In this paper, the influence of a non-uniform magnetic field on biomagnetic fluid flow in a duct with a constriction is investigated numerically. The magnetic field is generated by a wire carrying electric current located outside the duct. The biomagnetic fluid dynamics model, which is based on the ferrohydrodynamics and magnetohydrodynamics, is used to study the fluid flow, and a computational grid properly covering the magnetic field is used for the simulation. In this investigation, the influence of magnetic field on biomagnetic fluid flow in various percentages of the duct constriction, and the effect of the magnetic field on the biomagnetic fluid flow in various strengths of magnetic force are studied. The magnetic field is spatially varying, and the magnetic field strength decreases by increasing the distance from the wire carrying electric current which is the magnetic source. The results show that, the influence of the magnetic field on biomagnetic fluid flow is considerable near the magnetic source. Applying the magnetic field with enough strength causes the recirculation areas downstream of constriction to become smaller. In addition, applying the magnetic field has significant effects on the wall shear stress, so that it can decrease the shear stress on the wall away from the magnetic source.
