Mathematical Analysis of Unsteady Solute Dispersion with Chemical Reaction Through a Stenosed Artery

Authors

  • Nurul Aini Jaafar Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor, Johor Bahru, Malaysia
  • Siti NurulAifa Mohd ZainulAbidin Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor, Johor Bahru, Malaysia
  • Zuhaila Ismail Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor, Johor Bahru, Malaysia
  • Ahmad Qushairi Mohamad Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor, Johor Bahru, Malaysia

DOI:

https://doi.org/10.37934/arfmts.86.2.5673

Keywords:

Blood flow, Dispersion function, Generalized dispersion model, Herschel-Bulkley, Non-Newtonian fluids, Stenosed artery

Abstract

One major kind of arterial disease in blood flow that attracted many researchers is arterial stenosis. Arterial stenosis occurs when a lumen of artery is narrowed by the accumulation of fats, cholesterols and lipids plaques at the inner layer of the wall of an artery. To treat this arterial disease, the drug (solute) is injected into the blood vessels. Injection of the drug into the blood vessel cause the occurrence of chemical reaction between the drug and blood proteins and it affects the effectiveness of the solute transportation in blood flow. Hence, this study examines the unsteady dispersion of solute with the influence of chemical reaction and stenosis height through a very narrow artery with a cosine-curved stenosis. The blood is treating as Herschel-Bulkley (H-B) fluid. The momentum and constitutive equations are solved analytically to gain velocity of H-B blood flow. The convective-diffusion equation is solved by applying the generalized dispersion model to gain the dispersion function of solute. The influence of chemical reaction, power-law index, plug flow radius and stenosis height on the solute dispersion process is investigated. The results are validated with the previous solution without the effect of chemical reaction and stenosis. The results showed a good conformity between the two solutions. An increase in the chemical reaction coefficient, stenosis height, power-law index and plug flow radius reduces the dispersion function. It is observed that the solute dispersion in blood flow is affected by chemical reaction and stenosis height. H-B fluid is an appropriate fluid to investigate the blood velocity and transportation of the drug in blood flow to the targeted stenosed region through a very narrow artery for the treatment of arterial diseases. The results of the present study can potentially be used to predict the changes of blood flow behavior and dispersion process in blood flow.

Author Biographies

Nurul Aini Jaafar, Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor, Johor Bahru, Malaysia

nurulaini.jaafar@utm.my

Siti NurulAifa Mohd ZainulAbidin, Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor, Johor Bahru, Malaysia

aifazainul94@gmail.com

Zuhaila Ismail, Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor, Johor Bahru, Malaysia

zuhaila@utm.my

Ahmad Qushairi Mohamad, Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor, Johor Bahru, Malaysia

ahmadqushairi@utm.my

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Published

2021-08-20

How to Cite

Jaafar, N. A. ., Mohd ZainulAbidin, S. N., Ismail, Z., & Mohamad, A. Q. (2021). Mathematical Analysis of Unsteady Solute Dispersion with Chemical Reaction Through a Stenosed Artery. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 86(2), 56–73. https://doi.org/10.37934/arfmts.86.2.5673
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