The pulsatile flow of Oldroyd-B fluid in a multi-stenosis artery with a time-dependent wall

In this study, the fundamental problem of unsteady blood flow in a tube with multi-stenosis is studied. An appropriate shape of the time-dependent multi-stenosis which is overlapping in the realm of formation of arterial narrowing is constructed mathematically. Blood is considered as a viscoelastic fluid characterized by the Oldroyd-B model. For the numerical solution of the problem, which is described by a coupled, non-linear system of partial differential equations (PDEs), with appropriate boundary conditions, the finite difference scheme is adopted. The solution is obtained by the development of an efficient numerical methodology based on the predictor-corrector method. The effects of parameters such as pulsatility, non-Newtonian properties and the flow time on the velocity components, the rate of flow, and the wall shear stress are investigated through their graphical representations quantitatively at the end of the paper in order to validate the applicability of the present improved mathematical model under consideration.