Abstract
A theoretical study of three metallic nanoparticles like gold, copper and silver and non-metallic nanoparticles like aluminium oxide and titanium oxide in a multi-stenosed artery with a regular catheter is studied. Blood in the artery is considered Newtonian fluid due to the presence of plasma. By the assumptions of mild stenosis, the governing equations of nanoparticles are simplified, and using Cauchy–Euler method, the solutions are found. We focus on the study of various thermal conductivity models in nanofluids. The effects of thermal conductivity on these nanoparticles are studied and graphically plotted. The study reveals that the non-metallic nanoparticles enhance the flow of blood in the arteries and regulate the flow in axial velocity. Multiple stenosis in the artery with parameters such as shape parameter, stenosis height, and catheter radius has significant effects on velocity, temperature, wall shear stress, and resistance impedance. The effect of the Grashof number on different physical parameters is also discussed. Models depending on the thermal conductivity factors rather than nanofluid volume fraction are highly reliable.
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Abbreviations
- Gr:
-
Grashof number
- K :
-
Thermal conductivity
- F :
-
Flow rate (\(\hbox {m}^{3}\,\hbox {s}^{-1}\))
- L :
-
Radius of artery with stenosis
- \(L_{0}\) :
-
Radius of artery without stenosis
- H :
-
Height of the artery
- \(S_{rz}\) :
-
Wall shear stress (\({\hbox {N m}}^{-2}\))
- c :
-
Radius of catheter
- d :
-
Stenosis height
- h :
-
Dimensional stenosis position
- i :
-
Dimensionless stenosis position
- \(q_{0}\) :
-
Heat source
- r :
-
Radial axis
- t :
-
Temperature of the fluid (K)
- \(t_{0}\) :
-
Temperature in the inner wall of the artery (K)
- \(t_{1}\) :
-
Temperature in the outer wall of the artery (K)
- u :
-
Average velocity (\({\hbox {m s}}^{-1}\))
- w :
-
Velocity taken over axial z (\(\hbox {m s}^{-1}\))
- n :
-
Shape parameter
- z :
-
Axial axis
- \(c_{{\mathrm{p}}}\) :
-
Specific heat capacitance (\({\hbox {J kg}}^{-1}\,{\hbox {K}}\))
- \(\rho \) :
-
Density (\({\hbox {kg m}}^{-3}\))
- \(\gamma \) :
-
Thermal expansion coefficient
- \(\mu \) :
-
Viscosity (\(\hbox {N s m}^{-2}\))
- \(\psi \) :
-
Shape parameter
- \(\theta \) :
-
Dimensionless temperature
- \(\Delta p\) :
-
Pressure gradient
- \(\lambda \) :
-
Resistance impedance
- \(\beta \) :
-
Heat source
- \(\varPhi \) :
-
Nanofluid volume fraction
- bf:
-
Basefluid
- nf:
-
Nanofluid
- np:
-
Nanoparticles
References
Abdelsalam SI, Bhatti M (2019) New insight into AuNP applications in tumour treatment and cosmetics through wavy annuli at the nanoscale. Sci Rep 9(1):1–14. https://doi.org/10.1038/s41598-018-36459-0
Abdullah I, Naser N, Talib A, Mahali S (2015) Effects of magnetic field and hall current to the blood velocity and LDL transfer. J Phys Conf Ser 633(1):012133. https://doi.org/10.1088/1742-6596/633/1/012133
Ahmed A, Nadeem S (2016) The study of (Cu, Ti0\(_{2}\), SAl\(_{2}\)O\(_{3}\)) nanoparticles as antimicrobials of blood flow through diseased arteries. J Mol Liq 216:615–623. https://doi.org/10.1016/j.molliq.2016.01.059
Ahmed A, Nadeem S (2017) Effects of magnetohydrodynamics and hybrid nanoparticles on a micropolar fluid with 6-types of stenosis. Results Phys 7:4130–4139. https://doi.org/10.1016/j.rinp.2017.10.032
Akbar NS (2016) Non-Newtonian model study for blood flow through a tapered artery with a stenosis. Alex Eng J 55(1):321–329. https://doi.org/10.1016/j.aej.2015.09.010
