## 3 Results and Discussions
### Characteristics of Nanoparticles
Figure 13b shows the pressure drop of the 0.05 wt% Fe\({}_{3}\)O\({}_{4}\) nanofluid according to the change in the magnetic field. For Re = 1000, the pressure drops at 0, 250, 500, and 750 G were 1.7, 1.87, 1.88, and 1.9 kPa. At a maximum Re of 1600, the pressure drops were 2.68, 2.9, 2.9, and 2.95 kPa for magnetic fields of 0, 250, 500, and 750 G, respectively. As Figure 13c shows, when the magnetic field of the 0.1 wt% Fe\({}_{3}\)O\({}_{4}\) nanofluid was varied as 0, 250, 500, and 750 G, the pressure drops at Re = 1000 were 1.78, 1.85, 1.88, and 1.9 kPa, respectively, and at a maximum Re of 1600, the pressure drops were 2.8, 2.9, 2.92, and 2.95 kPa, respectively. Similar to Figure 13a, the pressure drop increased by 10% according to the change in the magnetic field. Figure 13d shows the pressure drop of the 0.2 wt% Fe\({}_{3}\)O\({}_{4}\) nanofluid as the magnetic field varied. Even in the absence of a magnetic field, the pressure drop was high due to the addition of a large amount of Fe\({}_{3}\)O\({}_{4}\) nanoparticles. The pressure drop of the 0.2 wt% Fe\({}_{3}\)O\({}_{4}\) nanofluid without a magnetic field at Re = 1600 was 3.22 kPa. The pressure drops of the 0.2 wt% Fe\({}_{3}\)O\({}_{4}\) nanofluid at 250, 500, and 750 G under the same Re were 3.35, 3.37, and 3.39 kPa, respectively, which increased by 4.73% on average compared with the pressure drop without the magnetic field. Based on the experimental results of this study, we confirmed that the pressure drop increased as the concentration of the Fe\({}_{3}\)O\({}_{4}\) nanofluid increased in the laminar flow region. When the magnetic field strength was increased from 0 to 250 G, the pressure drop of the Fe\({}_{3}\)O\({}_{4}\) nanofluid increased significantly, but the increase in the pressure drop decreased as the strength of the magnetic field increased. This is because the magnetic nanofluid flow increased the microturbulence in the tube through the aggregation and arrangement of Fe\({}_{3}\)O\({}_{4}\) nanoparticles on the wall due to the magnetic field, thereby increasing the pressure drop and convective heat transfer coefficient. Figure 13: _Cont._  
Figure 7:0 Pressure drop of Fe\({}_{3}\)O\({}_{4}\) nanofluid under an external magnetic field. Figure 14 shows the pressure drop of the Fe\({}_{3}\)O\({}_{4}\)-MWCNT hybrid nanofluid in the tube as the nanofluid concentration and magnetic intensity varied. Similar to the variation in the pressure drop of the Fe\({}_{3}\)O\({}_{4}\) nanofluid, the pressure drop of the Fe\({}_{3}\)O\({}_{4}\)-MWCNT hybrid nanofluid increased as Re increased. When Re increased from 1000 to 1600, the overall pressure drop increased, with an average increment of approximately 52.7%. In addition, the pressure drop of the Fe\({}_{3}\)O\({}_{4}\)-MWCNT hybrid nanofluid increased as the magnetic intensity increased. When the magnetic field strength was increased from 0 to 750 G, an average pressure drop increase of 6.7% was observed for Re = 1000. In this study, the maximum heat transfer coefficient and Nu of the Fe\({}_{3}\)O\({}_{4}\)-MWCNT hybrid nanofluid were observed at 0.1 wt%, but the maximum pressure drop was observed at 0.2 wt%. This is due to the increase in thermal conductivity as the concentration of the nanofluid increased. However, as shown in Figure 10, the viscosity increased proportionally with the concentration; thus, the pressure drop increased. Although MWCNT nanoparticles were added to increase the thermal conductivity of Fe\({}_{3}\)O\({}_{4}\) nanofluids, the MWCNT nanoparticles are considered as a significant factor that causes aggregation of particles, resulting in a high-pressure drop [20]. In addition, because of the effect on the external magnetic field, the dispersion stability of the two nanoparticles in the hybrid nanofluid reduced compared with that of the single nanofluid, which caused an increase in the pressure drop.