Travelling waves in a cylindrical magnetohydrodynamically forced flow Phys. Fluids 24, 044101 (2012) Two-dimensional numerical analysis of electroconvection in a dielectric liquid subjected to strong unipolar injection Phys. Fluids 24, 037102 (2012) We numerically investigate dynamics of magnetic chains and flow characteristics in a two-dimensional shear flow under the influence of a magnetic field applied externally. A direct simulation method is employed to solve the particulate flow in the creeping flow regime, taking into account both magnetic and hydrodynamic interactions in a coupled manner. In a periodic channel, the dynamics of chains is found to be significantly influenced by the Mason number (the ratio of viscous force to magnetic force), the magnetic susceptibility, and the particle fraction. Below a critical Mason number, a chain rotates and reaches an equilibrium. Above the critical value, however, the chain continuously rotates as a rigid body. Thinning behavior in the wall shear stress is found above a threshold value of the Mason number.