## 2 Materials and Methods  
### Theoretical Background  
A one-dimensional problem is considered for the analysis of transient heat flux on the interior surface of a building wall (see Figure 1), where \(q_{\text{IN}}\) represents the rate of heat transfer per unit area, i.e., the heat flux, from the interior to the surface element, \(q_{\text{OUT}}\) represents the heat flux from the surface element to the wall, and \(x\) is the thickness of wall element. Assuming that thickness of the element is infinitesimally small, i.e., \(x\to 0\), then thermal storage in the element can be practically neglected implying that  
\[q_{\text{IN}}\approx q_{\text{OUT}}, \tag{1}\]  
at any time. In Equation (1), \(q_{\text{IN}}\) (W\(\cdot\)m\({}^{-2}\)) is the heat flux from the interior to the wall surface, \(q_{\text{OUT}}\) (W\(\cdot\)m\({}^{-2}\)) is the heat flux from the wall surface to the wall. For this case, \(q_{\text{IN}}\) can be expressed using the [PERSON]'s law of cooling as \[q_{\text{IN}}=\alpha\ (T_{\text{s}}-T_{\text{i}}), \tag{2}\]  
where \(\alpha\ (\text{W}\cdot\text{m}^{-2}\cdot\text{K}^{-1})\) is the heat transfer coefficient, \(T_{\text{i}}\) (\({}^{\circ}\)C) is the ambient wall (indoor) temperature, and \(T_{\text{s}}\) (\({}^{\circ}\)C) is the interior surface temperature of the wall. The heat flux from the surface element to the wall, \(q_{\text{OUT}}\), can be expressed using [PERSON]'s equation as  
\[q_{\text{OUT}}=\lambda\ \Delta T/\Delta x, \tag{3}\]  
where \(\lambda\ (\text{W}\ \text{m}^{-1}\ \text{K}^{-1})\) is the thermal conductivity, \(\Delta T\) (\({}^{\circ}\)C) is the temperature difference of the element surfaces in the direction of the heat flow, \(\Delta x\) (m) is the thickness of the element in the main direction of the heat flux. When a validated computational model is integrated then the heat transport in the surface element can be included to define a new computational-experimental domain allowing for a complex analysis, which might help to extend the current methods or design new principles for heat flux measurement and building performance simulations. For the computational modeling of heat transfer, which can provide thermal performance data of the wall to form a complex dataset for the performance check procedure, the modified [PERSON]'s model of heat and moisture transport was used [29; 30]. This model was developed for applications in building engineering and validated several times in the past [31]. A detailed information on the modifications of the original [PERSON]'s model [32] was given in [30]. The following equations were used to govern the heat and moisture transport:  
\[\frac{dH}{dT}\frac{\partial T}{\partial t}=\text{div}(\lambda\text{grad}T)+L_{ \text{s}}\text{div}\big{(}\delta_{p}\text{grad}p_{v}\big{)}, \tag{4}\]  
\[\bigg{[}\rho_{\text{w}}\frac{\text{d}w}{\text{d}p_{\text{v}}}+(\psi-w)\frac{M }{RT}\bigg{]}\frac{\partial p_{\text{v}}}{\partial t}=\text{div}\big{[}D_{ \text{g}}\text{grad}p_{\text{v}}\big{]}, \tag{5}\]  
where \(H\) (\(\text{J}\cdot\text{m}^{-3}\)) is the enthalpy density, \(T\) (K) is the absolute temperature, \(t\) (s) is the time, \(D_{\text{g}}\) (s) is the global moisture transport function, \(L_{\text{v}}\) (\(\text{J}\cdot\text{kg}^{-1}\)) is the latent heat of evaporation of water, \(\delta_{\text{p}}\) (s) is the water vapor diffusion permeability, \(M\) (\(\text{kg}\cdot\text{mol}^{-1}\)) is the molar mass of  
Figure 1: Scheme of heat transfer in the surface element of building wall. water vapor, \(p_{\
u}\) (Pa) is the partial pressure of water vapor in the porous space, \(w\) (m\({}^{3}\cdot\)m\({}^{-3}\)) is the moisture content by volume, \(\rho_{w}\) (kg\(\cdot\)m\({}^{-3}\)) is the density of water, \(\psi\) (-) is the total open porosity, and \(R\) (J\(\cdot\)K\({}^{-1}\cdot\)mol\({}^{-1}\)) is the universal gas constant. More details and insights into model formulation and parameter description can be found in [30].