A computational treatment of Leslie-Ericksen constitutive equations of nematodynamics, is applied to an infinite planar sample, in the presence of mechanical stresses and magnetic torques. Dynamical regimes are explored in order to investigate the competing effects of magnetic and mechanical torques and backflow effects resulting from coupling of velocity and director fields and to understand the transient behaviour of the nematic director, when the magnetic field is parallel or perpendicular to the shear direction.