Mathematical Modelling of an Atherosclerotic Blood Flow Through Double Stenosed Region with Application of Treatment

Abstract

The aim of the present article is to model atherosclerotic blood flow through double stenosis in the arterial lumen with application of treatment subject to some boundary conditions in the channel. The research focused also on mathematical formulation of momentum equation governing the blood flow, driven by the oscillatory pressure gradient due to the contraction of muscles of the heart tissues and externally applied magnetic field. The nonlinear partial differential equation and geometries of the double stenosis are scaled using some quantities which made them dimensionless with some pertinent physical parameters such as the womersley number, the treatment parameter, Hartmann number, Darcy number at the region. The oscillatory perturbation method was adopted to further reduce the dimensionless equation to a Bessel differential equation of order zero. An exact solution of equation governing the flow is obtained with quantities coefficients. Mathematica codes were developed to investigate the influence of the pertinent parameters on the velocity profile, shear stress and volumetric flow rate of the first segment of stenosis δ 1 , while we considered the second stenosis δ 2 segment fixed and present the results graphically. In conclusion, it is observed from the results and analysis that the pertinent parameters influenced the blood flow through a double stenosed region of an arterial lumen withholding the second stenosis fixed. These results could help in raising the awareness and the need for treatment of patients with double stenosis focusing on the most delicate.