A two-dimensional direct simulation method, based on the Maxwell stress tensor and a fictitious domain method, has been employed to investigate the dynamics of elliptic paramagnetic particles suspended in a non-magnetic incompressible Newtonian fluid. A single-particle problem is chosen to investigate the rotational behavior of the particle in the presence of both shear flow and a uniform magnetic field applied externally. The dynamic of the elliptic particle is found to be significantly affected by a dimensionless number called the Mason number, the ratio of the viscous force to the magnetic force acting on the particle. We found a critical Mason number separating two regimes with different particle dynamics. Below the critical number the particle reaches an equilibrium position after finite rotation. Above the critical number, however, the particle rotates continuously. As for the multi-particle problem in the presence of an external field and imposed shear flow, three regimes of the Mason number were found, showing different topology of the chain of particles and fluid flow due to the combined effect of the magnet and viscous forces.

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