Effect of Catheter and Stenosis on Solute Diffusion in Non-Newtonian Blood Flow through a Catheterized Stenosed Artery
DOI:
https://doi.org/10.37934/cfdl.14.12.1126Keywords:
Steady blood flow, Unsteady solute dispersion, Herschel-Bulkley model, Generalized Dispersion Model, Catheterized stenosed arteryAbstract
The presence of stenosis at the wall of the artery lead to further cardiovascular diseases such as heart attack, stroke and many more. Treatment of a stenosed artery includes the insertion of a catheter through the artery which affects the blood flow and solute dispersion. This present study focuses on the effect of catheter radius and stenosis height on the blood flow and solute dispersion behavior. The problem is modelled using the Herschel-Bulkley fluid to represent the blood rheology, with catheter and stenosis as the boundary conditions. Analytical solutions in integral form are obtained by solving the momentum equation and Herschel-Bulkley constitutive equation. The integrals are numerically evaluated using the Simpson’s 3/8 rule and Regula-Falsi method to obtain the blood velocity. The obtained velocity is employed into the unsteady convective-diffusion equation and solved using the generalized dispersion model (GDM) to analyse the behaviour of solute diffusion. The influence of catheter radius and stenosis height on the diffusion coefficient and mean concentration of solute are observed. Results show that the diffusion coefficient decreases as the catheter radius and stenosis height increases. A decrease in diffusion coefficient simultaneously increases the solute mean concentration.Downloads
References
ZainulAbidin, Siti Nurulaifa Mohd, Zuhaila Ismail, and Nurul Aini Jaafar. "Mathematical Modeling of Unsteady Solute Dispersion in Bingham Fluid Model of Blood Flow Through an Overlapping Stenosed Artery." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 87, no. 3 (2021): 134-147. https://doi.org/10.37934/arfmts.87.3.134147
Feltes, Timothy F., Emile Bacha, Robert H. Beekman III, John P. Cheatham, Jeffrey A. Feinstein, Antoinette S. Gomes, Ziyad M. Hijazi et al. "Indications for cardiac catheterization and intervention in pediatric cardiac disease: a scientific statement from the American Heart Association." Circulation 123, no. 22 (2011): 2607-2652. https://doi.org/10.1161/CIR.0b013e31821b1f10
Debnath, Sudip, Apu Kumar Saha, B. S. Mazumder, and Ashis Kumar Roy. "Transport of a reactive solute in a pulsatile non-Newtonian liquid flowing through an annular pipe." Journal of Engineering Mathematics 116, no. 1 (2019): 1-22. https://doi.org/10.1007/s10665-019-09999-1
Gill, W. N., and R. Sankarasubramanian. "Exact analysis of unsteady convective diffusion." Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 316, no. 1526 (1970): 341-350. https://doi.org/10.1098/rspa.1970.0083
Sebastian, Binil Thomas, and P. Nagarani. "Convection-diffusion in unsteady non-Newtonian fluid flow in an annulus with wall absorption." Korea-Australia rheology journal 30, no. 4 (2018): 261-271. https://doi.org/10.1007/s13367-018-0025-7
Nagarani, P., G. Sarojamma, and G. Jayaraman. "Effect of boundary absorption on dispersion in Casson fluid flow in an annulus: application to catheterized artery." Acta Mechanica 202, no. 1 (2009): 47-63. https://doi.org/10.1007/s00707-008-0013-y
Nagarani, P., and B. T. Sebastian. "Effect of flow unsteadiness on dispersion in non-Newtonian fluid in an annulus." Journal of applied mathematics & informatics 35, no. 3_4 (2017): 241-260. https://doi.org/10.14317/jami.2017.241
Ratchagar, Nirmala P., and R. VijayaKumar. "Dispersion of solute with chemical reaction in blood flow." Bulletin of Pure and Applied Sciences-Mathematics and Statistics 38, no. 1 (2019): 385-395. https://doi.org/10.5958/2320-3226.2019.00042.0
