*3.2. System Efficiency*

The results of our experiments and theoretical calculations are summarized in Tables 3–5. The results show useful gains and losses in energy with the water temperature in the water storage tank for the clear days of December, March, and June. The lowest rate of useful energy is in the evening and morning. However, the highest value of useful energy at solar noon is due to the increasing gain in solar energy. Due to the greater temperature difference between the water and the ambient, heat loss is greater at noon than in the morning and evening. The experimental efficiency of the hydronic solar system was estimated by ( *Qusef ul I Ac* ). It is clear from the tables that the system efficiency rises progressively from sunrise to solar noon, the maximum value, then falls off. The maximum experimental efficiency is around 80% in December, 81% in March, and 84% in June. The instantaneous efficiency of the system without using PCMs is around 60%. So, the positive effect of using PCMs on the performance of the hydronic solar system is clear.

Figure 11 illustrates the relationship between the system's thermal efficiency (ᢡ *system*) and the temperature difference between hot water and ambient (Δ*T*/*I*), based on the data for December, March, and June. The relationship shows a straight line with the overall heat loss coefficient as a slope. The optical efficiency of the hydronic system is the intercept of the straight line. The values of the determining factor of the relation (R2 > 0.9) point out an intense correlation between both parameters. Each figure shows the comparison of the relationship between systems with and without PCM. It can be concluded from Figure 11 that the case of PCM has higher efficiency than that without PCM.


**Table 3.** Experimental and calculated results for December 2021 with paraffin.

**Table 4.** Experimental and calculated results for March 2022 with paraffin.



**Table 5.** Experimental and calculated results for June 2022 with paraffin.

**Figure 11.** Efficiency of the system versus ΔT/I with and without PCM; (**a**) December, (**b**) March and (**c**) June.

Situta-Olcha et al., 2021 [43] examined the thermal efficiency of the solar system with a heat pipe without a PCM under weather conditions similar to December. Their results show less than 40% thermal efficiency. Moreover, the results of Azimi et al., 2015 and Tong et al., 2016 [42,44] present lower thermal efficiency than that achieved in this study, which was less than 70% and 80%, respectively. Kumar et al., 2020 [21] investigated adding paraffin wax as a PCM inside a cylindrical container through a hot water storage tank. One case of their study was carried out under conditions similar to our study through June; the daily efficiency was less than 70%.

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