Mathematical analysis of dispersion of solutes in blood flow using herschel-bulkley fluid model through an inclined uniform artery

Abstract

his study aims to analyse the effect of inclination of the artery on the blood velocity and solute dispersion in an artery when it is inclined to a certain angle. Herschel-Bulkley fluid model is considered in representing the blood flow. The method of integration and perturbation are used to obtain the solution for the velocity of the steady and unsteady blood flow, respectively. The steady convection-diffusion equation is solved for the concentration of the solute using method of integration. Taylor-Aris method has been implemented to obtain the effective and relative axial diffusion. This present work focuses on the effect of arterial inclination angle on the blood flow characteristic in terms of velocity, concentration of solute, effective axial diffusion and relative axial diffusion. Other parameters’ effect such as yield stress, gravitational acceleration and power-law index on the behaviour of the blood are also investigated and presented by graph representation. Observation shows that the angle of artery inclination directly influences the gravitational acceleration parameter, which correlates to the resulting blood velocity and solute concentration. 90? and 270? angles of inclination have the highest effect in increasing and decreasing the velocity, concentration of solute and diffusivity, respectively. Meanwhile, 0?, 180? and 360? angles eliminate the gravitational acceleration effect on the blood behaviour and dispersion process. This study concludes that the angle of inclination has a strong impact on blood flow and solute dispersion behaviour.