Exact Analysis of Unsteady Convective Diffusion in Herschel-Bulkley Fluid Flow- Application to Catheterised Stenosed Artery

Abstract

One of the major causes of cardiovascular disease is atherosclerosis or stenosis. This study is designed to improve the current body of knowledge regarding the condition by inserting a long thin tube called a catheter to widen the narrow part in the artery. The study reviewed the effects of catheter radius, yield stress, and power law index on the velocity distribution, and transport coefficients of solute. A mathematical model is deployed to investigate the dispersion of solute in the flow of a Herschel-Bulkley (H-B) fluid in an annulus, whereas the dispersion process is studied using the generalised dispersion model (GDM) by solving the convective diffusion equation. Resultan tly, the velocity reduces following an increase in the yield stress, catheter size, and power law index. Meanwhile, the dispersion coefficient exhibits a same behaviour as the aforementioned parameters ascend considerably. The dispersion coefficient alterations occurred rapidly for small values of time and became significantly constant following an increase in the time values. Conclusively, this study can be useful in dispersion of a drug to the affected artery where an abnormal plaque was formed.

Unsteady Flow of Bingham Model: Investigating the Impact of Arterial Inclination on Solute Transport in Stenosed Artery

“…Abidin et al, [10] adopted the Generalized Dispersion Model (GDM) to solve for the diffusion coefficient in a Herschel-Bulkley flow through a catheterized stenosed artery and found that the diffusion coefficient increases to a constant value as the time increases. Elias et al, [11] also utilized the GDM method to obtain the dispersion function and mean concentration of solutes in a Casson model flow through a stenosed artery with the presence of body acceleration and slip velocity.…”

Blood Flow with Heat Transfer through Different Geometries of Stenotic Arteries

“…A model of blood flow through a constricted artery due to heat in the presence of a magnetic field is proposed by Bunonyo et al [9]. Abidin et al [10] explored the problem of unsteady solute dispersion in blood flow using the generalised dispersion model and the Herschel-Bulkley fluid model in an overlapped catheterized stenosed artery.…”