Finite element model of biomagnetic fluid flow in a bifurcated channel with an overlapping stenosis

Abstract

The flow of biomagnetic fluid is considerably influenced by the presence of magnetic field especially in the case of spatially varying magnetic field. Blood is known as the most common biofluid where its magnetic properties are governed by the existence of high concentration of hemoglobin, which is a form of iron oxide in mature red blood cells. Biomagnetic fluid dynamics is a study for the relationship between fluid dynamics of biological blood with the magnetic field. The problems of blood flow in the presence of magnetic field with an overlapping stenosis in the straight and bifurcated channel are investigated numerically. In this study, the flow is considered to be steady, two-dimensional, laminar, and electrically nonconducting under the influence of spatially varying magnetic field. The mathematical model for biomagnetic fluid dynamics for isothermal case is constructed based on modified Navier-Stokes equations coupled with the principles of ferrohydrodynamics (FHD) and magnetohydrodynamics (MHD), which consider force arising due to magnetization and Lorentz force, respectively. Based on these assumptions, the nonlinear system of the governing equations is then discretized by employing Galerkin finite element method and the source code is developed by using MATLAB software in order to solve the problem. The numerical result shows that the intensity of the applied magnetic field could alters the behaviour of blood flow at the area near the magnetic source and cause the formation of new vortex. This could be seen from the velocity profile and streamline pattern of both straight and bifurcated artery. When the magnetic intensity is increased, the flow velocity can be seen to be reduced considerably near the stenosis area compared to the velocity of the flow before magnetic field is introduced. This shows that the study on magnetic field on biomagnetic fluid is proven to be beneficial for future development in biomedical area.