## 2 Methodology
### Wall Assemblies  
With the purpose of identifying the alterations caused by the application of the mortar layers, all mortared assemblies were compared against a plain solid brick wall, i.e., a 220-mm solid brick wall (Figure 2a), which is considered as the standard case (SC). The study includes three types of mortared walls--exterior surface (Figure 2b), interior surface (Figure 2c), and both surfaces (Figure 2d)--and three types of mortar--line, cement-line, and cement. All tested mortars are 15 mm thick, and the solid brick is 220 mm thick. In order to identify the differences between the steady-state and transient thermal transmittances, these factors were calculated for every studied wall in the four climates (Section 2.4.1). The thermal transmittance in steady-state conditions was calculated using standard thermal conductivities and the usual surface thermal resistances (i.e., 0.0588 m\({}^{2}\)K/W for the exterior ambience and 0.1250 m\({}^{2}\)K/W for the interior ambience [6]). The thermal transmittance in transient conditions was calculated using the thermal conductivity that takes into account the moisture content of the material and the wind-dependent surface thermal resistance [8]. WUFI was used to obtain the water contents for each layer, which allows the calculation of the thermal conductivity that considers the moisture. The surface thermal resistance was calculated using WUFI's wind-dependent equations, which depend on the wind direction and wall inclination. The simulated materials were characterized by the Fraunhofer--Institute for Building Physics (IBP), and their characteristics can be seen in Table 1. By taking a closer look at the table, it is possible to notice that the moisture permeability decreases from lime to cement mortar. This is visible since the water absorption coefficient decreases (liquid moisture) and the water vapour diffusion resistance factor increases (vapour moisture), which means a lower drying potential [36]. All of the mortars have a much lower A-value than the solid brick, which corroborates the values obtained in the simulations (Section 3.2.1). The higher the mortar's bulk density, the lower its thermal conductivity, which makes sense due to the fact that the thermal conductivity of the materials is related to the dimension and quantity of pores, which are inversely proportional to the bulk density [43]. Lastly, it is visible that lime has the lowest thermal conductivity among the tested mortar, and cement the highest, but this is not very significant due to this layer thickness, corresponding to a small contribution to the total thermal resistance of the tested assemblies, which varies in the range of 3.3-5.5%. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Building Properties**} & \multirow{2}{*}{**Solid Brick**} & \multicolumn{3}{c}{**Mortars**} \\ \cline{3-5}  & & **Line** & **Line-Cement** & **Cement** \\ \hline Bulk density, \(\rho\) (kg/m\({}^{3}\)) & 1900.0 & 1600.0 & 1900.0 & 2000.0 \\ Porosity, \(\epsilon\) (m\({}^{3}\)/m\({}^{3}\)) & 0.24 & 0.30 & 0.24 & 0.30 \\ Specific heat capacity, \(\
u_{\mathrm{p}}\) (\(\mathrm{D}/\)kg\(\cdot\)K) & 850.0 & 850.0 & 850.0 & 850.0 \\ Thermal conductivity, Dry, \(\chi\) (W/m\(\cdot\)K) & 0.60 & 0.70 & 0.80 & 1.20 \\ Water vapour diffusion resistance factor, \(\mu\) (\(\cdot\)) & 10.0 & 7.0 & 19.0 & 25.0 \\ Reference water content, \(\mathrm{w}_{\mathrm{80}}\) (kg/m\({}^{3}\)) & 18.0 & 30.0 & 45.0 & 35.0 \\ Free water saturation, \(\mathrm{w}_{\mathrm{80}}\) (kg/m\({}^{3}\)) & 190.0 & 250.0 & 210.0 & 280.0 \\ Moisture-related thermal conductivity supplement, b (\%/M\(\cdot\)%) & 15.0 & 8.0 & 8.0 & 10.0 \\ Water absorption coefficient, A (kg/m\({}^{2}\)s\({}^{0.5}\)) & 0.1100 & 0.0470 & 0.0170 & 0.0076 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Properties of the materials that constitute the simulated walls. Data taken from Fraunhofer-IBP database in WUFI [9].