## 3 Results and Discussions
### Characteristics of Nanoparticles
When the strength of the magnetic field was 750 G, the convective heat transfer coefficients of the 0.2 wt% Fe\({}_{3}\)O\({}_{4}\) nanofluid were 1534, 1578, 1654, and 1676 W/m\({}^{2}\) K at Re = 1000, 1200, and 1400, respectively, which indicated an improvement of approximately 24.6% on average compared with the base fluid. As the concentration increased, the convective heat transfer coefficient was increased by forming more chain-shaped nanoparticles according to the effect of the magnetic field. Figure 11: _Cont._  
Figure 11: Variation in the convective heat transfer coefficient of the Fe\({}_{3}\)O\({}_{4}\) nanofluid under an external magnetic field. Figure 12 shows the enhancement in the convective heat transfer coefficient of the Fe\({}_{3}\)O\({}_{4}\)-MWCNT hybrid nanofluid compared with the base fluid as the concentrations of nanofluids and magnetic field strength varied. The maximum convective heat transfer coefficient of the Fe\({}_{3}\)O\({}_{4}\)-MWCNT hybrid nanofluid occurred at 0.1 wt%. In the absence of a magnetic field, the convective heat transfer coefficients of the 0.1 wt% Fe\({}_{3}\)O\({}_{4}\)-MWCNT hybrid nanofluids were 1514, 1555, 1620, and 1647 W/m\({}^{2}\) K for Re values of 1000, 1200, 1400, and 1600, respectively. It was confirmed that the convective heat transfer coefficient increased by 22.6% on average compared with the base fluid. When a magnetic field was applied to the Fe\({}_{3}\)O\({}_{4}\)-MWCNT hybrid nanofluid at various concentrations, the addition of Fe\({}_{3}\)O\({}_{4}\) nanoparticles increased the convective heat transfer coefficient. Under the given operating conditions, the maximum convective heat transfer coefficient of the 0.1 wt% Fe\({}_{3}\)O\({}_{4}\)-MWCNT hybrid nanofluid was observed at 750 G. For Re values of 1000, 1200, 1400, and 1600, the convective heat transfer coefficients were 1545, 1597, 1679, and 1688 W/m\({}^{2}\) K, respectively, indicating an improvement of 25.9% on average compared with the base fluid. Based on the thermal conductivity measurement results of magnetic nanofluids presented in Figure 9, the maximum convective heat transfer coefficient was expected in the 0.2 wt% Fe\({}_{3}\)O\({}_{4}\)-MWCNT hybrid nanofluid. However, in this experiment, the convective heat transfer coefficient decreased slightly compared with that at 0.1 wt%. This indicated that the thermal conductivity increases as the concentration of the nanofluid increases, but for hybrid nanofluids with two or more different nanoparticles, the dispersion stability can decrease compared with that of a single nanofluid. The agglomeration of nanoparticles occurs because the magnetic field forms fine turbulence, which increases convective heat transfer. However, convective heat transfer is considered to be decreased by blocking heat transfer between the inner wall and the fluid when more nanoparticles aggregate beyond the limit of dispersion stability. Figure 12: _Cont._  
Figure 12: Convective heat transfer coefficient of the Fe\({}_{3}\)O\({}_{4}\)–MWCNT hybrid nanofluid under an external magnetic field. Pressure Drop of Fe\({}_{3}\)O\({}_{4}\) and Fe\({}_{3}\)O\({}_{4}\)-MWCNT Hybrid Nanofluids under a Magnetic Field  
Figure 13 shows the pressure drop of the Fe\({}_{3}\)O\({}_{4}\) nanofluid as the magnetic field intensity varied in the tube. As Re increased, the convective heat transfer coefficient of the working fluid and pressure drop increased. In addition, the pressure drop increased owing to the effect of the magnetic field. Figure 13a shows the pressure drop of the 0.025 wt% Fe\({}_{3}\)O\({}_{4}\) nanofluid according to the change in the magnetic field. When the magnetic field strength was 0 G at Re = 1600, the pressure drop of 0.025 wt% Fe\({}_{3}\)O\({}_{4}\) nanofluid was 2.55 kPa, and when the magnetic field strength was 250, 500, and 750 G under the same Re number, the pressure drops were 2.84, 2.85, 2.86 kPa, respectively. The pressure drop of the 0.025 wt% Fe\({}_{3}\)O\({}_{4}\) nanofluid exhibited an average increment of 11.5% under a magnetic field.