Herschel-Bulkley model for mathematical analysis of blood flow through an asymmetric stenosed artery with unsteady reactive solute dispersion

Abstract

This study examined the effects of chemical reaction, stenosis shape parameter and non-Newtonian behaviour on solute dispersion in blood flow via an asymmetric stenosed artery using the generalised dispersion model (GDM). The Herschel- Bulkley (H-B) fluid model, which consists of a yield stress and power-law index, is used to represent the non-Newtonian characteristics of blood in a narrow artery at a low shear rate. The impact of stenosis shape parameter, chemical reaction, power-law index and plug flow radius on the dispersion coefficient and effective axial diffusion of solute is shown. The findings showed that the aforementioned parameters significantly impact the overall process of the chemically reactive solute in a bulk flow. The dispersion coefficient and effective axial diffusion decreases with an increase in the chemical reaction rate, stenosis shape parameter and power-law index. As time passes, the dispersion process slows and becomes almost constant implying a steady state of diffusion. In short, this study provides further insights into the physiological processes involved in the dispersion of drugs and nutrients in the circulatory system.