This research focuses on utilizing non-uniform magnetic fields, induced by dipoles, to control and enhance thermal energy transfer in a two-dimensional cooling conduit including a double backward-facing step. The presence of electronic equipment along the straight channel path creates such arrangements, and cooling is often ineffective in the corners of the formed steps. The use of a non-constant magnetic field is a passive technique to improve the cooling rate in these sections without changing the internal geometry, thereby increasing the heat transfer rate. A commercial software based on the finite volume technique is employed to solve the governing equations of fluid flow and heat transfer. Multiple parameters are examined in this study, including the flow Reynolds number (12.5–50), dipole location and strength (0.1–5 A-m), and the number of dipoles (single or double). The results indicate that all of these parameters have a significant impact on the thermal energy transfer. The results of the study show that a single dipole increase the average heat transfer by about 22%, two magnetic fields by 40%, the strength of the magnetic source by 24% with respect to the non-magnetic field in the present study.