## 4 Conclusions  
The cooling performance of a traction inverter using an MHD pump-based cooling system is numerically investigated under the influence of inlet velocity, electromagnetic parameters, and volume fraction of ferrofluid. COMSOL Multiphysics is used to simulate the velocity, inverter maximum temperature, and Nusselt number as cooling performance parameters, considering the influence of various factors. The following key findings have been summarized from the present work.  
1. The outlet velocity increases with an increase in inlet velocity for both water and ferrofluid cooling, whereas with an increase in voltage, the outlet velocity of ferrofluid increases and water remains constant. The maximum outlet velocities of 4.03 mm/s and 7.02 mm/s are evaluated for water and ferrofluid cooling, respectively, at an inlet velocity of 10 mm/s and voltage of 0.5 V.
2. The inverter maximum temperature decreases with an increase in inlet velocity for both water and ferrofluid cooling. Further reduction in inverter maximum temperature is noticed in ferrofluid cooling with an increase in voltage. The inverter maximum temperature ranges from 169.84 \({}^{\circ}\)C to 49.65 \({}^{\circ}\)C in the case of water cooling and 100.3 \({}^{\circ}\)C to 40.96 \({}^{\circ}\)C in the case of ferrofluid cooling for a change in inlet velocity from 2 mm/s to 10 mm/s and in voltage from 0.1 V to 0.5 V.
3. The Nusselt number improves with inlet velocity for water cooling and that with both inlet velocity and voltage for ferrofluid cooling. The MHD pump-based cooling  
Figure 13: Effect of ferrofluid volume fraction on Nusselt number.  
system shows the improved cooling performance of traction inverters for ferrofluid cooling compared to water cooling. The maximum Nusselt numbers of 15.35 and 18.49 are evaluated for water cooling and ferrofluid cooling, respectively, at 10 mm/s inlet velocity and 0.5 V. 4. The cooling performance of ferrofluid cooling further increases with an increase in magnetic field intensity. The maximum outlet velocity of 12.08 mm/s, lowest inverter maximum temperature of 32 \({}^{\circ}\)C, and highest Nusselt number of 21.43 are evaluated at the highest magnetic field intensity of 0.4 T. 5. The increase in the ferrofluid volume fraction reflects significant improvement in cooling performance of traction inverters. The Nusselt number varies from 2.76 to 9.92 with an increase in ferrofluid volume fraction from 2% to 10%.  
Conceptualization, S.-G.H., Y.K., K.S.G. and M.-Y.L.; methodology, S.-G.H., Y.K. and K.S.G.; formal analysis, S.-G.H., Y.K. and K.S.G.; investigation, S.-G.H., Y.K. and K.S.G.; resources M.-Y.L.; data curation, S.-G.H., Y.K. and K.S.G.; validation, S.-G.H., Y.K. and K.S.G.; software, S.-G.H., Y.K. and K.S.G.; writing--original draft preparation, S.-G.H., Y.K. and K.S.G.; writing--review and editing, K.S.G. and M.-Y.L.; visualization, S.-G.H. and Y.K.; supervision, M.-Y.L.; project administration, M.-Y.L.; funding acquisition, M.-Y.L. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Dong-A University research fund.  
Not applicable.  
The data presented in this study will be available on request to the corresponding author.  
The authors declare no conflict of interest.