## Materials and Methods
### PCM-Water Hybrid Thermal Storage
#### 2.1.2 Experimental Setup, Test Procedure, and Model Assessment  
The experimental test rig presented in Figure 2 was already described in previous works of the authors [10; 20; 23]. However, for reader's convenience, the main characteristics of the experimental setup are reported here. It is designed to study the heat transfer performance of PCMs with and without Al foam as a heat transfer medium in hybrid water TESs. The temperature of the water in the tank was kept at the desired value by controlling the electrical power and the water flow rate. The hot water coming from the 70 L water tank first passed through a brazed plate heat exchanger (BPHE) to be cooled down by tap water, and then it was pumped into an electrical heater (9 kW) driven by a PID (Proportional, Integrative, Derivative) regulator. Then it entered again into the water tank. As illustrated in Figure 2, two similar tubes could be tested at the same time, both containing around 1 kg of paraffin wax, but only one was implementing the enhanced surface. Both tubes were tested at constant water temperatures in order to monitor and to directly compare the loading and unloading times, and to study the effects of Al foams on the heat transfer performance during the solid-liquid phase change of the paraffin wax. The commercial paraffin wax Rubitherm(r) RT40 was used in the tests. Table 1 reports its main thermophysical properties. As it can be noticed, the selected paraffin shows many desirable characteristics: high latent heat, low vapor pressure in the melt, chemical inertia and stability, non-toxicity, and a very low price. Nevertheless, two main drawbacks are present: low thermal conductivity and high volume change during the melting process. The test samples consisted of 800 mm long, 2\" (50.8 mm) OD tubes, closed on one side. One of these tubes was empty and it was filled up with the selected paraffin wax; the others were manufactured to locate different 600 mm long Al-foam cylinders, which were brazed to the inside tube wall to minimize the contact resistance. As reported in Figure 2b, each tube was equipped with 6 calibrated T-type thermocouples with an accuracy of \(\pm\)0.05 K to monitor the phase-change process at different tube heights: two thermocouples, one in the centre (25 mm from the surface) and one at half of the section (12.5 mm from the surface), at three different heights of the tubes called top, centre, and bottom. The tests involved both the melting and solidification processes. The water contained in the tank (around 70 L) was heated up to the set temperature, 50 \({}^{\circ}\)C, by means of the electrical heater. Then, the two instrumented tubes were inserted in the water tank and all the data were recorded (i.e., loading process). Once the measured paraffin temperatures read by the installed thermocouples asymptotically approached the water temperature and remained almost constant, the hot water was purged out and the tank reloaded with tap water to study the solidification (i.e., unloading process). The unloading (i.e., solidification) process was considered concluded when all the paraffin temperature readings became constant, close to that of the water tank. The imposed experimental boundary condition was  
Figure 2: **(a)** Schematic of the experimental setup and **(b)** location of the temperature probes (in millimeters). then \"constant water temperature\", and it was fixed by monitoring the water temperatures at different tank heights (Figure 2) with registered differences always less than 0.1 K.  
Simulations were aimed to determine the radial (along the section of the tubes) temperature distribution at different heights of the tubes, in order to compare it against experimental results. The comparison is between a tank with two tubes with paraffin only, and one with two tubes with the paraffin/Al-foam composite PCM. Each tube, which was 700 mm high, was divided in 35 nodes. Thus, the PCM occupied the height from the 6 th to the 35 th node from the top (Figure 1a).