic flow of Cu-water nanofluids. J. Comut. Theor. Nanosci., 11 (2014), 1150-1155.
[33] T. Elnaqeeb, K. S. Mekheimer, F. Alghamdi, Cu-blood flow model through a catheterized mild stenotic artery with a thrombosis. Math. Biosci., 282 (2016), 135-146.
[34] A. Zaman, N. Ali, I. Ali, Effects of nanoparticles (Cu, Ag) and slip on unsteady blood flow through a curved stenosed channel with aneurysm. Thermal. Sci. Eng. Prog., 5 (2018), 482-491.
[35] A. Zaman, A. A. Khan, N. Ali, Modelling of unsteady non-Newtonian blood flow through a stenosed artery with nanoparticles. J. Brazilian Soc. Mech. Sci. Eng., 40 (2018), 307. https://doi.org/10.1007/s40430-018-1230-5
[36] T. Elnaqeeb, N. A. Shah, K. S. Mekheimer, Hemodynamic characteristic of gold nanoparticle blood flow through a tapered stenosed vessel with variable nanofluid viscosity. Bio. Nano. Sci. 9 ( 2019), 245-255. https://doi.org/10.1007/s12668-018-0593-5
[37] K. S. Mekheimer, T. Elnaqeeb, M. A. El-Kot, F. Alghamdi, Simultaneous effect of magnetic filed and metallic nanoparticles on a micropolar fluid through an overlapping stenotic artery: Blood flow model. Phy. Essays., 29 (2016), no. 2, 272-283.
[38] S. Nadeem, S. Ijaz, Nanoparticles analysis on the blood flow through a tapered catheterized elastic artery with overlapping stenosis. Eur. Phys. J. Plus., 129 (2014), no.11, 249.
[39] N. S. Akbar, A. W. Butt, Magnetic field effects for copper suspended nanofluid venture through composite stenosed arteries with permeable walls. J. Magn. Magn. Mater., 381 (2015), 285-291.
[40] A. Zaman, N. Ali, N. Kousar, Nanoparticles (Cu, TiO2, Al2O3) analysis on unsteady blood flow through an artery with a combination of stenosis and aneurysm. Compt. Math. Appl., 76 (2018), no.9, 2179-2191. https://doi.org/10.1016/j.camwa.2018.08.019
[41] N. S. Akbar, Metalic nanoparticle analysis for the blood Flow in tapered stenosed arteries: Application in nanomedicines. Int. J. Bio. Math., 9 (2016), no.1, 1-18. https://doi.org/10.1142/S1793524516500029
[42] B. C. Pak, Y. I. Cho, Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles. Exp. Heat Transf., 11 (1998), no.2, 151-170.
[43] K. S. Mekheimer, M. S. Mohamed, T. Elnaqeeb, Metallic nanoparticles influence on blood flow through a stenotic artery. Int. J. Pure. Appl. Math. 107 (2016), no. 1, 201-220.
[44] T. Elnaqeeb, Modeling of Au (NPs)-blood flow through a catheterized multiple stenosed artery under radial magnetic field. Eur. Phys. J. 228 (2019), 2695-2712. https://doi.org/10.1140/epjst/e2019-900059-9
[45] Y. Pratumwal, W. Limtrakaran, S. Muengtaweepongsa, P. Phakdeesan, K. Intharakham, Whole blood viscosity modelling using power las, Casson, and Carreau Yasuda models interegrated with image scanning U-tube viscometer technique. Songklanakarin J. Sci. Technol. 39 (2017), no. 5, 625-631
[46] J.V.R. Reddy, D. Srikanth, D. Samir, K. Das Modelling and simulation of temperature and concentration dispersion in a couple stress nanofluid flow through stenotic tapered arteries, Eur. Phys. J. Plus. 132 (2017), no. 8, 365.
[47] L. H. Madkour, Vision for life sciences: Interfaces between nanoelcectronic and biological systems. Glob Drugs. Therap. 2 (2017) no. 4, 1-4.
