## 3 Results and Discussions
### Characteristics of Nanoparticles
Although the nanofluid concentration increased over a certain value, the decrease in the dispersion stability of the nanofluid resulted in a decrease in the heat transfer performance of the nanofluid as a result of the reduction in the convective heat transfer coefficient. Moreover, it was a major cause of the increase in the pressure drop of the fluid in a tube. Figure 7:1 _Cont._  
Figure 7:2 Pressure drop of Fe\({}_{3}\)O\({}_{4}\)–MWCNT hybrid nanofluid under an external magnetic field. Comparison of Convective Heat Transfer Performance between Fe\({}_{3}\)O\({}_{4}\) and Fe\({}_{3}\)O\({}_{4}\)-MWCNT Nanofluids  
This study compared the convective heat transfer characteristics of a single nanofluid and a hybrid nanofluid. The convective heat transfer coefficient and Nu of the 0.2 wt% Fe\({}_{3}\)O\({}_{4}\) and 0.1 wt% Fe\({}_{3}\)O\({}_{4}\)-MWCNT nanofluids presented the maximum convective heat transfer coefficient for each nanofluid, are compared and illustrated in Figure 7:3 When comparing the Fe\({}_{3}\)O\({}_{4}\) and Fe\({}_{3}\)O\({}_{4}\)-MWCNT nanofluids, we observed that the convective heat transfer coefficient of the latter was higher than that of the former. This indirectly indicated that the effect of increasing the convective heat transfer coefficient of the Fe\({}_{3}\)O\({}_{4}\) nanofluid was achieved through the addition of MWCNT nanoparticles with high thermal conductivities. The convective heat transfer coefficients of the 0.2 wt% Fe\({}_{3}\)O\({}_{4}\) and 0.1 wt% Fe\({}_{3}\)O\({}_{4}\)-MWCNT nanofluids at Re = 1400 were compared. When the magnetic field strength was 0, 250, 500, and 750 G, the convective heat transfer coefficients of the 0.1 wt% Fe\({}_{3}\)O\({}_{4}\)-MWCNT hybrid nanofluid were 1620, 1650, 1662, and 1679 W/m\({}^{2}\) K, respectively, and those of the 0.2 wt% Fe\({}_{3}\)O\({}_{4}\) nanofluid were 1597, 1618, 1631, and 1654 W/m\({}^{2}\) K, respectively. We confirmed that the convective heat transfer coefficients of the 0.1 wt% Fe\({}_{3}\)O\({}_{4}\)-MWCNT hybrid nanofluid increased by 1.73% on average compared with that of the 0.2 wt% Fe\({}_{3}\)O\({}_{4}\) nanofluid, although the total concentration of the Fe\({}_{3}\)O\({}_{4}\)-MWCNT hybrid nanofluid was lower than that of a single Fe\({}_{3}\)O\({}_{4}\) nanofluid. Most previous studies reported that convective heat transfer characteristics are increased by the effect of an external magnetic field [21; 22; 23; 24; 25; 26]. However, some authors have reported a tendency to decrease convective heat transfer characteristics due to an external magnetic field [39]. This is caused by the aggregation of magnetic nanoparticles on the inner wall of the tube due to the effect of an external magnetic field. Moreover, under the magnetic field effect, magnetic nanoparticles form a chain-like structure, thereby creating fine turbulence and micro-vortices in the flow of the fluid. However, studies indicated that the convective heat transfer could be reduced by blocking heat transfer if a large amount of magnetic nanoparticles aggregate in the tube. In this study, Fe\({}_{3}\)O\({}_{4}\) nanoparticles were aggregated under the effect of an external magnetic field to form micro-vortices, thereby  
Figure 7:4 Comparison of convective heat transfer coefficient for different nanofluids. improving convective heat transfer. However, when the MWCNT nanoparticles were added to the Fe\({}_{3}\)O\({}_{4}\) nanofluid, the convective heat transfer performance was lower than the expected value for heat transfer improvement considering the increase in thermal conductivity because more nanoparticles were aggregated under the effect of an external magnetic field. Therefore, the increase in convective heat transfer performance degraded as more nanoparticles clumped on the inner wall of the tube. Even if MWCNT nanoparticles were added to the Fe\({}_{3}\)O\({}_{4}\) nanofluid, it is observed that the convective heat transfer coefficient did not significantly increase.