Magnetohydrodynamics effects on generalised power law fluid model of blood flow in a stenosed bifurcated artery

Abstract

The production of Lorentz force arises according to the magnetohydrodynamics principle which allows fluid motion to slow down an accelerated fluid and thus resulted in a uniform, calm flow. Due to that, most of the clinical treatments of certain cardiovascular diseases utilise this principle in magnetic therapy. Unfortunately, an excessive exposure to high magnetic intensity may contribute to an irreversible change and it can be harmful towards the organ. Hence, in this research, the effects of uniform external magnetic field along the bifurcated artery that possesses an overlapping stenosis at the parent’s arterial lumen are investigated for further understanding. Several assumptions are considered in this study. In particular, the streaming blood is considered steady, laminar, incompressible, fully developed and electrically conducted. In addition, the rheological behaviour of the streaming blood is assumed to be characterised by a generalised power law model corresponding to shear-thinning, Newtonian and shear-thickening nature of blood. However, in these conditions, applying the finite element technique using the classical Galerkin approach may result in spurious oscillation. In order to deal with this issue, the resulting governing equations are solved using a stabilized finite element technique called Galerkin least-squares method. This method is convenient to compute a highly viscous streaming blood and compatible to circumvent the Babuska-Brezzi stability conditions. Comparison of velocity contour, pressure drop and skin friction obtained from this present study using MATLAB and COMSOL Multiphysics softwares are found in satisfactory agreement with previous work in the literature. Thus, convincing enough to be extended by including the magnetohydrodynamics and non-Newtonian effects along a bifurcated channel. The results from pattern of streamlines show that shear-thinning fluid creates the largest recirculation area in comparison to shear-thickening and Newtonian fluids. In addition, when external magnetic field is applied in a transverse direction, the flow velocity is reduced considerably, restricting the occurrence of flow reversal, consequently generating a uniform, calm flow. However, the magnetic intensity shows little effect on the constricted region due to the smaller diameters of the vessel. Furthermore, as the severity of stenosis is increased, significant rise in wall shear stress magnitudes at the throat of an overlapping stenosis are noticed which may lead to thrombosis occurrence. Therefore, application of Galerkin least-squares method to the flow of blood in a stenosed bifurcated artery with the influence of an external magnetic field can be beneficial for magnetic therapy predictions and helps to understand the flow dynamics in a stenotic region.