From brake to booster: magnetic control of hybrid-ferrofluid shaft cooling in a tri-lobe e-drive housing, decoded by CFD and interpretable machine learning

Integrated e-drives place a motor and a two-stage gearbox in one housing, where the rotating shafts are major heat sources that are hard to cool. This study examines whether a magnetic field can improve shaft cooling in a trilobe gearbox housing filled with a Fe3O4–CoFe2O4/water hybrid ferrofluid, in which three conducting, heated hubs counter-rotate as meshing gears under a horizontal field. Steady laminar conjugate mixed convection was solved with the finite-element method for 250 cases (Re = 50–250, Ri = 0.5–2.5, Ha = 0–80, two rotation senses) after a mesh study and two benchmark validations. Without a field each hub drives a closed cell that runs along the isotherms, so the heat crosses the fluid by conduction. The field breaks these cells into flat cells that open radial exchange paths at the hubs, and it does so in the same way at every speed. Whether this helps is decided by the P´ eclet number. At Re = 50 the new flow carries too little heat to offset the lost conduction, and the mean Nusselt number falls by 3% (brake); at Re = 250 it carries 60% of the hub heat, and the mean Nusselt number rises by 26–32% (booster), with up to 44% for the input hub. The gain carries no secondlaw penalty. Among six regressors, a Gaussian process is the most accurate (test R2 ≥ 0.9995, maximum error 1.07%), gives calibrated uncertainty and needs half the training data of the others, while a power-law correlation fails (R2 ≤ 0.82). The surrogate places the brake-to-booster crossover at Re ≈ 62, and exact Shapley values recover the speed–field interaction behind it.