**2. Methodology**

#### *2.1. Experimental Setup*

The manufactured hydronic solar system is located on the Jordan University of Science and Technology campus. Its geographic coordinates are 32.49◦ N (latitude) and 35.99◦ E (longitude). The solar collector that was used is an evacuated tube setup with an inclined angle of 45◦. The inclined angle was chosen after making calculations to obtain higher gains in energy in the winter and solve the overheating problem in the summer. The main features of the evacuated tube of the solar collector are presented in Table 1.


**Table 1.** Features of the evacuated tube of the solar collector.

In addition to evacuated tubes, the system contains a water storage tank with a total capacity of 0.200 m3, a length of 1.6 m, and a diameter of 0.45 m. It is made of galvanized steel with an outer shell with a diameter of 0.53 m and contains paraffin wax as PCM with a thickness of 2 cm at the top and 4 cm in the bottom portion; such an asymmetric design is believed to assist in charging and discharging heat into the system since it provides more effective buoyancy motion for the liquid PCM. The tank was thermally insulated by rock wool to reduce the loss of energy. The insulation shell is covered with galvanized steel sheet. All specifications of the storage tank are shown in Figure 1.

**Figure 1.** Schematic representation of the storage tank with instrumentation.

The phase change material that was used in this system was paraffin wax with a melting temperature of 48 ◦C. It was chosen due to its thermal stability, low price, no sub-cooling problem, and suitable latent heat. The thermal specifications of paraffin wax are presented in Table 2.

**Table 2.** Thermal specifications of paraffin wax [39].


Additionally, the system consists of a solenoid valve that is programmed to meet the level of family consumption of hot water throughout the day. This valve withdraws hot water at specific times; the following diagram shows the proposed water consumption pattern, which presents the distribution of hot water throughout the day. Figure 2 shows a daily water consumption pattern according to real observed consumption and required estimations.

The system contains a cold water tank to recover hot water discharged from the hot water tank. Thermocouples (Type K) were fixed through the storage tank to notice and record water and PCM temperatures during the heating process. Thermocouples were installed in the system to detect the temperatures of the water, PCM, and ambient. They were placed in the water region in three positions: two at the top and one at the bottom. Additionally, other thermocouples were placed in three positions throughout the PCM region: two at the top and one at the bottom. One thermocouple reads the ambient temperature. All thermocouples were connected to a converter that gives temperature

readings in Celsius. The data logger was connected to read and record the temperatures with Windows software easily plugged into a computer. For measuring irradiance (w/m2), a pyranometer was used. The data was acquired and stored every 4 min. An additional experiment was performed every 5 s and the reading was recorded. The hot water tank was discharged completely in the evening (specifically at sunset) to investigate the water and PCM temperature behavior in this case.

**Figure 2.** The hot water consumption pattern throughout the day.

As for the hot water region, the PCM region was also equipped with two holes and a lid to fill and discharge the PCM at any time based on necessity. Moreover, the problem of high pressure throughout the system is resolved by setting up vents for both the water and the PCM regions. A photographic view and schematic diagram of the system are presented in Figure 3. The water is replenished from the water supply tank. The hot water storage cylinder receives hot water passively from the evacuated tube, whereas the hot water flows up to the tank naturally due to thermosiphon circulation. The hot water was then used for domestic use, and hot water consumption was recovered by the water supply tank. When water gains heat from solar energy, it conductively exchanges this energy with the PCM. Conversely, as the temperature of water decreases, the latent heat will be released to the water from the PCM during the liquid phase until solidification in the absence of the sun.

#### *2.2. Thermal Model*

Energy balance is applied to both parts of the hydronic solar system under steady-state conditions: the evacuated tube and hot water storage tank. The useful energy gained from solar radiation by evacuated tubes can be expressed by [40,41]:

$$Q\_{useful} = I \ A\_c \left( \tau \alpha \right)\_{eff} k\_{\theta i} - Q\_{loss} \tag{1}$$

and

$$Q\_{loss,\ tube} = \mathcal{U}\_{L,\ tube} A\_c \left( T\_w - T\_a \right) \tag{2}$$

where *I* represents a global solar irradiance, *Ac* represents a solar collector area, (*τα*)*eff* represents an effective transmissivity-absorptivity product coefficient, *kθ<sup>i</sup>* represents an incident angle modifier, *UL*,*tube*. represents an over-all heat transfer coefficient of heat loss from the evacuated tubes, and *Tw* and *Ta*. represent water and ambient temperatures, respectively.

