## 4 Results and Discussion
### Forced Convective Heat Transfer Study  
Figure 10 plots the experimentally determined \(N_{Nu}\) of water and the four TiO\({}_{2}\)-W NFs with NP volume concentrations of 0.2, 0.5, 1.0, and 1.5 _v/v_% against \(N_{Re}\). The flow regimes in the CFI can be identified by adopting the criteria used by [PERSON] and [PERSON] [26] for laminar flow conditions (\(22\leq N_{Re}<1265\)) and that used by [PERSON] and [PERSON] [27] for turbulent regimes (10,000 \(\leq N_{Re}<\) 30,000). As shown in Figure 10, the \(N_{Nu}\) is an increasing function of \(N_{Re}\), and is 41-52% higher in the NF containing 1.0 _v/v_% NPs than in the base fluid (i.e., water) for Reynolds numbers in the range of \(6000\leq N_{Re}\leq 9500\). However, in the same \(N_{Re}\) range, the \(N_{Nu}\) of the NF containing 1.5 _v/v_% NPs is 36-40% lower than that for NF at 1.0 _v/v_% TiO\({}_{2}\) NPs, but 4-8% higher than in pure water. Moreover, in the \(1400\leq N_{Re}<6000\) range, the TiO\({}_{2}\) NFs do not noticeably enhance the heat transfer. The effect of adding TiO\({}_{2}\) NPs is marginal in this flow region, for example, the NF containing 1.0 _v/v_% TiO\({}_{2}\) NPs exhibits an enhancement on \(N_{Nu}\) of 2-5% compared to the base fluid. In general, the heat transfer characteristics of all the tested working fluids are comparable over the \(1400\leq N_{Re}<6000\) range. The reason behind this behavior is hypothesized to be associated with the fluid flow characteristics in that region. As the viscous forces are dominant at low \(N_{Re}\), the boundary layer increases in thickness, leading to a negligible enhancement of the heat transfer, despite the fact that the tested NFs have an enhanced thermal conductivity (compared to the base fluid), as discussed in Section 4.2.1. This may imply that, for the \(1400\leq N_{Re}<6000\) range, the conductive resistance imposed by the boundary layer of the tested NFs outweighs their thermal benefits. When the \(N_{Re}\) increases, in addition to thinning of the boundary layer, the effect of flow inversion also becomes more significant as the homogenization of the temperature fields in the Dean vortices takes place, and hence, the increase in the \(N_{Nu}\) occurs. Figure 9: (**a**) Experimental specific heat of TiO\({}_{2}\)–W NFs as a function of temperature and NP volume concentration. (**b**) Comparison of the measured specific heat at 35 \({}^{\circ}\)C and that predicted by the [PERSON] and [PERSON] [51] model. The greatest heat transfer enhancement was achieved by using the NF at 1.0 _v/v_% TiO\({}_{2}\) NPs under \(6000\leq N_{Re}\leq 9500\). The flow regime criteria based on the theoretical and simulation studies by [PERSON] and [PERSON] [26] and [PERSON] and [PERSON] [27] could suggest that this flow region corresponds to transitional flow. The behavior found in the NP volume concentration agrees with the results of [PERSON] and [PERSON] [54] using TiO\({}_{2}\)-W NFs, who also reported maximal thermal performance at 1.0 _v/v_% TiO\({}_{2}\) and a decline in performance at higher TiO\({}_{2}\) concentrations. This NP concentration behavior on the heat transfer may be due to the combined effect on increasing both \(k_{NF}\) and \(\mu_{NF}\). As evidenced in Figures 6 and 7, increasing the volume fraction of the NPs in NFs increases \(k_{NF}\) and \(\mu_{NF}\). As previously discussed, the \(\mu_{NF}\) may compromise the thermal benefits of NFs unless its increased \(k_{NF}\) can surpass the increased conductive resistance imposed by the boundary layer. From the experimental results, it is possible to infer that in the NF containing 1.5 _v/v_% TiO\({}_{2}\) NPs, the increased \(\mu_{NF}\) effect overcomes the heat transfer enhancement. Conversely, in the 1.0 _v/v_% NF, the thermal conduction enhancement outweighs the dynamic flow effect, and this positive effect likely contributed to the intensified heat transfer phenomenon that occurred in the CFI test section.