## 4 Results and Discussion
As shown in Figure 3, the \(\varepsilon\) of MWCNTs-FIRC is higher than TiO\({}_{2}\)-FIRC only when the wavelength is greater than 9.43 (sample temperature of 80 \({}^{\circ}\)C for \(\varepsilon\) test) and 9.52 \(\upmu\)m (test sample temperature of 40 \({}^{\circ}\)C for \(\varepsilon\) test) at the wavelength range of 9.72\(-\)8.57 \(\upmu\)m. The temperatures calculated by the two wavelengths, as based on [PERSON]'s displacement law, are 34.2 and 31.3 \({}^{\circ}\)C, respectively; in other words, most of the water temperatures of TiO\({}_{2}\)-FIRC in the experiment had a higher  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{\(\mathbf{T_{T_{2}}}\)(\({}^{\circ}\)C)} & \multirow{2}{*}{**Item**} & \multicolumn{4}{c}{**40 W**} & \multicolumn{4}{c}{**80 W**} \\ \cline{3-10}  & & **Blank** & **Base** & **TiO\({}_{2}\)** & **MWCNTs** & **Blank** & **Base** & **TiO\({}_{2}\)** & **MWCNTs** \\ \hline \multirow{8}{*}{43} & \(S_{tr}\) (\({}^{\circ}\)C/s) & 0.01491 & 0.01482 & 0.01453 & 0.01404 & 0.02829 & 0.02745 & 0.02775 & 0.02804 \\  & \(R_{Str}\) (\%) & 0.00 & \(-\)0.60 & \(-\)2.60 & \(-\)5.84 & 0.00  
\(\varepsilon\) corresponding to this range of wavelengths (9.72-8.57 \(\upmu\)m) than MWCNTs-FIRC. In theory, when TiO\({}_{2}\)-FIRC is used in hot water heaters, the improved performance of the hot water heaters should be better than MWCNTs-FIRC, which is because the higher radiation energy of FIR can promote the disturbance of water during heating. However, the ranked results of the performance indicators show that the sample coated with MWCNTs-FIRC is better than the sample coated with TiO\({}_{2}\)-FIRC under the heating power of 40 W. FIRCs with higher \(\varepsilon\) should be able to provide higher FIR radiation energy to disturb the water in the hot water heater and make the overall water temperature more uniform (lower \(STD_{d\overline{T}w}\)). Due to the disturbance of the FIR radiation energy (\(S_{tr}\) is only calculated by \(T_{1}\) without considering \(T_{2}\)), the uniformity of \(T_{2}\) and \(T_{1}\) will suppress \(S_{tr}\) when the overall water temperature is more uniform; in the same way, the more uniform water temperatures at \(T_{2}\) and \(T_{1}\) will also make \(T_{lat10}\) lower (\(T_{lat10}\) calculated only by \(T_{1}\) without considering \(T_{2}\)). The \(STD_{d\overline{T}w}\) in Table 1 shows that the sample coated with TiO\({}_{2}\)-FIRC has only one experimental parameter (\(T_{Tur}=53\ ^{\circ}\)C, heating power = 80 W), which is slightly higher (within 1%) than the sample coated with MWCNTs-FIRC. The above analysis shows that \(STD_{d\overline{T}w}\) suppresses the two performance indicators of \(S_{tr}\) and \(T_{lat10}\). Furthermore, it is well known that the thermal conductivity (\(k\)) of MWCNTs is much higher than that of TiO\({}_{2}\), which makes the \(k\) of MWCNTs-FIRC higher than that of TiO\({}_{2}\)-FIRC. High \(k\) material is coated on the outside of hot water heater will be detrimental to the thermal insulation performance of the hot water heater. Therefore, in terms of all the experimental parameters in this study, the sample coated with TiO\({}_{2}\)-FIRC should be better than the sample coated with MWCNTs-FIRC for improving the performance of the hot water heater in this study. This study suggests that the FIRC with high \(\varepsilon\) and low \(k\) should be selected for the practical application of FIRC to hot water heaters, which should be better for improving the relevant performance of hot water heaters. However, FIRC with high \(\varepsilon\) and high \(k\) can be considered in the field of heat dissipation.