Since the international environmental treaty was established to combat climate change, almost all fields, including agriculture, industry, transportation, and building, have been looking for effective ways to save energy and reduce emissions ^[1][2]. Water utilities are no exception since water and energy always work together. Studies showed that the proportion of energy used for domestic water heating among the total energy consumption was 18% in the United States ^[3], 15% in Poland ^[4], 13–18% in Australia ^[5], and 20% in Hong Kong ^[6]. Moreover, these proportions have continuously increased in recent years because of decreased energy consumption in other fields, such as space heating and lighting ^[7].

According to the investigation of energy consumed in the United States, approximately 4.8 × 10¹⁶ kJ of energy was consumed for water-related purposes. Most of them were lost at the point of transmission, distribution, and end-use ^[8]. Furthermore, Spang et al. ^[9] estimated that 1830 GWh of electricity could be saved by water conservation in California in one year. One of the daily actions that are responsible for both energy and water consumption is showering. In Hong Kong, hot water showers consume around 40% and 19% of the total domestic water and energy consumption, respectively ^[10]. According to a field survey conducted in 1300 households in Hong Kong ^[11], the shower frequency was around 1.4 times (SD = 0.6) per day, which is more than three times as many as in other cities in England (0.4 times) ^[12]. Moreover, as indicated in an energy consumption survey conducted by Wan and Yik ^[13] in Hong Kong, the annual electricity consumption for water heaters accounted for almost half of the total electricity consumption per household and was more tensive in winter. This demonstrates considerable energy-saving potential during shower time in Hong Kong, especially in winter.

Although significant energy saving could be achieved through the optimal operation of the hot water system during showering, it might decrease occupants’ comfort ^[14]. Energy-saving and maintaining comfort appear to conflict with each other. As stated by Pomianowski et al. ^[7], people tend to increase the number and duration of showers to obtain comfort, and the water must be delivered at the required temperature. Thus, efforts still need to be made to reach the balance between energy efficiency and comfort indicators during showering.

2. Impact of Air Temperature and Water Temperature on Energy Consumption

A previous study found that air and water temperatures are the main variables influencing the occupants’ thermal comfort during showering ^[15], consistent with the results shown in Table 1. The Pearson coefficients for air temperature (r = 0.76) and water temperature (r = 0.87) were >0.5, demonstrating their strong and positive effects on occupants’ TSV. Figure 1 shows the average values of energy consumption and TSVs under the same air temperatures and the trends in energy consumption and TSV with the changes in air temperature during showering. It demonstrates that when the air temperature was between 24–40 °C, it positively correlated with the total energy consumption and an occupant’s thermal sensation. AccBording to Table 1, botth correlations were strong (r > 0.5). It should be noted that although the air temperature setting was 20–40 °C, no cases with air temperature lower than 24 °C existed since the radiator and hot water continuously heated the bathroom air during showering. As shown in Figure 1, the thermal neutral air temperature (TSV = 0) during showering was 32.8 °C and the thermal neutral zone (−0.5 < TSV < 0.5) was 30.8–34.9 °C (the shadow area in Figure 1). The corresponding energy consumption range was 7.9–9.8 kW to maintain a comfortable air temperature. As mentioned above, the water temperature significantly and positively impacted occupants’ TSV. Figure 2 shows the trends in energy consumption and TSV with the changes in air temperature during showering. During showering, the thermal neutral water temperature was 34.6 °C and the comfort zone was 33.5 to 35.7 °C. Correspondingly, the total energy consumption was 8.6–9.9 kW. Regarding the impact on the total energy consumption, as shown in Table 1, w water temperature only had a moderate effect (r = 0.39), which was less significant than the air temperature. Similarly, the relatively flat trendline of energy consumption in Figure 2 demonstrates the water temperature’s less substantial impact.

3. Impact of Ventilation Rate and Water Flow Rate on Energy Consumption

Unlike the impacts of air and water temperatures, the effects of ventilation and water flow rate on occupants’ TSV were relatively weak, with the Pearson correlation coefficients much less than 0.3 (see Table 1). Furthermore, as shown in Figure 3 and Figure 4, no matter which values the ventilation rates or water flow rates were, the average TSV of these cases was always slightly warm (from 0 to 1) and hardly any changes were identified. Therefore, the current study considers ventilation and water flow rates in the practical ranges insignificant to an occupants’ thermal sensations. In terms of the impact of the ventilation rate on the total energy consumption, it was also weak (r = 0.162). As shown in Figure 3, even though the ventilation rate increased twice (from 0.01 to 0.03 kg·s⁻¹), the energy consumption only increased within 2 kW (from 8.4 to 10.1 kW). In contrast, the impact of the water flow rate on the total energy consumption was quite strong, and the Pearson correlation coefficient between them was the highest (r = 0.833) among the coefficients between other influencing variables and the total energy consumption (see Table 1).

4. Integrated Impact of Air Temperature, Water Temperature, Water Flow Rate, and Ventilation Rate on Energy Consumption

Considering the interaction between the air temperature, water temperature, water flow rate, and ventilation rate, a multiple regression model was established between these variables and the total energy consumption to understand their integrated impact better. Detailed information about this model is shown in Table 21. All the variables significantly impacted the energy consumption and no multicollinearity was identified between them (VIF < 4). In addition, the R² of this model is 0.987, which means this regression model can explain 99% of the variability observed in the total energy consumption: $${\mathrm{Q}}_{\mathrm{total}{}_{}=0.19\times {\mathrm{T}}_{\mathrm{a}}+0.51\times {\mathrm{T}}_{\mathrm{w}}+62.08\times { \mathrm{m}{\mathrm{a}}_{}+43.37\times {\mathrm{m}}_{\mathrm{w}}-23.85 ({\mathrm{R}}^2=0.987)}_{}}$$

Variables	β Coefficient	Standardized Coefficients Beta	95.0% Confidence Interval for β	p Value a	VIF b
Air temperature (°C)	0.193	0.237	0.188–0.197	<0.001	1.441
Water temperature (°C)	0.512	0.388	0.505–0.519	<0.001	1.279
Ventilation rate (kg·s−1)	62.081	0.122	59.569–64.593	<0.001	1.147
Water flow rate (kg·s−1)	43.372	0.807	43.103–43.641	<0.001	1.183