## Materials and Methods
### Data Reduction  
The density and specific heat of the Fe\({}_{3}\)O\({}_{4}\) nanofluid used in this study can be expressed by Equations (1) and (2) [49].  
\[\rho_{nf}=(1-\phi)\rho_{bf}+\phi\rho_{np} \tag{1}\]  
\[c_{p,nf}=\frac{(1-\phi)\rho_{b}c_{p,bf}+\phi\rho_{np}c_{p,np}}{(1-\phi)\rho_{bf} +\phi\rho_{np}} \tag{2}\]  
where \(\phi\) is the volume fraction of the nanofluid, \(\rho_{nf}\) and \(\rho_{np}\) are the densities of the base fluid and nanoparticles, respectively, and \(c_{p,bf}\) is the specific heat of the nanofluid.  
The density and specific heat of the Fe\({}_{3}\)O\({}_{4}\)-MWCNT hybrid nanofluid were calculated using Equations (3) and (4) [50].  
\[\rho_{np}=\frac{\phi_{1}\rho_{np1}+\phi_{2}\rho_{np2}}{\phi} \tag{3}\]  
Figure 4: Schematic of the forced convective heat transfer experimental setup.  
Figure 5: Magnetic field experimental device.  
\[c_{p,nf}=\frac{\phi_{1}\rho_{np1}c_{p,np1}+\phi_{2}\rho_{np2}c_{p,np2}}{\rho_{np}\phi} \tag{4}\]  
The local convective heat transfer coefficient was calculated using Equation (5).  
\[h=\frac{Q}{A(t_{w}-t_{b})} \tag{5}\]  
The bulk temperature of the fluid at each point where the thermocouple was attached was calculated using the measured inlet and outlet temperatures, specified specific heat, and heat flux measured using a flow meter. The local convective heat transfer coefficient at that point was calculated using the difference between the bulk temperature of the fluid and the temperature measured by the thermocouple attached to the surface of the tube. By applying the convective heat transfer coefficient calculated using Equation (5) and the measured thermal conductivity of the nanofluid, the Nu number of the nanofluid was calculated using the following equation:  
\[Nu=\frac{hD}{k} \tag{6}\]  
In this study, before experimenting on the characteristics of the convective heat transfer coefficient of the nanofluid, the reliability of the fabricated experimental device was verified by comparison with the widely known [PERSON]'s equation in the laminar flow region, as presented in Equation (7), with deionized water as the working fluid [25].  
\[Nu(x)=\begin{cases}1.953\left(\text{Re.Pr.}\frac{D}{x}\right)^{0.33333}&\left( \text{Re.Pr.}\frac{D}{x}\right)\geq 33.3\\ 4.3640.0722\text{Re.Pr.}\frac{D}{x}&\left(\text{Re.Pr.}\frac{D}{x}\right)<33.3 \end{cases} \tag{7}\]  
Figure 6 shows the comparison between the measurement results obtained in this study and the Nu number of water suggested by [PERSON]. As Figure 6 shows, the maximum error between the experimental results using water in the laminar flow region with a Re of 1000-1600 and the result of [PERSON]'s equation was approximately 4.75%, and the average error was approximately 3.25%. These results confirmed the reliability of the fabricated experimental device.  
Figure 6: Comparison of the measured Nu number with the theoretical correlation of [PERSON]’s equation for pure water.  
In this study, the factors affecting the uncertainty of the obtained experimental results included a T-type thermocouple, differential pressure transmitter, mass flow meter, power meter, and magnetic strength meter. The uncertainties of the experimental devices used in this study are listed in Table 2.