Analysis on the Solute Dispersion in Blood Flow Through an Inclined Artery with the Presence of Chemical Reaction

Abstract

The present study discusses on the solute dispersion in a blood flow through an inclined artery with the presence of chemical reaction. The blood flow is considered to be laminar, incompressible and steady flow of Bingham model. The continuity and momentum equations are solved in cylindrical coordinate for the velocity solution using direct integration method. The steady convective-diffusion equation with the presence of chemical reaction is in the form of non-homogeneous Bessel differential equation and is solved analytically for the solute concentration. The obtained solutions are then utilized for the Taylor-Aris method for obtaining the solution for effective axial diffusion. The solutions of velocity, solute concentration and effective axial diffusion are plotted graphically to analyse the effect of angle of arterial inclination, gravitational force and chemical reaction rate on the blood flow and solute dispersion. Result shows an increase in velocity profile of blood flow as the angle of inclination increases until 90 • inclination which has the highest velocity profile. As the artery inclined more, the velocity profile decreases until it reaches the lowest velocity at 270 • inclination. Consequently, increase in velocity decreases the solute concentration inside the artery. Nevertheless, solute concentration increases as the angle of inclination increase. Additionally, the increase in chemical reaction rate decreases the solute concentration and leads to decrease in effective axial diffusion.