The development rules of ferrofluid flow and heat exchange in curved channels under the influence of external magnetic field were thoroughly investigated using the finite element method. The comprehensive strengthening performance of elbows under magnetic fields was evaluated based on the factors including the dimensionless pressure coefficient, heat transfer coefficient, and comprehensive strengthening factor. The results demonstrate that the heat transfer coefficient can be improved by increasing the volume fraction of ferrofluid in the presence of lower or no magnetic field, while it exhibits no significant variation with the increase of the volume fraction for higher magnetic fields. For a given volume fraction, a lower magnetic field may slightly inhibit heat transport of ferrofluid. A higher magnetic field can induce a complex swirling flow of the fluid along the curved axis. As the curvature decreases, the magnetic field effect becomes stronger, leading to the coupling of the magnetic field force with the centrifugal force. This coupling results in three pairs of secondary vortices on the cross-section and the heat exchange capacity is significantly enhanced. Within the study, the heat transfer coefficient of the curved tube with a dimensionless curvature of 0.067 for the magnetic field intensity of 1800G increased by 43.51%, and the comprehensive strengthening factor is 1.326, compared to without a magnetic field.