[48] M. Dhange, S. Salgare, K. Das, B. Ebenezer, H. Alemayehu, Hemodynamic Properties of Blood Flow in an Angled Overlying Stenosed Blood Vessel via Force Field and Gold Nanoparticle Suspension, Sci. Afr. 28 (2025), e02652.
[49] R. Sardar, A.M. Funston, P. Mulvaney et al., Gold nanoparticles: past, present, and future. Langmuir. 25 (2009), no. 24, 13840-13851.
[50] L. H. Madkour, Applications of gold nanoparticles in medicine and therapy. Pharm. Pharmacol. Int. J. 6 (2018), no. 3, 157-174.
[2] G. Bugliarello, J. Sevilla, Velocity distribution and other characteristics of steady and pulsatile blood flow in fine glass tubes. Biorheol., 7 (1970), no. 2, 85-107. https://doi.org/10.3233/BIR-1970-7202.
[3] G. R. Cokelet, The rheology of human blood (Doctoral dissertation, Massachusetts Institute of Technology), 1963.
[4] R. H. Haynes, Physical basis of the dependence of blood viscosity on tube radius. Am. J. Physiol.-Legacy Content., 198 (1960), no.6, 193-200. https://doi.org/10.1152/ajplegacy.1960.198.6.1193
[5] N. Iida, Influence of plasma layer on steady blood flow in microvessels. Japanese J. Appl. Phy., 17 (1978), 1, 203. https://doi.org/10.1143/JJAP.17.203
[6] J. B. Shukla, R. S. Parihar, S. P. Gupta, S.P. Effects of peripheral layer viscosity on blood flow through the artery with mild stenosis. Bull. Math. Biol., 42 (1980), 797-805. https://doi.org/10.1007/BF02461059
[7] V. P. Srivastava, M. Saxena, Two-layered model of Casson fluid flow through stenotic blood vessels: applications to the cardiovascular system. J. Biomech., 27 (1994), no.7, 921-929. https://doi.org/10.1016/0021-9290(94)90264-X
[8] D. F. Young, Effect of a time dependent stenosis of flow through a tube. J. Eng. Indust. Trans. ASME., 90 (1968), 248-254.
[9] T. Azuma, T. Fukushima, Flow patterns in stenotic blood vessel models. Biorheol., 13 (1976), 337-355.
[10] D. A. Macdonald, On Steady flow through modelled vascular stenosis. J. Biomech. 12 (1979), 13-30.
[11] N. Verma, R. S. Parihar, Effect of magneto-hydrodynamics and haematocrit on blood flow in an artery with multiple mild stenosis. Int. J. Appl. Math. Comput., 1 (2009), no.1, 30-46.
[12] K. M. Prasad, G. Radhakrishnamacharya, Flow of Herschel-Bulkley fluid through an inclined tube of non-uniform cross-section with multiple stenoses. Arch. Mech., 60 (2008), 161-172.
[13] J. H. Forrester, D. F. Young, Flow through a conversing diverging tube and its implications in occlusive vascular disease. J. Biomech., 3 (1970), 297-316.
[14] J. Perkkio, R. Keskinen, the effect of the concentration profile of red cells on blood flow in the artery with stenosis. Bull. Math. Biol., 45 (1983), no.2, 259-267.
[15] J. C. Misra, B. K. Kar, Momentum integral method for studying flow characteristics of blood through a stenosed vessel. Biorheol., 26 (1989), 23-35.
[16] P. N. Tandon, U. V. Rana, M. Kawahara, V. K. Katiyar, A model for blood flow through stenotic tube. Int. J. Biomed. Comput., 32 (1993), .62-78.
[17] M. Nakamura, T. Sawada, Numerical study on the flow of a non-Newtonian fluid through an axisymmetric stenosis. J. Biomech. Eng., 110 (1988), 137-143.
[18] M. K. Sharma P. R. Sharma, V. Nasha, Pulsatile MHD arterial blood flow in the presence of double stenosis. J. Appl. Fluid Mech., 6 (2013), no.3, 331-338.
