## 2 Materials and Methods
### Analysis at the Material Level
#### 2.1.1 Application of the HFM Measurement Method  
For the experimental analysis, a TA instrument--FOX 600, single sample Heat Flux Meter (HFM) apparatus was used, the main characteristic of the device are resumed in Table 1.  
Only the lower plate surface was taped with a vinyl foil and then painted with a low emissivity paint or coated with aluminium foil since the painting of both the upper and the lower surfaces results costly from the point of view of the preparation of the experiments, as illustrated in Figure 3a. For this reason, the measurement was carried out in two steps. In the first step, the emissivity of the uncoated heat flux meter plate was determined according to Equation (8). In the second step, the measurements of the radiation specific heat flow were carried out with one coated surface according to Equation (9). To avoid the lateral heat losses, the measurement was performed placing a soft ring of polyester fibre between the two HFM plates and maintaining a central empty area of \(400\times 400\) mm\({}^{2}\) (Figure 3b), while the instrument measurement area is \(254\times 254\) mm\({}^{2}\) (the effective area where the sensors are placed)  
\[\varphi_{\text{rad}}=\frac{\sigma\big{(}\text{T}_{1}^{4}-\text{T}_{2}^{4}\big{)} }{\frac{1}{\varepsilon_{1}}+\frac{1}{\varepsilon_{2}}-1} \tag{8}\]  
Subsequently, the coating emissivity \(\varepsilon_{1}\) was determined by replacing \(\varepsilon_{2}\) in Equation (8) with the previously measured \(\varepsilon\) of the uncoated HFM plates. \[\varepsilon_{1}=\frac{\varphi_{\text{rad}}\cdot\varepsilon_{2}}{\varphi_{ \text{rad}}(\varepsilon_{2}-1)+\sigma\varepsilon_{2}\big{(}\text{T}_{1}^{4}- \text{T}_{2}^{4}\big{)}} \tag{9}\] \begin{table}
\begin{tabular}{c c} \hline \hline Temperature operation & \(-15\)\({}^{\circ}\)C to \(88\)\({}^{\circ}\)C \\ Temperature control & \(0.01\)\({}^{\circ}\)C \\ Maximum specimen size & \(610\times 610\) mm \\ Measurement area & \(254\times 254\) mm \\ Conductivity range & \(0.001\) to \(0.35\) W/m K \\ Absolute accuracy & \(\pm 1\%\) \\ Reproducibility & \(\pm 0.5\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of the HFM apparatus specifications. Figure 3: (a) Coating of the lower Heat Flux Meter (HFM) plate; (b) Polyester ring. As mentioned in Section 2.1, the described methodology can only be adopted if convection heat transfer contributes is suppressed. A preliminary measurement campaign was performed changing the air gap thickness (from \(\sim\)5 to \(\sim\)12.5 mm) and the temperature difference between the HFM plates (from 5 to 15 \({}^{\circ}\)C) while the average temperature between the upper and lower plate (T\({}_{\text{m}}\)) was kept constant at 25 \({}^{\circ}\)C, to verify this hypothesis and identify the measurement condition to be utilized for further analyses. Moreover, only downward heat fluxes were applied to reduce the buoyancy effects. Table 2 resumes the measured values of specific heat flow and emissivity, while the measured total specific heat flow and the radiation heat transfer contribution are plotted in Figure 4a,b, respectively. As it is possible to observe, the determined emissivity does not present any dependency by the temperature difference, i.e., with 5 mm of the air gap thickness the variation of emissivity is negligible (from 0.410 to 0.412). Nevertheless, a small but not insignificant influence on the measured emissivity is due to the variation of the thickness s. This variation is also visible in Figure 4b, which shows the higher measured value of radiation heat transfer \(\varphi_{\text{rad}}\) for 12.5 mm air gap (+5% if compared to 5 mm air gap), while from 5 to 10 mm the differences are lower than 2.5% and can be considered to be negligible. It is possible to assert that the increase of \(\varphi_{\text{rad}}\) can be attributed to the unsuppressed convection heat transfer, which became significant for thickness \(>\) 10 mm, since radiation heat transfer cannot be influenced by the air gap thickness.