Modelling of MHD Micropolar Nano Fluid Flow in an Inclined Porous Stenosed Artery with Dilatation
Abstract
In this paper, the impact of a magnetic field on blood flow with nanofluid particles through an inclined porous stenosed artery and dilatation was studied. Here blood is treated as micropolar fluid. The equations are solved by using Homotopy perturbation method [HPM] under the assumption of mild stenosis. The closed form solutions of velocity, temperature profile, and concentration distribution are obtained. The effects of pertinent parameters on flow phenomena have been observed and results are analyzed graphically. This study examines the impact of the magnetic parameter on flow characteristics and reveals that the presence of a magnetic field increases resistance to the flow while decreasing shear stress at the wall. A result is found that the flow resistance and shear stress at the wall decreased for heights of the stenosis dilatation. Additionally, the study finds that resistance to the flow increases and shear stress at the wall decreases with viscosity. The stream lines are drawn to examine the flow pattern and properties of momentum transfer.
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References
D.F. Young, “Effect of a time dependent stenosis of flow through a tube,” Journal of Engineering for Industry, 90(2), 248 254 (1968). https://doi.org/10.1115/1.3604621
J.B. Shukla, R.S. Parihar and B.R.P. Rao, “Effects of stenosis on non-newtonian flow of the blood in an artery,” Bulletin of Mathematical Biology, 42(3), 283–294 (1980). https://doi.org/10.1016/s0092-8240(80)80051-6
J.-S. Lee and Y.-C. Fung, “Flow in Locally Constricted Tubes at Low Reynolds Numbers,” Journal of Applied Mechanics, 37(1), 9–16 (1970). https://doi.org/10.1115/1.3408496
P. Chaturani and R.P. Samy, “Pulsatile flow of Casson’s fluid through stenosed arteries with applications to blood flow,” Biorheology, 23(5), 499–511 (1986). https://doi.org/10.3233/bir-1986-23506
G. Radhakrishnamacharya and S. Rao, “Flow of a magnetic fluid through a non-uniform wavy tube,” Proceedings of the National Academy of Sciences, India. Section A. Physical Sciences, 77, (2007).
D.F. Young and F.Y. Tsai, “Flow characteristics in models of arterial stenosis-I: steady flow,” Journal of Biomechanics, 6, 395 410 (1973). https://doi.org/10.1016/0021-9290(79)90004-6
K.M. Prasad and P.R. Yasa, “Micropolar fluid flow in tapering stenosed arteries having permeable walls,” Malaysian Journal of Mathematical Sciences, 15(1), 147–160 (2021).
D.J. Schneck and S. Ostrach, “Pulsatile blood flow in a channel of small exponential divergence-I. The linear approximation for low mean Reynolds number,” J. Fluids Eng. 16, 353–360 (1975). https://doi.org/10.1115/1.3447314
K.M. Prasad and G. Radhakrishnamacharya, “Effect of multiple stenoses on Herschel–Bulkley fluid through a tube with non-uniform cross-section,” International e-journal of engineering mathematics: Theory and Application, 1, 69–76 (2007).
A.C. Eringen, “Theory of micropolar fluids,” Journal of Mathematics and Mechanics, 16(1), 1–18 (1966). https://www.jstor.org/stable/24901466
G.R. Charya, “Flow of micropolar fluid through a constricted channel,” In International Journal of Engineering Science, 15(12), 719–725 (1977). https://doi.org/10.1016/0020-7225(77)90022-2
T. Ariman, M.A. Turk, and N. Sylvester, “Application of microcontinum fluid mechanics,” Int. J. Eng. Sci. 12, 273–293 (1974). http://dx.doi.org/10.1016/0020-7225(74)90059-7
K.M. Prasad, B. Sreekala and P.R. Yasa, “Analysis of micropolar fluid with nanoparticles flow through a core region in a stenosed artery having mild stenoses,” Palestine Journal of Mathematics, 12(4) (2023).
D. Srinivasacharya, M. Mishra and A. Rao, “Peristaltic pumping of a micropolar fluid in a tube,” Acta Mechanica, 161, 165–178 (2003). https://doi.org/10.1007/s00707-002-0993-y
K.M. Prasad and P.R. Yasa, “Flow of non-Newtonian fluid through a permeable artery having non-uniform cross section with multiple stenosis,” Journal of Naval Architecture and Marine Engineering, 17(1), 31–38 (2020). https://doi.org/10.3329/jname.v17i1.40942
E. Yeom, Y.J. Kang and S.J. Lee, “Changes in velocity profile according to blood viscosity in a microchannel,” Biomicrofluidics, 8, 034110 (2014). https://doi.org/10.1063/1.4883275
E. Karvelas, G. Sofiadis, T. Papathanasiou and I. Sarris, “Effect of micropolar fluid properties on the blood flow in a human carotid model,” Fluids, 5(3), 125 (2020).
S.U.S. Choi and J.A. Eastman, “Enhancing thermal conductivity of fluids with nanoparticles,” in: ASME International Mechanical Engineering Congress & Exposition, (San Francisco, United States, 1995).
Noreen Sher Akbar and S. Nadeem, “Peristaltic Flow of a Micropolar Fluid with Nanoparticles in Small Intestine,” Applied Nanoscience, 3(6), 461-468 (2013). https://doi.org/10.1007/s13204-012-0160-2
S. Nadeem and S. Ijaz, “Theoretical analysis of metallic nanoparticles on blood flow through stenosed artery with permeable walls,” Physics Letters A, 379(6), 542-554 (2015). https://doi.org/10.1016/j.physleta 2014.12.013
A.M. Abd-Alla, E.N. Thabet and F.S. Bayones, “Numerical solution for MHD peristaltic transport in an inclined Nano fluid symmetric channel with porous medium,” Sci. Rep. 12(1), 1-11 (2022). https://doi.org/10.1038/s41598-022-07193-5
J. He, N.S. Elgazery, K. Elagamy and A.N.Y. Elazem, “Efficacy of a modulated viscosity-dependent temperature/nanoparticles concentration parameter on a nonlinear radiative electromagnetic-Nano fluid flow along an elongated stretching sheet,” J. Appl. Comput. Mech. 9(3), 848-860 (2023). https://doi.org/10.22055/jacm. 2023 42294.3905
K. Prasad, Y. Prabhaker and A.R. Mohammed, “Thermal effects of two immiscible fluids through a permeable stenosed artery having nanofluid in the core region,” Heat Transfer, 51(5), 4562-4583 (2022). https://doi.org/10.1002/htj.22513
K.M. Prasad, N. Subadra, P.R. Shekhar and R.B. Vijaya, “Jeffrey fluid flow driven by peristaltic pumping with nanoparticles in an inclined tube,” Journal of Naval Architecture & Marine Engineering, 20(2), 165–175 (2023). https://doi.org/10.1002/htj.22513N
A.S. Dawood, F.A. Kroush, R.M. Abumandour, and I.M. Eldesoky, “Multi-effect analysis of nanofluid flow in stenosed arteries with variable pressure gradient: analytical study,” SN Applied Sciences, 5(12), 382 (2023). https://doi.org/10.1007/s42452-023-05567-6
Md.A. Ikbal, S. Chakravarty, K.K.L. Wong, J. Mazumdar and P.K. Mandal, “Unsteady response of non-Newtonian blood flow through a stenosed artery in magnetic field,” In Journal of Computational and Applied Mathematics, 230(1), 243–259 (2009). https://doi.org/10.1016/j.cam.2008.11.010
R. Bali and U. Awasthi, “Effect of a magnetic field on the resistance to blood flow through stenotic artery,” Applied Mathematics and Computation, 188(2), 1635–1641 (2007). https://doi.org/10.1016/j.amc.2006.11.019
J.C. Misra, A. Sinha and G.C. Shit, “Mathematical modelling of blood flow in a porous vessel having double stenoses in the presence of an external magnetic field,” International Journal of Biomathematics, 04(02), 207–225 (2011). https://doi.org/10.1142/s1793524511001428
J.-H. He, “A coupling method of a Homotopy technique and a perturbation technique for non-linear problems,” In International Journal of Non-Linear Mechanics, 35(1), 37–43 (2000). https://doi.org/10.1016/s0020-7462(98)00085-7
J.-H. He, “Application of homotopy perturbation method to nonlinear wave equations,” Chaos, Solitons & Fractals, 26(3), 695–700 (2005). https://doi.org/10.1016/j.chaos.2005.03.006
I.J.D. Craig and P.G. Watson, “Magnetic reconnection solutions based on a generalized Ohm’s law,” Solar Phys. 214, 131–150 (2003). https://doi.org/10.1023/A:1024075416016
V.K. Sud, G.S. Sephon and R.K. Mishra, “Pumping action on blood flow by a magnetic field,” Bull. Math. Biol. 39, 385 (1977). https://doi.org/10.1007/BF02462917
H.L. Agrawal and B. Anwaruddin, “Peristaltic flow of blood in a branch,” Ranchi Univ. Math. J. 15, 111–121 (1984).
T. Sochi, “Non-Newtonian flow in porous media,” Polymer, 51(22), 5007–5023 (2010). https://doi.org/10.1016/j.polymer.2010.07.047
K.M. Prasad and P.R. Yasa, “Mathematical Modelling on an Electrically Conducting Fluid Flow in an Inclined Permeable Tube with Multiple Stenoses,” International Journal of Innovative Technology and Exploring Engineering, 9(1), 3915–3921 (2019). https://doi.org/10.35940/ijitee.a4989.119119
W.F.W. Azmi, A.Q. Mohamad, L.Y. Jiann and S. Shafie, “Mathematical fractional analysis on blood Casson fluid in slip and small arteries with the cholesterol porosity effect,” Malaysian Journal of Mathematical Sciences, 18(4), 755–774 (2024). https://doi.org/10.47836/mjms. 18.4.05
K.M. Prasad, and P.R. Yasa, “Flow of non-Newtonian fluid through a permeable artery having non-uniform cross section with multiple stenosis,” Journal of Naval Architecture and Marine Engineering, 17(1), 31–38 (2020). https://doi.org/10.3329/jname.v17i1.40942
T. Sudha, C. Umadevi, M. Dhange, S. Manna, and J.C. Misra, “Effects of stenosis and dilatation on flow of blood mixed with suspended nanoparticles: A study using Homotopy technique,” 26(1), 251-265 (2021). https://doi.org/10.2478/ijame-2021-0015
M.K. Prasad, R.B. Vijaya and C. Umadevi, “Effects of Stenosis and Post Stenotic Dilatations on Jeffrey Fluid Flow in Arteries,” International Journal of Research in Engineering and Technology, 4, 195-201 (2015). https://doi.org/10.15623/ijret.2015.0413032
B. Pincombe, B. Mazumdar, and J. Hamilton-Craig, “Effects of multiple stenoses and post- stenotic dilation on non- Newtonian blood flow in small arteries,” Medical & Biological Engineering & Computing, 37(5), 595–599 (1999). https://doi.org/10.1007/bf02513353
M. Dhange, G. Sankad, R. Safdar, W. Jamshed, M.R. Eid, U. Bhujakkanavar, et al., “A mathematical model of blood flow in a stenosed artery with post-stenotic dilatation and a forced field,” PLoS ONE, 17(7), e0266727 (2022). https://doi.org/10.1371/journal.pone.0266727
K.M. Prasad, N. Subadra and M.A.S. Srinivas, “Peristaltic transport of a micropolar fluid with nanoparticles in an inclined tube with permeable walls,” International Journal of Advanced Research Trends in Engineering and Technology (IJARTET), 4(10), (2017). https://ijartet.com/2750/v4i10/journal
K.M. Prasad and T. Sudha, “The effects of post-stenotic dilatations on the flow of micropolar fluid through stenosed artery with suspension of nanoparticles,” AIP Conference Proceedings, 2246(1), 020082 (2000). https://doi.org/10.1063/5.0014455
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