Herschel-Bulkley model of blood flow through a stenosed artery with the effect of chemical reaction on solute dispersion

Abstract

A non-Newtonian mathematical model of blood flow described as the Hershel- Bulkley fluid model in a stenosed artery is studied together with the effect of its chemical reaction. The expressions of the shear stress, velocity, mean velocity, and relative velocity in the plug and non-plug flow field were evaluated. The convective-diffusion equation was solved using the Taylor-Aris technique subjected to the relevant boundary condition in determining the concentration as well as the relative and effective axial diffusivity of the solute. The efficiency of the dispersion process was affected by the presence of chemical reactions and stenosis in blood flow. The normalised velocity decreased as the power-law index and yield stress increased. The height and length of the stenosis, as well as the power-law index, increased with an increase in the parameters of the chemical reaction rate. In contrast, the relative axial diffusivity and effective axial diffusivity showed a reverse behaviour. The existence of stenosis restricted the blood flow and drug dispersion. In short, this study improved the understanding of the physiological processes involved in the dispersion of drugs and nutrients in the circulatory system. Furthermore, it proved that the dispersion of a solute in the blood flow happened at a low shear rate through narrow arteries.