A non-Newtonian mathematical model of blood described as a Hershel-Bulkley fluid model flowing in a stenosed artery with the effect of a chemical reaction is mathematically studied. The expressions of the shear stress, mean velocity and absolute velocity in the plug and non-plug flow field are evaluated analytically. The convective-diffusion equation is solved using the Taylor-Aris technique subject to the relevant boundary constraint in determining the concentration, relative and effective axial diffusivity. The efficiency of the dispersion process is affected by the presence of chemical reaction and stenosis in blood flow. The normalized velocity decreases as stenosis height and stenosis length increase. The relative axial diffusivity is significantly lower while the effective axial diffusivity decreases considerably as the chemical reaction rate, the height of the stenosis and the length of the stenosis increase. Besides, it is observed that as the solute disperses in the presence of stenosis, the flow quantities are lesser than in the absence of stenosis. Further, this study helps in understanding many physiological processes for instance dispersion of drugs or nutrients in the circulatory system. Also, to enhance the dispersion of a solute in blood flow through narrow arteries in the presence of chemical reaction and stenosis.
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.
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