Mathematical analysis of casson fluid model fordispersion of solute in blood flow through stenosed artery with chemical reaction

Abstract

The dispersion of solute in blood flow has gained great attention by scientists for long time due to its importance in medical field and drug manufacture. The main interest in this study is mathematical analysis for steady dispersion of solute in blood flow with chemical reaction through a stenosed artery. In this study, the blood is treating as a non-Newtonian of Casson fluid model. The momentum equation and constitutive equation of Casson fluid have been used to obtain the solutions of velocity and average velocity for stenosed artery. The Taylor-Aris technique is applied to get the distribution of concentration, effective axial diffusion and relative axial diffusion by considering chemical reaction. The solutions between the dispersion of solute through an artery with stenosis and without stenosis have been compared. It is found that the radius of stenosed artery decreases because of the stenosis length and stenosis height increases while in case of without stenosis the radius of the artery does not change. The effective axial diffusion decreases with the increase of yield stress of Casson fluid and chemical reaction. The relative axial diffusion decreases slightly with the increase of yield stress of Casson fluid. The increase of yield stress and Peclet number can increase the viscosity of fluid, therefore, it minimizes the relative axial diffusion. Finally, the relative axial diffusion decreases slowly with the increase of the yield stress while the relative axial diffusion increases slowly with the increase of the radius of stenosed artery.