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In this study, the effects of magnetic field (MF) gradient on the ferrofluid (water/Fe 3 O 4 ) heat transfer and entropy generation in a horizontal channel under constant heat flux were numerically investigated. Two permanent magnets were installed at different angles (0°, 45°, 90°) around the channel to create a magnetic field. By installing the magnets at different directions, the intensity of MF, the amount of Kelvin force, and the effects of magnets on hydrodynamic behavior, heat transfer, and entropy generation were investigated. The remnant magnetic flux density ( B r) of the magnets was set to 0–0.4 T, While, the volume percentage of nanoparticles and the Reynolds number were considered to be 5% and 100, respectively. The results showed that increasing the angle of the magnets increased the MF gradient, and the Kelvin force was greater when the MF gradient was higher. Furthermore, the angle of the magnets affects the hydrodynamics and ferrofluid velocity. Also, the presence of the MF and increasing the angle of the magnets increased the Nusselt number. So that, when  B rwas 0.4 T, the average Nusselt number in the 90° configuration of the magnets was about 4.5% more than that of 0° and 45°. In addition, entropy generation analysis showed that generally, the presence of an MF reduced the total entropy generation. Also, the effect of the MF gradient caused that the total entropy to decrease in 0° and 45° configurations was approximately 2%, while this reduction was 14% in the 90° configuration.

Effects of magnetic field gradient on heat transfer and irreversibility in a channel