A finite element method is employed to examine the impact of a magnetic field on the development of plaque in an artery with stenotic bifurcation. Consistent with existing literature, blood flow is characterized as a Newtonian fluid that is stable, incompressible, biomagnetic, and laminar. Additionally, it is assumed that the arterial wall is linearly elastic throughout. The hemodynamic flow within a bifurcated artery, influenced by an asymmetric magnetic field, is described using the arbitrary Lagrangian–Eulerian (ALE) method. This technique incorporates the fluid–structure interaction coupling. The nonlinear system of partial differential equations is discretized using a stable P2P1 finite element pair. To solve the resulting nonlinear algebraic equation system, the Newton-Raphson method is employed. Magnetic fields are numerically modeled, and the resulting displacement, velocity magnitude, pressure, and wall shear stresses are analyzed across a range of Reynolds numbers (Re = 500, 1000, 1500, and 2000). The numerical analysis reveals that the presence of a magnetic field significantly impacts both the displacement magnitude and the flow velocity. In fact, introducing a magnetic field leads to reduced flow separation, an expanded recirculation area near the stenosis, as well as an increase in wall shear stress.

Atherosclerosis, marked by elevated plaque formation, occurs due to stenosis, which narrows the arterial walls and alters the natural flow path. Previous research has shown that the likelihood of high-rupture stenosis can be linked to temperature distribution variations in bifurcated arteries. In this study, we employ a monolithic Arbitrary Lagrangian–Eulerian (ALE) finite element approach to model heat transfer in fluid–structure interactions within stenosed bifurcated arteries, considering the elasticity of arterial walls. We analyze unsteady, incompressible Newtonian blood flow in a two-dimensional laminar regime, focusing on key factors such as velocity, wall displacement, temperature effects, and the average Nusselt number. Our findings reveal that under pulsatile inflow conditions, minor temperature fluctuations occur under specific waveform flow boundary conditions. Additionally, greater arterial wall flexibility enhances heat transfer between the blood and vessel walls, with flow reflections further contributing to this effect. Lastly, we examine wall shear stress (WSS) at its minimum and maximum values, emphasizing the role of arterial elasticity in influencing these forces.

This study presents a numerical investigation into the heart valve through a fluid–structure interaction (FSI) framework using a two-dimensional, steady-state, Newtonian flow assumption. While simplified, this approach captures core biomechanical effects and provides a baseline for future extension toward non-Newtonian, pulsatile, and three-dimensional models. The analysis focuses on the influence of magnetic field intensity characterized by the Hartmann number (Ha) and flow regime defined by the Reynolds number (Re) on critical hemodynamic parameters, including wall shear stress (WSS), velocity profiles, and pressure gradients in the valve region. The results demonstrate that stronger magnetic fields significantly stabilize intravalvular flow by suppressing recirculation zones and reducing flow separation distal to valve constrictions, offering protective hemodynamic benefits and serving as a non-invasive method to modulate vascular behavior and reduce the risk of cardiovascular pathologies such as atherosclerosis and hypertension.

This study presents a numerical investigation into heart valve dynamics through a fluid–structure interaction (FSI) framework that incorporates biomagnetic blood flow and elastic arterial walls. The analysis focuses on the influence of magnetic field intensity—characterized by the Hartmann number (Ha)—and flow regime—defined by the Reynolds number (Re)—on critical hemodynamic parameters, including wall shear stress (WSS), velocity profiles, and pressure gradients in the valve region. Results demonstrate that stronger magnetic fields significantly stabilize intravalvular flow by suppressing recirculation zones and reducing flow separation distal to valve constrictions, offering protective hemodynamic benefits and serving as a non-invasive method to modulate vascular behavior and reduce the risk of cardiovascular pathologies such as atherosclerosis and hypertension.

Atherosclerosis is an accumulation of plaque, which can result in changes in blood flow in the vicinity, leading to severe heart attack. This paper presents a phenomenological fluid–structure interaction study of plaque rupture in stenosed bifurcated elastic arteries. We use the coupled monolithic Arbitrary Lagrange Euler (ALE) formulation for fluids and solids. We consider the Navier–Stokes equation to govern the non-Newton blood flow and linear elastic model for walls. We treat the interface as a continuum. We utilize the stable $P_2{P}_1$ finite element pair for velocity and pressure discretization in space. The nonlinear discretized algebraic system is tackled using the Newton method, with the Jacobian matrices approximated via a divided differences approach. The resulting linear systems are addressed using the direct solver MUltifrontal Massively Parallel Sparse direct Solver (MUMPS). We then determine the wall shear stress (WSS) for both minimum and maximum times, accounting for elastic walls. The study’s findings enhance our understanding of the mechanisms behind plaque rupture and aid in developing better diagnostic and therapeutic strategies.