## 4 Results and Discussion  
Figures 5-7 show the average water temperature (from \(T_{1}\)) of the four repeated experiments for each test sample under different \(T_{Tar}\) and heating powers. It can be seen from these figures that there are slight differences between the test samples, and the maximum water temperature (\(T_{max}\)) under each experimental parameter is slightly higher than the \(T_{Thr}\). In this study, the temperature difference between \(T_{max}\) and \(T_{Thr}\) is named \(dT_{Thr}\) (\({}^{\circ}\)C). This phenomenon is mainly caused by the continued heating of the water by the residual heat after the heater was turned off, and the residual heat of the heater after the power was turned off should be the same under the same heating power. In addition, the \(dT_{Thr}\) with heating power of 80 W had a higher residual heat than the 40 W after the power was turned off; therefore, it can be expected that the \(dT_{Thr}\) with heating power of 80 W was higher than that of the 40 W. The higher \(dT_{Thr}\) shows the higher heating capacity of the water by the residual heat of the heater that had better thermal insulation performance. However, the residual heat of the heater after the power was turned off should be the same under the same heating power. Therefore, the high \(dT_{Thr}\) may be caused by the poor natural convection of the water in the hot water heater, which caused the higher local temperature, and this issue can be determined by referring to the temperature difference between \(T_{2}\) and \(T_{1}\). Furthermore, whether the high \(dT_{Thr}\) comes from the better thermal insulation effect can be determined by referring to \(T_{lat10}\). Moreover, based on the \(T_{Thr}\), \(S_{tr}\) will also affect the overshoot of \(T_{1}\). According to the above analysis, it can be known that  
As shown in Table 1, all experimental results are further aggregated into various performance indicators such as the heating rate (\(S_{tr}\)), the average water temperature (\(T_{1}\)) within 10 min before the end of the experiment (\(T_{lat10}\)), the standard deviations (\(STD_{dTw}\)) of the temperature difference between the upper (\(T_{2}\)) and center (\(T_{1}\)) water temperatures during the experiment, and its change ratios to facilitate comparison. It can be seen from Table 1 that \(S_{tr}\), and \(T_{lat10}\) do not have a certain trend; however, \(STD_{dTw}\) presents all the experimental parameters, and shows that the uniform water temperatures of the samples coated with TiO\({}_{2}\)-FIRC and MWCNTs-FIRC are better. Since the heating load used by the hot water heater in this study is only 480 g of pure water, it is expected that the experimental results of each test sample have little difference under the same experimental parameters. In order to comprehensively evaluate the performance of hot water heaters, the different heating powers are divided into two groups of 40 and 80 W, and the four samples are ranked 1 to 4 according to the sorted order of the performance indicators (\(S_{tr}\), \(T_{lat10}\), and \(STD_{dTw}\)); the smaller the sorted cumulative number, the better the overall performance. When the accumulated numbers are the same, \(STD_{dTw}\) is used to distinguish the difference. The order of the overall performance of the hot water heater at the heating power of 40 W is MWCNTs, TiO\({}_{2}\), Base, and Blank; while the order is TiO\({}_{2}\), MWCNTs, Blank, and Base for the heating power of 80 W. The results show that the sample with MWCNTs-FIRC has better performance at the low heating power (40 W); while the sample with TiO\({}_{2}\)-FIRC has better performance at the high heating power (80 W). Next, this study conducted a more in-depth discussion on the relationship between the three performance indicators of \(S_{tr}\), \(T_{lat10}\), and \(STD_{dTw}\).