## 2 Materials and Methods
### Analysis at Room Level  
The analysed room having a dimension of 312 cm length, 272 cm depth, and 241 cm height, was heated at 22 \(\pm\) 0.3 \({}^{\circ}\)C by using an electric radiator placed in the opposite side of the coated wall. The cold room representing the exterior environment was maintained at 10 \(\pm\) 1 \({}^{\circ}\)C by a direct expansion cooling system (Figure 7a). The party-wall is made by 6 mm thick MDF board (Medium Density Fibreboard), with a thermal conductivity \(\lambda\) of 0.102 \(\pm\) 0.002 W/m K (previously measured by HFM apparatus). The wall thermal behaviour was monitored by placing two heat flux sensors HFP02 (uncertainty \(<\) 3%) and six thermocouples (uncertainty \(<\) \(\pm\)0.25 \({}^{\circ}\)C) for the measurement of the air and surface temperatures on both sides of the wall. The experiments were repeated for three wall configurations, with each configuration being coated on the interior side with different paints described in Section 2.1.2:  
* Config. 1: a100 paint (\(\varepsilon\) = 0.41) (Figure 7b);
* Config. 2: a50 paint (\(\varepsilon\) = 0.60) (Figure 7c); and,
* Config. 3: a0 paint (\(\varepsilon\) = 0.88) (Figure 7d). The wall thermal transmittance U was determined by applying the average method according to ISO 9869-1:2015 standard [22] (Equation (10)). Moreover, Equation (11) determines the indoor surface heat transfer coefficient. \[\mathrm{U}=\frac{\sum_{j=1}^{n}\varphi_{j}}{\sum_{j=1}^{n}\left(T_{\mathrm{ air,j}}-T_{\mathrm{air,e,j}}\right)} \tag{10}\]  
\[\mathrm{h_{i}}=\frac{\sum_{j=1}^{n}\varphi_{j}}{\sum_{j=1}^{n}\left(T_{\mathrm{ air,j}}-T_{\mathrm{s,i,j}}\right)} \tag{11}\]  
where: \(\varphi\) is the specific heat flow measured through the partition wall (W/m\({}^{2}\)); T\({}_{\mathrm{s,i}}\) is the internal surface temperature (\({}^{\circ}\)C); and, T\({}_{\mathrm{air,i}}\) and T\({}_{\mathrm{air,e}}\) are, respectively, the internal (heated room) and external (cooled room) air temperature. Figure 6: Photographic survey (samples a series); (up) Aluminium paint mixed with white matt paint; (down) Aluminium paint mixed with red paint. The measurements of the parameters to be adopted for the determination of the thermal comfort conditions were performed by using a Bruel & Kjaer--Indoor Climate Analyzer n.1213 (Figure 8) [23]. The instrument is equipped with a hygrometer, a dry bulb temperature sensor, a hot-wire anemometer, and a net radiometer for the measurement of the planar radiative temperature. A grid of sixteen points with equidistance of 60 cm was defined to mapping the indoor conditions, as illustrated in Figure 7a (Section 2.2). The sensors were positioned to measure the operative temperature at 60 cm height. For each point, the mean radiant temperature T\({}_{\text{mr}}\) was calculated by measuring the planar radiative temperature T\({}_{\text{pr-i}}\) in the six directions of the space (up, down, left, right, front, and back) and the projected surface factor A\({}_{\text{p-i}}\) for a person in the six direction of the space by using (Equation (12)) [23]:  
Figure 8: Brüel & Kjaer—Indoor Climate Analyzer n.1213. Figure 7: **(a)** Experimental test rig; **(b)** Sample C (a100 paint); **(c)** Sample B (a50 paint); and, **(d)** Sample A (a0 paint). \[T_{mr}=\left(\sum_{i=1-6}T_{pr-i}\cdot A_{pr-i}\right)\cdot\left(\sum_{i=1-6}A_{pr- i}\right)^{-1} \tag{12}\]  
where, for a sitting person the projected surface factor A\({}_{\text{P-i}}\) correspond to 0.3 (X-axis), 0.22 (Y-axis), and 0.18 (Z-axis) ([PERSON] 1970 [24]) (Figure 9).