Akram J, Akbar NS, Tripathi D (2020) Blood-based graphene oxide nanofluid flow through capillary in the presence of electromagnetic fields: a Sutterby fluid model. Microvasc Res 132:104062. https://doi.org/10.1016/j.mvr.2020.104062
Alhussain ZA (2022) Mixed convective flow in a multiple port ventilation square cavity with insulated baffle. Case Stud Thermal Eng 30:101785. https://doi.org/10.1016/j.csite.2022.101785
Alhussain ZA, Renuka A, Muthtamilselvan M (2021) A magnetobioconvective and thermal conductivity enhancement in nanofluid flow containing gyrotactic microorganism. Case Stud Thermal Eng 23:100809. https://doi.org/10.1016/j.csite.2020.100809
Azmi W, Sharma K, Mamat R, Najafi G, Mohamad M (2016) The enhancement of effective thermal conductivity and effective dynamic viscosity of nanofluids—a review. Renew Sustain Energy Rev 53:1046–1058. https://doi.org/10.1016/j.rser.2015.09.081
Back L (1994) Estimated mean flow resistance increase during coronary artery catheterization. J Biomech 27(2):169–175. https://doi.org/10.1016/0021-9290(94)90205-4
Ellahi R, Rahman S, Nadeem S, Akbar NS (2014) Blood flow of nanofluid through an artery with composite stenosis and permeable walls. Appl Nanosci 4(8):919–926. https://doi.org/10.1007/s13204-013-0253-6
Elnaqeeb T (2019) Modeling of Au (NPs)-blood flow through a catheterized multiple stenosed artery under radial magnetic field. Eur Phys J Spec Top 228(12):2695–2712. https://doi.org/10.1140/epjst/e2019-900059-9
Elnaqeeb T, Mekheimer KS, Alghamdi F (2016) Cu-blood flow model through a catheterized mild stenotic artery with a thrombosis. Math Biosci 282:135–146. https://doi.org/10.1016/j.mbs.2016.10.003
Ghandi R, Sharma B, Kumawat C, Bég OA et al (2022) Modeling and analysis of magnetic hybrid nanoparticle (Au-Al\(_{2}\)O\(_{3}\) blood) based drug delivery through a bell-shaped occluded artery with joule heating, viscous dissipation and variable viscosity effects. Proc Inst Mech Eng Part E J Process Mech Eng. https://doi.org/10.1177/09544089221080273
Ghassemi M, Shahidian A (2017) Nano and bio heat transfer and fluid flow. Academic Press, New York. https://www.perlego.com/book/1831050/nano-and-bio-heat-transfer-and-fluid-flow-pdf
Hamilton RL, Crosser O (1962) Thermal conductivity of heterogeneous two-component systems. Ind Eng Chem Fundam 1(3):187–191. https://doi.org/10.1021/i160003a005
Hussain A, Sarwar L, Rehman A, Al Mdallal Q, Almaliki AH, ElShafay A (2022) Mathematical analysis of hybrid mediated blood flow in stenosis narrow arteries. Sci Rep 12(1):1–10. https://doi.org/10.1038/s41598-022-15117-6
Ijaz S, Nadeem S (2017) A biomedical solicitation examination of nanoparticles as drug agents to minimize the hemodynamics of a stenotic channel. Eur Phys J Plus 132(11):1–13. https://doi.org/10.1140/epjp/i2017-11703-6
Mansour M, Ahmed S, Hady F, Ibrahim F, Ismaeel A (2022) Numerical simulation for nanofluid leakage from a single 2D blood vessel. Alex Eng J 61(5):3999–4010. https://doi.org/10.1016/j.aej.2021.09.029
Mathew A, Areekara S, Sabu A, Saleem S (2021) Significance of multiple slip and nanoparticle shape on stagnation point flow of silver-blood nanofluid in the presence of induced magnetic field. Surf Interfaces 25:101267. https://doi.org/10.1016/j.surfin.2021.101267
Maxwell JC (1873) A treatise on electricity and magnetism. Clarendon Press, London. http://hdl.loc.gov/loc.rbc/General.15568v1.1
