Fractional Model for Blood Flow in a Stenosed Artery Under MHD Effect Through a Porous Medium

Abstract

This paper presents a fractional approach as a substitute to the integer-order model, describing the magnetohydrodynamics (MHD) effect of blood flow in a stenosed artery. We not only obtain an analytical solution for the fractional governing equation but also present an expression for the wall-shear stress. After the successful verification of our model with established models, we carry out a two-step validation with the experimental data existing in literature. Then, we analyze the obtained plots by using the analytic expression. We exhibit how fractional model (FM) is helpful for controlling the blood flow through a stenosed artery. This study also indicates that magnetic field intensity significantly controls the flow velocity and wall-shear stress to a great extent. We also show that the external magnetic field, along with the fractional order of the governing equation, plays a pivotal role in the solution of the problem involving the treatment of stenosis. Finally, we conduct some experimental data approximation by the solution to establish the credibility of the proposed fractional-order model.