The solar collector's efficiency ᢡ . is determined by the value of the ratio between useful energy and solar radiation that falls on the collector. This can be expressed by:

$$\mathfrak{N} = \frac{Q\_{useful}}{I \, A\_c} \tag{3}$$

Solar collector efficiency (evacuated tubes) can be explained by:

$$\mathfrak{N}\_{collector} = \left(\tau \mathfrak{a}\right)\_{eff} k\_{\theta \bar{i}} - \frac{\mathcal{U}\_{L,tube} \left(T\_w - T\_a\right)}{I} \tag{4}$$

**Figure 3.** Hydronic evacuated tube solar system with a PCM: (**a**) photographic view; (**b**) schematic diagram.

The following equation clarifies how the useful energy leaving the evacuated tubes moves to the water tank, which transfers to paraffin, giving rise to temperature changes:

$$Q\_{\rm PCM} = \left(m\_{\rm PCM} \ c\_{p,\rm PCM} \,\Delta T\right)\_{\rm solid} + m\_{\rm PCM} \,\lambda\_{\rm PCM} + \left(m\_{\rm PCM} \, c\_{p,\rm PCM} \,\Delta T\right)\_{\rm liquid} \tag{5}$$

Energy balance in the water tank can be expressed by:

$$E\_{\text{accumulation}} = Q\_{\text{useful}} \pm Q\_{\text{PCM}} - Q\_{\text{load}} - Q\_{\text{loss,tank}} \tag{6}$$

Useful energy, load energy, and the heat loss of the water tank can be calculated by:

$$Q\_{useful} = m\_{w,\text{ tank}} \cdot c\_{p\_{\text{\textquotedblleft}w}} \cdot (T\_{out,\text{ w}} - T\_{in,\text{ w}}) \tag{7}$$

$$Q\_{load} = m\_{w,load} \cdot c\_{p,w} \cdot (T\_w - T\_a) \tag{8}$$

$$Q\_{loss,\ tank} = \mathcal{U}\_{L,\ tank} \, A\_{tank} \, \left( T\_w - T\_a \right) \tag{9}$$

The overall heat transfer coefficient of energy losses in the system (*UL,sys*) is equivalent to the losses of both the evacuated tube and the water tank. This can be expressed by:

$$
\mathcal{U}\_{L,sys} = \mathcal{U}\_{L,tubb} + \mathcal{U}\_{L,\,tank} \tag{10}
$$

The efficiency of the system with paraffin as the PCM is:

$$
\mathfrak{n}\_{system} = \mathfrak{n}\_{collector} \cdot \mathfrak{n}\_{PCM} \tag{11}
$$

$$\mathfrak{N}\_{system} = \left[ (\pi \alpha)\_{eff} \, k\_{\theta i} - \frac{\mathcal{U}\_{L, \text{sys}} \left( T\_{H \sharp O} - T\_a \right)}{I} \right] \cdot \left[ \frac{\mathcal{Q}\_{PCM}}{I \, A\_c} \right] \tag{12}$$

The domestic hydronic solar system was evaluated according to EN 12976 standards, where the solar radiation, water temperature, ambient, and PCM temperatures were recorded for more than 9 months consecutively under two test types: with PCMs and without PCMs. According to ISO 9459-5 DST, the withdrawals of hot water from the storage tank depended on family consumption patterns throughout the testing period. Thermal output characterization tests were conducted according to the results of calculating instantaneous system performance experimentally and theoretically and calculating water storage tank heat losses. The hydronic solar system's thermal performance was measured on days with daily solar radiation and temperatures recorded over consecutive months at different water storage inlet temperatures. Protection against overheating and pressure resistance standards were considered necessary to save the system from deformation.

#### **3. Results and Discussion**

The average values of the solar radiation at the JUST campus throughout the year are shown in Figure 4. The temperature distributions of the ambient, water, and PCM at the storage tank were recorded during system testing. All parameters of the system were studied for many months over a year to investigate the effect under different weather conditions.

#### *3.1. Temperature Distributions*

The temperature distributions of the ambient, PCM, and water at the storage tank (average) with and without PCMs are shown in Figures 5–7. In these figures, it is noticeable that the water temperature increases from sunrise until it reaches the melting temperature of paraffin. The water temperature remains at a fixed value until the paraffin melts completely, at which point it increases to a specific value. The temperatures decrease with the decrease in energy gained from the sun at the end of the day. While the water temperature rises through circulation in the evacuated tubes, water flows into a storage tank where thermal energy exchange starts between hot water and paraffin, which further raises the paraffin's temperature. So, the temperature of the paraffin at the beginning of the day increases gradually with the increasing water temperature that comes from the evacuated tubes. When paraffin reaches its melting point, the temperature stays constant, increases to the maximum specified value, and then gradually decreases at night as a result of the absence of energy from solar radiation. At the melting and solidification temperature of the PCM, the water temperature stays at a fixed value, which can be observed in Figures 5–7.

