This paper investigates numerically the various parameters dictating the vortical (self)-mixing induced by a non-uniform magnetic field in a ferrofluid flow in an elbow channel. The elbow bend region of the channel has two current carrying conductors placed symmetrically and parametrically from the channel and are used to generate a non-uniform magnetic field. The ferrofluid is assumed to be pre-magnetized, isothermal and electrically non-conductive as it enters the channel and has a prescribed inlet magnetization and temperature. The mixing efficiency is characterized by introducing different mixing scalars based on velocity of the fluid and are compared in order to determine the overall suitability of each scalar to quantify the flow vortical (self)-mixing. Parametric studies were performed by varying parameters influencing the magnetic field and the initial flow field. This resulted in variations in non-dimensional groups which control different aspects of the flow and helped establish their relationship with mixing efficiency. It was found that at higher Reynolds numbers the flow mixing induced by the lateral gradient in the Kelvin Body Force (KBF) dissipates and higher electrical inputs are required to sustain mixing in the flow. The effects of mixing enhancement on the pressure gradient across the channel was also established, along with the introduction of an enhanced viscosity term which is due to the non-collinearity of the magnetization vector and the magnetic field vector.