Unsteady Two-Layered Blood Flow Through a -Shaped Stenosed Artery Using the Generalized Oldroyd-B Fluid Model

Abstract

A theoretical study of an unsteady two-layered blood flow through a stenosed artery is presented in this article. The geometry of a rigid stenosed artery is assumed to be $w$-shaped. The flow regime is assumed to be laminar, unsteady and uni-directional. The characteristics of blood are modelled by the generalized Oldroyd-B non-Newtonian fluid model in the core region and a Newtonian fluid model in the periphery region. The governing partial differential equations are derived for each region by using mass and momentum conservation equations. In order to facilitate numerical solutions, the derived differential equations are nondimensionalized. A well-tested explicit finite-difference method (FDM) which is forward in time and central in space is employed for the solution of a nonlinear initial boundary value problem corresponding to each region. Validation of the FDM computations is achieved with a variational finite element method algorithm. The influences of the emerging geometric and rheological parameters on axial velocity, resistance impedance and wall shear stress are displayed graphically. The instantaneous patterns of streamlines are also presented to illustrate the global behaviour of the blood flow. The simulations are relevant to haemodynamics of small blood vessels and capillary transport, wherein rheological effects are dominant.

Numerical computation of nonlinear oscillatory two‐immiscible magnetohydrodynamic flow in dual porous media system: FTCS and FEM study

“…33 Further details for other nonlinear multiphysical problems have been documented elsewhere. [34][35][36][37][38]…”

“…The applications that have successfully simulated complex nonlinear flow problems with FEM algorithms include micropolar magnetic squeeze film flows, 39 smart biomagnetic tribology, 40 rotating magnetized nanofluid dynamics, 41 double-diffusive unsteady rheological flow, 42 and chemically reacting magnetoconvection. 38 FEM uses the opposite approach to FDM, namely numerical integration rather than numerical differentiation. Dropping* notation and applying the Galerkin FEM to Equations (8) to (9)…”

Comparative Mathematical Study of Blood Flow Through Stenotic and Aneurysmatic Artery with the Presence and Absence of Blood Clots

“…[67] have analyzed the slip effects on unsteady non-Newtonian blood flow having an inclined catheterized overlapping stenotic artery. They [66] have also discussed a theoretical study of an unsteady two-layered blood flow through a w-shaped stenosed artery using generalized Oldroyd-B fluid. The pulsatile blood flow has been described by Achab et al [3] to evaluate the blood flow characteristics and the wall shear stress under physiological conditions through a stenosis artery.…”

Moment analysis of unsteady bi-component species (drug) transport with coupled chemical reaction in non-Newtonian blood flow

“…Vasu et al [19] also implemented the Eringen micropolar model to compute the timedependent nano-pharmacodynamic transport in a tapered stenotic vessel. Other non-Newtonian models which have been employed to analyse blood flow include Jeffery's viscoelastic model [20], the generalized Oldroyd-B fluid model [21] and the modified Herschel-Bulkley model [18,22].…”