Vajravelu, Kuppalapalle, Sreedharamalle Sreenadh, Palluru Devaki, and Kerehalli Prasad. "Mathematical model for a Herschel-Bulkley fluid flow in an elastic tube." Open Physics 9, no. 5 (2011): 1357-1365. https://doi.org/10.2478/s11534-011-0034-3
Venkatesan, Jayavelu, D. S. Sankar, K. Hemalatha, and Yazariah Yatim. "Mathematical analysis of Casson fluid model for blood rheology in stenosed narrow arteries." Journal of Applied Mathematics 2013 (2013). https://doi.org/10.1155/2013/583809
Rajashekhar, C., G. Manjunatha, K. V. Prasad, B. B. Divya, and Hanumesh Vaidya. "Peristaltic transport of two-layered blood flow using Herschel–Bulkley Model." Cogent Engineering 5, no. 1 (2018): 1495592. https://doi.org/10.1080/23311916.2018.1495592
Sankar, D. S., and K. Hemalatha. "Pulsatile flow of Herschel–Bulkley fluid through catheterized arteries–A mathematical model." Applied Mathematical Modelling 31, no. 8 (2007): 1497-1517. https://doi.org/10.1016/j.apm.2006.04.012
Sankar, D. S., and Usik Lee. "Two-fluid Herschel-Bulkley model for blood flow in catheterized arteries." Journal of Mechanical science and technology 22, no. 5 (2008): 1008-1018. https://doi.org/10.1007/s12206-008-0123-4
Neeraja, G., P. A. Dinesh, K. Vidya, and C. S. K. Raju. "Peripheral layer viscosity on the stenotic blood vessels for Herschel-Bulkley fluid model." Informatics in Medicine Unlocked 9 (2017): 161-165. https://doi.org/10.1016/j.imu.2017.08.004
Abbas, Z., M. S. Shabbir, and N. Ali. "Analysis of rheological properties of Herschel-Bulkley fluid for pulsating flow of blood in ω-shaped stenosed artery." AIP Advances 7, no. 10 (2017): 105123. https://doi.org/10.1063/1.5004759
Srivastava, V. P., and Rati Rastogi. "Blood flow through a stenosed catheterized artery: Effects of hematocrit and stenosis shape." Computers & mathematics with applications 59, no. 4 (2010): 1377-1385. https://doi.org/10.1016/j.camwa.2009.12.007
Gudekote, Manjunatha, Rajashekhar Choudhari, Hanumesh Vaidya, and Kerehalli Vinayaka Prasad. "Peristaltic flow of Herschel-Bulkley fluid in an elastic tube with slip at porous walls." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 52, no. 1 (2018): 63-75.
Jaafar, Nurul Aini, Siti NurulAifa Mohd ZainulAbidin, Zuhaila Ismail, and Ahmad Qushairi Mohamad. "Mathematical Analysis of Unsteady Solute Dispersion with Chemical Reaction Through a Stenosed Artery." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 86, no. 2 (2021): 56-73. https://doi.org/10.37934/arfmts.86.2.5673
Tey, Wah Yen, Yutaka Asako, Nor Azwadi Che Sidik, and Rui Zher Goh. "Governing equations in computational fluid dynamics: Derivations and a recent review." Progress in Energy and Environment 1 (2017): 1-19.
Rathore, Surabhi, and D. Srikanth. "Mathematical study of transport phenomena of blood nanofluid in a diseased artery subject to catheterization." Indian Journal of Physics 96, no. 7 (2022): 1929-1942. https://doi.org/10.1007/s12648-021-02166-2
Kumar, T. Prasanna. "Heat Transfer of SWCNT-MWCNT Based Hybrid Nanofluid Boundary Layer Flow with Modified Thermal Conductivity Model." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 92, no. 2 (2022): 13-24. https://doi.org/10.37934/arfmts.92.2.1324
Zokri, Syazwani Mohd, Nur Syamilah Arifin, Abdul Rahman Mohd Kasim, and Mohd Zuki Salleh. "Free convection boundary layer flow of Jeffrey nanofluid on a horizontal circular cylinder with viscous dissipation effect." Journal of Advanced Research in Micro and Nano Engineering 1, no. 1 (2020): 1-14.
Elfaghi, Abdulhafid MA, Alhadi A. Abosbaia, Munir FA Alkbir, and Abdoulhdi AB Omran. "CFD Simulation of Forced Convection Heat Transfer Enhancement in Pipe Using Al2O3/Water Nanofluid." Journal of Advanced Research in Numerical Heat Transfer 8, no. 1 (2022): 44-49.
