# Enhancement of Subcooled Flow Boiling Heat Transfer with High Porosity Sintered Fiber Metal
## 3 Results and Discussion  
### Comparison of [PERSON]'s Correlation for the Bare Surface  
The experimental data were compared with [PERSON]'s correlation for subcooled flow boiling heat transfer [25; 29; 30]. [PERSON] et al. extended [PERSON]'s correlation [31] and applied it to subcooled flow boiling [32]. [PERSON]'s correlation considers the effects on the forced convection (heat flux corresponding to the single-phase) and the nucleate boiling (heat flux corresponding to the two-phases) on a superposition model, expressed as follows. \[q_{\mathrm{T}}=q_{\mathrm{fc}}\Phi+q_{\mathrm{nb}}S \tag{4}\]  
The supersession factor S and correlation factor \(\Phi\) can be calculated by the following equations. \[S=\frac{1}{1+2.53\times 10^{-6}(R_{\mathrm{f}1}\Phi^{1.25})^{1.17}} \tag{5}\]  
\[\Phi=\left\{ \begin{array}{cc}2.35\Big{(}\frac{1}{\lambda_{\mathrm{nt}}}+0.2 13\Big{)}^{0.736}&x>0.1\\ 1&x\leq 0.1\end{array} \right. \tag{6}\]  
In this experiment, we assumed that \(\Phi\) = 1 for the subcooled flow boiling due to the vapor quality \(x\) < 0.1. Thus, the total amount of the heat flux \(q_{\mathrm{T}}\) from Equation (1) can be calculated by the forced convection on the single-phase term \(q_{\mathrm{fc}}\), and the nuclear boiling term on the two phases heat flux term \(q_{\mathrm{nb}}\) defined as follows. \[q_{\mathrm{fc}}=h_{\mathrm{fc}}(T_{\mathrm{w}}-T_{\mathrm{b}}) \tag{7}\]  
\[q_{\mathrm{nb}}=h_{\mathrm{nb}}\Delta T_{\mathrm{sat}} \tag{8}\]  
The heat transfer coefficient of nucleate boiling \(h_{\mathrm{nb}}\) is given by Foster-Zuber's correlation [33]. \[h_{\mathrm{nb}}=0.00122\frac{\lambda_{1}^{0.79}c_{\mathrm{p}1}^{0.45}\rho_{ 1}^{0.49}}{\rho_{1}^{0.5}\mu_{1}^{0.29}\mu_{\mathrm{lg}}^{0.24}\rho_{\mathrm{ g}}^{0.24}}\Delta T_{\mathrm{sat}}^{0.25}\Delta P_{\mathrm{sat}}^{0.75} \tag{9}\]  
The heat transfer coefficient of forced convection \(h_{\mathrm{fc}}\) is usually calculated using the Dittus-Boelter correlation. For the present research, the experimental heat flux on the  
Figure 5: Uncertainty of heat flux. single-phase was obtained with Equation (2), and the temperature measured by the thermocouples. In addition, we considered the single-phase when the \(\Delta T_{\text{sat}}\leq 0\). Figure 6a shows the comparison between the Dittus-Boelter correlation and the experimental data corresponding to the bare surface, and there was a decrease between the experimental heat flux and predicted heat flux. The experimental heat flux corresponding to the bare surface was around 50% lower than the predicted using Dittus-Boelter. This effect is due to the correlation considering a circular heated channel. [PERSON] et al. [26] and [PERSON] et al. [34] performed experiments using a rectangular channel heated on only one of its faces. The results show a considerable error in comparison with the Dittus-Boelter correlation. [PERSON] [26] proposed modifying the correlation for the one heated face square channels computing a linear regression. After performing the linear regression, the heat transfer coefficient of forced convection is defined as follows:  
\[\text{h}_{\text{fc}}=0.168 Re^{0.62}Pr^{0.545}\bigg{(}\frac{\lambda_{l}}{d} \bigg{)} \tag{10}\]  
In Figure 6b, the heat flux calculated by the modified Dittus-Boelter's correlation and the experimental heat flux corresponding to the bare surface is plotted. The coefficient of determination was 0.9522, which implies a high correlation. Figure 7 shows the comparison between the experimental heat flux corresponding to the bare surface and [PERSON]'s correlation in Equation (4). Here, the experimental heat flux data were between 10% and were 30% lower than this correlation. The reduction in the heat flux is attributed to the oxidation effects, as the heat transfer surface was sufficiently oxidized by performing approximately 10 heating experiments beforehand to obtain stable data. Therefore, these values are slightly lower than those of the formulas due to the deterioration of the heat transfer performance caused by oxidation.