Exact Analysis of Unsteady Convective Diffusion in Herschel-Bulkley Fluid Flow- Application to Catheterised Stenosed Artery
DOI:
https://doi.org/10.37934/cfdl.14.11.7587Keywords:
Blood flow, catheter, solute dispersion, Stenosis, Herschel-Bulkley fluidAbstract
One of the major causes of cardiovascular disease is atherosclerosis or stenosis. This study is designed to improve the current body of knowledge regarding the condition by inserting a long thin tube called a catheter to widen the narrow part in the artery. The study reviewed the effects of catheter radius, yield stress, and power law index on the velocity distribution, and transport coefficients of solute. A mathematical model is deployed to investigate the dispersion of solute in the flow of a Herschel-Bulkley (H-B) fluid in an annulus, whereas the dispersion process is studied using the generalised dispersion model (GDM) by solving the convective diffusion equation. Resultan tly, the velocity reduces following an increase in the yield stress, catheter size, and power law index. Meanwhile, the dispersion coefficient exhibits a same behaviour as the aforementioned parameters ascend considerably. The dispersion coefficient alterations occurred rapidly for small values of time and became significantly constant following an increase in the time values. Conclusively, this study can be useful in dispersion of a drug to the affected artery where an abnormal plaque was formed.Downloads
References
Das, Prosanjit, and Prashanta Kumar Mandal. "Solute dispersion in Casson fluid flow through a stenosed artery with absorptive wall." Zeitschrift für angewandte Mathematik und Physik 71, no. 3 (2020): 1-24. https://doi.org/10.1007/s00033-020-01322-8
Ndenda, J. P., S. Shaw, and J. B. H. Njagarah. "Solute dispersion of drug carrier during magnetic drug targeting for blood flow through a microvessel." Journal of Applied Physics 130, no. 2 (2021): 024701. https://doi.org/10.1063/5.0053645
Roy, Ashis Kumar, and O. Anwar Bég. "Mathematical modelling of unsteady solute dispersion in two-fluid (micropolar-Newtonian) blood flow with bulk reaction." International Communications in Heat and Mass Transfer 122 (2021): 105169. https://doi.org/10.1016/j.icheatmasstransfer.2021.105169
Debnath, Sudip, Weiquan Jiang, Mingyang Guan, and Guoqian Chen. "Effect of ring-source release on dispersion process in Poiseuille flow with wall absorption." Physics of Fluids 34, no. 2 (2022): 027106. https://doi.org/10.1063/5.0077957
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
Das, Prosanjit, Sarifuddin, Jyotirmoy Rana, and Prashanta Kumar Mandal. "Solute dispersion in transient Casson fluid flow through stenotic tube with exchange between phases." Physics of Fluids 33, no. 6 (2021): 061907. https://doi.org/10.1063/5.0052770
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
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
Tripathi, Jayati, B. Vasu, O. Anwar Bég, Rama Subba Reddy Gorla, and Peri K. Kameswaran. "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 139 (2021): 105009. https://doi.org/10.1016/j.compbiomed.2021.105009
Zidan, A. M., L. B. McCash, Salman Akhtar, Anber Saleem, Alibek Issakhov, and Sohail Nadeem. "Entropy generation for the blood flow in an artery with multiple stenosis having a catheter." Alexandria Engineering Journal 60, no. 6 (2021): 5741-5748. https://doi.org/10.1016/j.aej.2021.04.058
Sarifuddin. "CFD modelling of Casson fluid flow and mass transport through atherosclerotic vessels." Differ Equ Dyn Syst (2020). https://doi.org/10.1007/s12591-020-00522-y
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
Sankar, D. S., and K. Hemalatha. "A non-Newtonian fluid flow model for blood flow through a catheterized artery—steady flow." Applied mathematical modelling 31, no. 9 (2007): 1847-1864. https://doi.org/10.1016/j.apm.2006.06.009
Abbas, Z., B. Iftikhar, M. S. Shabbir, M. Alghamdi, and J. Iqbal. "Numerical treatment of slip velocity and catheterization on the gravity flow of non-Newtonian fluid model through a uniform blood vessel." Physica Scripta 95, no. 5 (2020): 055006. https://doi.org/10.1088/1402-4896/ab6da2
Swarup, S. (2000). Chapter 5 - Fluid Dynamics. Page 622-633.
Layek, G. C., S. Mukhopadhyay, and Rama Subba Reddy Gorla. "Unsteady viscous flow with variable viscosity in a vascular tube with an overlapping constriction." International journal of engineering science 47, no. 5-6 (2009): 649-659. https://doi.org/10.1016/j.ijengsci.2009.01.011
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
Roy, Ashis Kumar, and O. Anwar Bég. "Asymptotic study of unsteady mass transfer through a rigid artery with multiple irregular stenoses." Applied Mathematics and Computation 410 (2021): 126485. https://doi.org/10.1016/j.amc.2021.126485
Kapur, J. N. (1985). Chapter 7 - Mathematical Models in Biology and Medicine. Page 455-480.
Ramana, B., G. Sarojamma, B. Vishali, and P. Nagarani. "Dispersion of a solute in a Herschel–Bulkley fluid flowing in a conduit." Journal of Experimental Sciences 3, no. 2 (2012).
Dash, R. K., G. Jayaraman, and K. N. Mehta. "Shear augmented dispersion of a solute in a Casson fluid flowing in a conduit." Annals of Biomedical Engineering 28, no. 4 (2000): 373-385. https://doi.org/10.1114/1.287
Abidin, Siti Nurul Aifa Mohd Zainul, Nurul Aini Jaafar, and Zuhaila Ismail. "Herschel-Bulkley Model of Blood Flow through a Stenosed Artery with the Effect of Chemical Reaction on Solute Dispersion." Malaysian Journal of Fundamental and Applied Sciences 17, no. 4 (2021): 457-474. https://doi.org/10.11113/mjfas.v17n4.2144
Jaafar, Nurul Aini. "Mathematical Analysis of Herschel-Bulkley Fluid Model for Solute Dispersion in Blood Flow Through Narrow Conduits." PhD diss., PhD thesis, Universiti Sains Malaysia, 2017.
Roy, Ashis Kumar, and Sachin Shaw. "Shear augmented microvascular solute transport with a two-phase model: Application in nanoparticle assisted drug delivery." Physics of Fluids 33, no. 3 (2021): 031904. https://doi.org/10.1063/5.0035754
Bessonov, Nikolay, Adélia Sequeira, Sergey Simakov, Yu Vassilevskii, and Vitaly Volpert. "Methods of blood flow modelling." Mathematical modelling of natural phenomena 11, no. 1 (2016): 1-25. https://doi.org/10.1051/mmnp/201611101
Ramachandra Rao, A., and K. S. Deshikachar. "An exact analysis of unsteady convective diffusion in an annular pipe." ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik 67, no. 3 (1987): 189-195. https://doi.org/10.1002/zamm.19870670315
Hussain, Mohammad A., Subir Kar, and Ram R. Puniyani. "Relationship between power law coefficients and major blood constituents affecting the whole blood viscosity." Journal of Biosciences 24, no. 3 (1999): 329-337. https://doi.org/10.1007/BF02941247