[19] A. K. Gupta, G. D. Gupta, Unsteady blood flow in an artery through a non-symmetrical stenosis. Acta Ciencia Indica. XXVII M, 2 (2001), 137-142.
[20] R. N. Pralhad, D. H. Schultz, Modelling of arterial stenosis and its applications to Blood diseases. Math. Biosci., 190 (2004), 203-220.
[21] R. Ponalagusamy, Two-fluid model for blood flow through a tapered arterial stenosis: Effect of non-zero couple stress boundary condition at the Interface. Int. J. Comput. Math. 3 (2017), no. D, 807- 824.
[22] S. U. S. Choi, J. A. Eastman, Enhancing thermal conductivity of fluids with nanofluids. ASME Fluids Engg. Div. 231 (1995), 99-105.
[23] B. Godin, J. H. Sakamoto, R. E. Serda, A. Grattoni, A. Bouamrani, A. M. Ferrari, Emerging of nano-medicine for the diagnosis and treatment of cardio-vascular diseases. Trends. Pharmacological Sci., 31 (2010), 199-205.
[24] J. Buongiorno, Convective transport in nanofluids. J. Heat Trans. 128 (2006), no.3, 240-250. http://dx.doi.org/10.1115/1.2150834
[25] N. S. Akbar, Z. , Metachronal beating of cilia under the influence of Casson fluid and magnetic field. J. Magn. Magn. Mater., 378 (2015), 320-326.
[26] K. M. Prasad, N. Subadra, S. K. Reddy, Peristaltic transport of a couple stress fluid with nanoparticles having permeable walls. J. Nanofluids., 6 (2017), 751-760.
[27] A. Rahbari, M. Fakour, A. Hamzehnezhad, M. A. Vakilabadi, D. D. Ganji , Heat transfer and fluid flow of blood with nanoparticles through porous vessels in a magnetic field: A quasi-one-dimensional analytical approach. Math. Biosc.,283 (2017), 38-47.
[28] M. D. Hatami, D. D. Ganji, Computer simulation of MHD blood conveying gold nanoparticles as a third grade non-Newtonian nanofluid in a hollow porous vessel. Comput. Meth. Prog. Bio., 113 (2014), no.2, 632-641.
[29] K. S. Mekheimer, E. L. Elnaqeeb, M. A. Kot, F. Alghamdi, Simultaneous effect of magnetic field and metallic nanoparticles on a micropolar fluid through an overlapping stenotic artery: Blood flow model. Phys. Essays., 29 (2016), no. 2, .272-283. https://doi.org/10.4006/0836-1398-29.2.272
[30] K. Vajravelu, K. V. Prasad, J. Lee, C. Lee, I. Pop, R. A. V. Gorder, Convective heat transfer in the flow of viscous Ag-water and Cu-water nanofluids over a stretching surface. Int. J. Therm. Sci., 50 (2011), 843.
[31] N. S. Akbar, M. Raza, M. R. Ellahi, Influence of heat generation and heat flux in peristalsis with interaction of nanoparticles. European Phys. J. Plus., 129 (2014), 185.
[32] N. S. Akbar, Endoscope effects on the peristaltic flow of Cu-water nanofluids. J. Comut. Theor. Nanosci., 11 (2014), 1150-1155.
[33] T. Elnaqeeb, K. S. Mekheimer, F. Alghamdi, Cu-blood flow model through a catheterized mild stenotic artery with a thrombosis. Math. Biosci., 282 (2016), 135-146.
[34] A. Zaman, N. Ali, I. Ali, Effects of nanoparticles (Cu, Ag) and slip on unsteady blood flow through a curved stenosed channel with aneurysm. Thermal. Sci. Eng. Prog., 5 (2018), 482-491.
