## 2 Materials and Methods
### Measurement Setup
#### 2.1.2 Quantitative Internal IRT Method  
In contrast to the HFM average method, quantitative internal IRT assumes that the facade is crossed by one-dimensional horizontal specific heat flux (\(q\)) resulting from radiation (\(q_{r}\)) and convection (\(q_{c}\)) processes under a stationary regime. According to the method extensively reported in [PERSON] et al. [61], the instantaneous and average measured U-values [W/m\({}^{2}\cdot\)K] can be defined by Equations (5) and (6):  
\[U_{\text{{mes}}_{i}\, IRT}\bigg{[}\frac{W}{m^{2}\cdot K}\bigg{]}=\frac{\left( 0.825+\frac{0.387\cdot E_{b}\frac{1}{6}}{\left[1+\left(\frac{0.825}{P_{T}} \right)\frac{1}{6}\right]^{\frac{2}{P_{T}}}}\right)^{2}}{\frac{L}{\cdot}[T_{IN} -T_{WALL}]+\varepsilon_{WALL}\cdot\sigma{\left[T_{REF}{}^{4}-T_{WALL}{}^{4} \right]}}. \tag{5}\]\[U_{mes_{avg}\ IRT}\left[\frac{W}{m^{2}\cdot K}\right]=\frac{\sum_{i=1}^{n}(q_{ri}+q _{ci})}{\sum_{i=1}^{n}(T_{INi}-T_{OUTi})}=\frac{\sum_{i=1}^{n}U_{msi}}{n}. \tag{6}\]  
where \(T_{IN}\) and \(T_{OUT}\) denote the inner and outer ambient air temperatures in [K], respectively, \(T_{REF}\) is the reflected ambient temperature in [K], \(T_{WALL}\) represents the wall-surface temperature in [K], \(\varepsilon_{WALL}\) refers to the wall surface emissivity, \(\sigma\) is the Stefan-Boltzmann's constant with a value of \(5.67\times 10^{-8}\) [W/m\({}^{2}\cdot\)K\({}^{4}\)], \(\lambda_{air}\) is defined as the air thermal conductivity measured in [W/m\(\cdot\)K], \(L\) is the wall height seen from the internal side of the prefabricated wall in meters, and n is the total number of thermograms. As regards Rayleigh (\(Ra\)) and Prandtl (\(Pr\)) numbers, they are dimensionless parameters for a laminar flow assuming that the wall is a vertical plate. It should be pointed out that \(Pr\) is set at 0.73 for dry air under atmospheric pressure and \(T_{IN}\) = 20-25 \({}^{\circ}\)C, while the Rayleigh number is computed by Equation (7). \[R_{a}=G_{r}\cdot P_{r}=\frac{g\cdot\beta\cdot(T_{IN}-T_{WALL})\cdot L^{3}}{v^{ 2}}.P_{r} \tag{7}\]  
The parameters that define \(Ra\) are the following: the Grashof number (\(Gr\)), the gravitation (\(g\) = 9.8 m/s\({}^{2}\)), the volumetric temperature expansion coefficient (\(\beta\) = 1/\(T_{m}\) where \(T_{m}\) is the average value of \(T_{IN}\) and \(T_{WALL}\)), and the air viscosity (\(v\) 1.4\(\cdot\)10\({}^{-5}\) m\({}^{2}\)/s for \(T_{IN}\) = 0-15 \({}^{\circ}\)C or \(v\)=1.5\(\cdot\)10\({}^{-5}\) m\({}^{2}\)/s for \(T_{IN}\) = 15-25 \({}^{\circ}\)C). In terms of operating conditions, the recommendations defined by [PERSON] et al. [61] should be taken into account, to guarantee the implementation of the quantitative internal \(IRT\) method in the mock-up and the detached house. Based on this, the measurements were performed in the early morning (from 6 a.m. to 9 a.m.), to ensure the temperature difference through the wall and to avoid the incident solar radiation as an external stimulus. For a thermal gradient between 7 and 16 \({}^{\circ}\)C, [PERSON] et al. [63] demonstrated that the variance of the measured thermal transmittance could be only predicted by changes of \(T_{OUT}\). The parameters \(T_{IN}\), \(T_{REF}\), and \(T_{WALL}\) often remain constant during the monitoring process. Finally, the variability of the results was assessed by calculating the standard deviation (\(SD\)) and the coefficient of variation (\(CV\)) among the instantaneous measurements of each test for the wall of the experimental mock-up \(W1\) and the wall of the detached house \(W2\) (Equations (8) and (9)). [PERSON] et al. [75] stated that the impact of \(CV\) was greater on walls with low U-values. Subsequently, the 95% confidence intervals were also computed following Equation (10), to analyze whether there was a relevant difference among \(U_{mes\ avg}\) resulting from quantitative internal \(IRT\).