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.

Blockage of blood flow due to cholesterol deposits at the arterial wall, known as stenosis, can lead to conditions such as heart attack and stroke. Treatment such as balloon angioplasty involves the catheterization of an artery where a stented catheter is inflated at the stenosis site to open the narrowed artery. The catheterization of the stenosed artery affects the surrounding blood flow and dispersion process. The present study analyses the effect of catheter radius and stenosis height on the blood velocity and solute dispersion behavior. Herschel-Bulkley fluid is used to model the problem with stenosis as the boundary condition. The momentum equation and Herschel-Bulkley constitutive equation are solved analytically into integral forms. Simpson’s 3/8 rule and Regula-Falsi method were used to evaluate the integral numerically to obtain the velocity. The velocity was utilized to solve the unsteady convective-diffusion equation using the generalized dispersion model (GDM) to obtain the dispersion function. This present research can potentially help the medical field and industry in determining the suitable catheter radius for patients, calculating drug dosage and improving stent catheter design. Results show that the velocity decreases as the catheter radius and stenosis height increase. A decrease in velocity simultaneously increases the solute dispersion function.

The presence of stenosis at the wall of the artery lead to further cardiovascular diseases such as heart attack, stroke and many more. Treatment of a stenosed artery includes the insertion of a catheter through the artery which affects the blood flow and solute dispersion. This present study focuses on the effect of catheter radius and stenosis height on the blood flow and solute dispersion behavior. The problem is modelled using the Herschel-Bulkley fluid to represent the blood rheology, with catheter and stenosis as the boundary conditions. Analytical solutions in integral form are obtained by solving the momentum equation and Herschel-Bulkley constitutive equation. The integrals are numerically evaluated using the Simpson’s 3/8 rule and Regula-Falsi method to obtain the blood velocity. The obtained velocity is employed into the unsteady convective-diffusion equation and solved using the generalized dispersion model (GDM) to analyse the behaviour of solute diffusion. The influence of catheter radius and stenosis height on the diffusion coefficient and mean concentration of solute are observed. Results show that the diffusion coefficient decreases as the catheter radius and stenosis height increases. A decrease in diffusion coefficient simultaneously increases the solute mean concentration.

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