[35] A. Zaman, A. A. Khan, N. Ali, Modelling of unsteady non-Newtonian blood flow through a stenosed artery with nanoparticles. J. Brazilian Soc. Mech. Sci. Eng., 40 (2018), 307. https://doi.org/10.1007/s40430-018-1230-5
[36] T. Elnaqeeb, N. A. Shah, K. S. Mekheimer, Hemodynamic characteristic of gold nanoparticle blood flow through a tapered stenosed vessel with variable nanofluid viscosity. Bio. Nano. Sci. 9 ( 2019), 245-255. https://doi.org/10.1007/s12668-018-0593-5
[37] K. S. Mekheimer, T. Elnaqeeb, M. A. El-Kot, F. Alghamdi, Simultaneous effect of magnetic filed and metallic nanoparticles on a micropolar fluid through an overlapping stenotic artery: Blood flow model. Phy. Essays., 29 (2016), no. 2, 272-283.
[38] S. Nadeem, S. Ijaz, Nanoparticles analysis on the blood flow through a tapered catheterized elastic artery with overlapping stenosis. Eur. Phys. J. Plus., 129 (2014), no.11, 249.
[39] N. S. Akbar, A. W. Butt, Magnetic field effects for copper suspended nanofluid venture through composite stenosed arteries with permeable walls. J. Magn. Magn. Mater., 381 (2015), 285-291.
[40] A. Zaman, N. Ali, N. Kousar, Nanoparticles (Cu, TiO2, Al2O3) analysis on unsteady blood flow through an artery with a combination of stenosis and aneurysm. Compt. Math. Appl., 76 (2018), no.9, 2179-2191. https://doi.org/10.1016/j.camwa.2018.08.019
[41] N. S. Akbar, Metalic nanoparticle analysis for the blood Flow in tapered stenosed arteries: Application in nanomedicines. Int. J. Bio. Math., 9 (2016), no.1, 1-18. https://doi.org/10.1142/S1793524516500029
[42] B. C. Pak, Y. I. Cho, Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles. Exp. Heat Transf., 11 (1998), no.2, 151-170.
[43] K. S. Mekheimer, M. S. Mohamed, T. Elnaqeeb, Metallic nanoparticles influence on blood flow through a stenotic artery. Int. J. Pure. Appl. Math. 107 (2016), no. 1, 201-220.
[44] T. Elnaqeeb, Modeling of Au (NPs)-blood flow through a catheterized multiple stenosed artery under radial magnetic field. Eur. Phys. J. 228 (2019), 2695-2712. https://doi.org/10.1140/epjst/e2019-900059-9
[45] Y. Pratumwal, W. Limtrakaran, S. Muengtaweepongsa, P. Phakdeesan, K. Intharakham, Whole blood viscosity modelling using power las, Casson, and Carreau Yasuda models interegrated with image scanning U-tube viscometer technique. Songklanakarin J. Sci. Technol. 39 (2017), no. 5, 625-631
[46] J.V.R. Reddy, D. Srikanth, D. Samir, K. Das Modelling and simulation of temperature and concentration dispersion in a couple stress nanofluid flow through stenotic tapered arteries, Eur. Phys. J. Plus. 132 (2017), no. 8, 365.
[47] L. H. Madkour, Vision for life sciences: Interfaces between nanoelcectronic and biological systems. Glob Drugs. Therap. 2 (2017) no. 4, 1-4.
[48] M. Dhange, S. Salgare, K. Das, B. Ebenezer, H. Alemayehu, Hemodynamic Properties of Blood Flow in an Angled Overlying Stenosed Blood Vessel via Force Field and Gold Nanoparticle Suspension, Sci. Afr. 28 (2025), e02652.
[49] R. Sardar, A.M. Funston, P. Mulvaney et al., Gold nanoparticles: past, present, and future. Langmuir. 25 (2009), no. 24, 13840-13851.
[50] L. H. Madkour, Applications of gold nanoparticles in medicine and therapy. Pharm. Pharmacol. Int. J. 6 (2018), no. 3, 157-174.
Published
2026-04-18
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Special Issue: Recent Advancements in Applied Mathematics and Computing
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