Mintsa HA, Roy G, Nguyen CT, Doucet D (2009) New temperature dependent thermal conductivity data for water-based nanofluids. Int J Therm Sci 48(2):363–371. https://doi.org/10.1016/j.ijthermalsci.2008.03.009
Muthtamilselvan M, Suganya S, Al-Mdallal QM (2021) Stagnationpoint flow of the Williamson nanofluid containing gyrotactic micro-organisms. Proc Natl Acad Sci India Sect A 91(4):633–648. https://doi.org/10.1007/s40010-021-00764-7
Nadeem S, Ijaz S (2015) Single wall carbon nanotube (SWCNT) examination on blood flow through a multiple stenosed artery with variable nanofluid viscosity. AIP Adv 5(10):107217. https://doi.org/10.1063/1.4934583
Nadeem S, Ijaz S (2015) Theoretical analysis of metallic nanoparticles on blood flow through tapered elastic artery with overlapping stenosis. IEEE Trans Nanobiosci 14(4):417–428. https://doi.org/10.1109/TNB.2015.2389253
Noreen S, Rashidi M, Qasim M (2017) Blood flow analysis with considering nanofluid effects in vertical channel. Appl Nanosci 7(5):193–199. https://doi.org/10.1007/s13204-017-0564-0
Pak BC, Cho YI (1998) Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles. Exp Heat Trans Int J 11(2):151–170. https://doi.org/10.1080/08916159808946559
Sadham Hussain I, Prakash D, Kumar S, Muthtamilselvan M (2021) Bioconvection of nanofluid flow in a thin moving needle in the presence of activation energy with surface temperature boundary conditions. Proc Inst Mech Eng Part E J Process Mech Eng. https://doi.org/10.1177/09544089211053969
Suganya S, Muthtamilselvan M, Alhussain ZA (2021) Activation energy and Coriolis force on Cu, TiO\(_{2}\) water hybrid nanofluid flow in an existence of nonlinear radiation. Appl Nanosci 11(3):933–949. https://doi.org/10.1007/s13204-020-01647-w
Torii R, Wood NB, Hughes AD, Thom SA, Aguado-Sierra J, Davies JE, Francis DP, Parker KH, Xu XY (2007) A computational study on the influence of catheter-delivered intravascular probes on blood flow in a coronary artery model. J Biomech 40(11):2501–2509. https://doi.org/10.1016/j.jbiomech.2006.11.004
Tripathi J, Vasu B, Subba Reddy Gorla R, Chamkha AJ, Murthy P, Anwar Beg O (2021) Blood flow mediated hybrid nanoparticles in human arterial system: recent research, development and applications. J Nanofluids 10(1):1–30. https://doi.org/10.1166/jon.2021.1769
Xuan Y, Li Q (2000) Heat transfer enhancement of nanofluids. Int J Heat Fluid Flow 21(1):58–64. https://doi.org/10.1016/S0142-727X(99)00067-3
Yang Z, Gao D, Guo X, Jin L, Zheng J, Wang Y, Chen S, Zheng X, Zeng L, Guo M et al (2020) Fighting immune cold and reprogramming immunosuppressive tumor microenvironment with red blood cell membranecamouflaged nanobullets. ACS Nano 14(12):17442–17457. https://doi.org/10.1021/acsnano.0c07721
Zaman A, Ali N, Bég OA, Sajid M (2016) Heat and mass transfer to blood flowing through a tapered overlapping stenosed artery. Int J Heat Mass Transf 95:1084–1095. https://www.cheric.org/research/tech/periodicals/doi.phpart_seq=1377161
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The author would like to thank the Deanship of Scientific Research at Majmaah University for supporting this work under Project No. R-2022-261.
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Alhussain, Z.A. A comprehensive study of thermal conductivity models with metallic and non-metallic nanoparticles in the blood flow through a regular catheter in multi-stenosed artery. Appl Nanosci 12, 4033–4045 (2022). https://doi.org/10.1007/s13204-022-02622-3
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DOI: https://doi.org/10.1007/s13204-022-02622-3