**Figure 5.** Temperature distribution of the system through December 2021: (**a**) using paraffin as PCM; (**b**) without PCM.

**Figure 6.** Temperature distribution of the system through March 2022: (**a**) using paraffin as PCM; (**b**) without PCM.

The following can be observed by using a PCM case: when the PCM temperature reaches its melting point throughout the day, the stored energy begins the PCM phase change from a solid to a liquid. This stored energy is used as released energy in water to maintain its temperature within the domestic usage range.

The temperatures of paraffin decrease constantly in the afternoon to reach a solidification point and stay at the same temperature for a short period, with an exchange of latent heat that is released in water. This process is reflected in the values of water temperatures, where the decrease is very small. Energy loss during the late afternoon and night hours is higher than at any other time during the day. The water temperatures are in the range for domestic use, which is the main goal of the system. The thermal energy that transfers between water and paraffin depends on the temperature difference between them and on the phase of paraffin (liquid or solid). Throughout the day, with the presence of solar energy,

the glazing temperature, energy collected, and water temperature increase. Approximately at solar noon, water temperatures reach their maximum.

**Figure 7.** Temperature distribution of the system through June 2022: (**a**) using paraffin as PCM; (**b**) without PCM.

It can be observed in Figures 5–7 that water temperatures at solar noon without using a PCM case are higher than those with PCMs. Higher values due to the transfer of energy from water to PCMs mean a reduction in overheating problems in the water tank. Conversely, through early morning and late afternoon, the water temperatures are lower than those reached when using paraffin as a PCM.

Figure 8 shows different temperature distributions, and the experiment of discharging the storage tank of hot water completely was performed. This experiment was conducted to study the behavior of the PCM and heat exchange with water by discharging all amounts of hot water in the water tank at 4:00 PM. The withdrawal of hot water is replaced by cold water. It is evident from Figure 8 that the water temperature decreases sharply through the discharge process, along with the PCM temperature. After that, the water temperature begins to rise as a result of the heat exchange from the PCM.

**Figure 8.** Temperature history of the system through complete hot water consumption.

The water and PCM reach the same temperature at a specific point in time. Additionally, the temperature of the water in the domestic use range can be considered optimal. This experiment shows the exchange of stored thermal energy in PCMs with water and its effect on water temperature. This experiment explains the family's sudden and complete drain of the hot water from the water storage tank and how the PCM raises the water temperature by 10 ◦C over a short period of time.

Furthermore, Figure 9 shows the temperature distributions of hot water, PCM, and ambient temperature in the absence of hot water consumption throughout the day. This experiment was performed in approximately similar weather conditions to the previous one. It can be noticed that higher values of hot water and PCM temperatures are due to the absence of load energy. Moreover, it is clear that the temperature difference between water and paraffin is small; this difference is less than 1 ◦C in the morning hours with increasing gains in energy.

**Figure 9.** Temperature history of the system through no hot water consumption.

Due to the design of the storage tank, the thickness of the PCM layer on the top and bottom of the tank was different. The thickness at the bottom is higher than the top, which means more mass of PCM and more stored energy through the sun's presence. This stored energy is released in the water at the bottom of the tank, which has a lower temperature than that in the top region. Releasing energy from PCMs means heating water, which makes the water through the whole tank have similar or small differences in temperature, especially in the late afternoon hours. Figure 10 presents the temperature distribution of water on the top and bottom regions; as can be seen, the maximum difference is approximately 5 ◦C during the daybreak hours. It can be observed that the water temperatures at the top and bottom of the tank are the same at solar noon. This study shows a decrease in water temperature compared with a hydronic solar system without a PCM, which is an advantage to reducing heat losses from the system and avoiding superheating through the tank. Furthermore, Azimi et al., 2015 found that the water temperature at the bottom of the tank is close to ambient temperature without PCMs [42].

**Figure 10.** Temperature distribution of water through the top and bottom of the storage tank [42].

Figure 10 presents a comparison and disparity between our study and that of Azimi et al. Not only do our results demonstrate a decrease in the difference between hot water and temperature at the top and bottom of the storage tank greater than that of Azimi et al., but they also show a decrease in the hot water in the system (within domestic use), which means less thermal energy losses and covers the hours of solar absence.
