A FEM approach to biomagnetic fluid flow in multiple stenosed channels

•The first application of FEM for solving biomagnetic fluid flow in irregularly stenosed channels.•Unknown vorticity boundary conditions are obtained by a FEM-based iterative procedure.•Effect of the magnetic field and the constriction on the fluid flow are analyzed.•Optimal location and intensity of the external magnetic field are investigated.•Several constrictions with different severities are studied.

The unsteady and laminar biomagnetic fluid flow of a viscous, incompressible, Newtonian and electrically conducting fluid is numerically investigated. Specifically, the two-dimensional flow driven in an infinite channel containing multiple stenosis and subject to a spatially varying external magnetic field is considered. The numerical method is based on the use of finite element method (FEM) in spatial discretization and unconditionally stable backward finite difference scheme for the time integration, for solving coupled nonlinear differential equations in terms of stream function, vorticity and temperature. Due to nonlinearity, an iterative process is employed between the equations. The study focuses on the alteration of the flow and its temperature behaviors due to the irregular constrictions along the channel. Also, the effects of the external magnetic field, its location and its intensity on the biomagnetic fluid flow are analyzed. The numerical results are presented in terms of streamlines, equivorticity and temperature contours for several values of magnetic field intensity in irregularly and multiply stenosed channels. It is shown that the lengths of the vortices appeared due to the stenosis and magnetic source, increase with an increase in the intensity of the magnetic field and the severity of the constriction.