Experimental activity Two experimental facilities were realized to determine the unknown parameters to be adopted in the thermal model。 In particular, the first set of experiments consisted of temperature measurements under real operating conditions, in order to evaluate the integral absorptivity and emissivity of the tile surface and to validate the assumption of lumped parameters for the tile。 The second set was carried out in a scaled-down channel (1:5) to estimate the airflow pressure drop into the under-slating ventilation channel under fluid-dynamic similarity for evaluating the energy loss term 。

Thermal experiments The experiments were conducted for both a simple tile and a PV one at Solar Tech Lab, at the Department of Energy of Politecnico di Milano。 Data-collection was held in the months of June and July for about 30 h of acquisition, concentrated during periods of major irradiation。 In particular, the measurements were carried out in days expected to be the sunniest and less windy to have steady and consistent conditions。 Moreover, a single tile and combinations of two up to four tiles properly assembled were tested and compared。 The equipment includes: 1。 Multimeter Agilent 34970A able to read input signals of different types: temperature, DC/AC current, resistance, frequency or DC/AC voltage。 The selected scanning speed is of a measurement every 30 seconds。 2。 Thermocouples type J with a measurable temperature range from -200 °C to 1200 °C approximately and accuracy of 0。5 K。 The measuring points in shown in Figure 4, with a distance of 5 cm from the edge of tile。 3。 Data acquisition software Agilent Benchlink Data Logger 3 4。 Meteorological station that provides information about ambient temperature, wind speed, solar radiation (direct normal radiation, total radiation on a flat surface and diffuse radiation)。

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9 5。 Support structure designed to ensure a slope of the tile equal to 20°。 Lateral openings were closed to prevent unwanted air circulations at the bottom of the tile。 Figure 5 shows one of the experimental set-up and measurements carried out to assess the tile temperature at different radiation conditions。 In the worst case for a single tile the maximum surface temperature difference resulted lower than 5 K。 On the other hand the maximum temperature difference across the tile thickness was lower than 3 K。 On the other hand, the highest value of the Biot number resulted about 0。1, therefore the lumped parameters assumption applies for most of the actual operating conditions。 Consequently, the average tile temperature has been calculated from the measured local values。 Then, using the thermal model, and have been numerically determined as the couples of values that minimize the RMS difference between the calculated and the measured tile temperature。 The resulting values are summarized in Table 4:

Fluid dynamic Analysis Experimental tests were carried out to estimate the friction factor for the under-slating ventilation ducts。 The experimental apparatus, described into detail in [32], basically consists of a ribbed rectangular channel, which allows reproducing the scaled down geometry of the ventilation channel (1:5) and suitable flow conditions。 Since the air flow is provided by a blower, fluid-dynamic similarity is based on an “apparent” Reynolds number, evaluated by means of the average air velocity resulting from the thermal model。 A float-type flow-meter with 2% nominal accuracy is used to set the flow rate to achieve the required Reynolds number。 The pressure drop between the inlet and the outlet section is measured by a differential micromanometer with 250 Pa full scale and 0。125 Pa sensitivity and the friction factor is calculated from Eq。 (7)。 The relationship between the friction factor and the Reynolds number is then determined in a range of conditions representative of the actual operation of the ventilation channel, namely 650 < Re < 8500。 According to a sensitivity analysis, the uncertainty on the friction factor results lower than 7%。 The main settings of the test channel are reported in Table 5。 Wooden ribs have been realized and attached with double-sided tape, ensuring perfect sealing to avoid any detachment or displacement caused by mechanical stress during test cycles。 T-type thermocouples measure the air inlet and outlet temperature in order to determine the average temperature for calculating air thermal properties。 Fitting the experimental data, the following correlation between the friction factor and the Reynolds number holds: (28) where: