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In recent years, fluid-structure interaction (FSI) analysis has generated remarkable interest of researchers in interdisciplinary sciences problems, for instance, mechanical engineering, biomedical engineering, i.e., incorporating elastic wall behaviour in human arteries. Here, in this paper, we considered incompressible Newtonian blood flow and the elastic bifurcated artery wall in a non-uniform magnetic field. The considered model of Biomagnetic Fluid Dynamics (BFD) describes both magnetization and electrical conductivity of blood. Moreover, an Arbitrary Lagrangian-Eulerian (ALE) formulation is used by two-way fluid-structure interaction coupling of the problem. Finally, for discretization, a stable P 2 P 1 finite element pair is employed to approximate the displacement, velocity and pressure spaces independently and the resulting nonlinear algebraic system is linearized by implementing the Newtons procedure. A quantitative analysis is made against Reynolds number Re and Hartmann number Ha on the bifurcated artery amidst elastic walls showing noticeable effects on recirculation. Also, the displacement field is plotted against Ha for different values of Re and their converse behaviour is observed. The decreasing behaviour for the wall shear stresses of the bifurcated artery are also drawn in context of Ha and Re. Finally, the conclusion is drawn at the end showing the significance of the elastic behaviour of artery walls.

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Fluid structure interaction (FSI) gained attention of researchers and scientist due to its applications in science fields like biomedical engineering, mechanical engineering etc. One of the major application in FSI is to study elastic wall behavior of stenotic arteries. In this paper we discussed an incompressible Non-Newtonian blood flow analysis in an elastic bifurcated artery. A magnetic field is applied along $$x$$ x direction. For coupling of the problem an Arbitrary Lagrangian–Eulerian formulation is used by two-way fluid structure interaction. To discretize the problem, we employed $$P_{2} P_{1}$$ P 2 P 1 finite element technique to approximate the velocity, displacement and pressure and then linearized system of equations is solved using Newton iteration method. Analysis is carried out for power law index, Reynolds number and Hartmann number. Hemodynamic effects on elastic walls, stenotic artery and bifurcated region are evaluated by using velocity profile, pressure and loads on the walls. Study shows there is significant increase in wall shear stresses with an increase in Power law index and Hartmann number. While as expected increase in Reynolds number decreases the wall shear stresses. Also load on the upper wall is calculated against Hartmann number for different values of power law index. Results show load increases as the Hartmann number and power law index increases. From hemodynamic point of view, the load on the walls is minimum for shear thinning case but when power law index increased i.e. for shear thickening case load on the walls increased.

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