## 5 Conclusions  
In this study, we presented experimental results and numerical simulations of a lightweight concrete wall with different insulation layers under transient- and steady-state temperature conditions. The purpose of this study was to compare thermal inertia behaviour of actual and numerical models of lightweight building walls. The numerical models were validated with experimental tests and numerical multicriteria optimizations using DOE. The following conclusions can be drawn from the results of this study:  
1. Experimental results - When the hot-box relative humidity is 70%, the measured thermal transmittance is 12% higher than at relative humidity of 30%. This demonstrates the importance of the moisture content in porous materials due to their hygroscopicity. In this sense, it is necessary to obtain the material thermal properties at specific humidity contents and account for the moisture transport inside multilayer walls. Moreover, the laboratory ambient conditions and the wall construction process can produce a non-uniform moisture content inside blocks and layers, affecting the thermal results. - Thermal transmittance in steady-state tests was higher than the empirical value calculated following the ISO 6946 standard [2], with differences ranging from 5 \begin{table}
\begin{tabular}{c c c} \hline \hline
**Case** & **\(\blacklozenge\)** (h) & **\(\boldsymbol{f}\) (c)** \\ \hline Hot-box test & 14.83 & 0.0241 \\ \hline Numerical FEM & 13.28 & 0.0072 \\ \hline Empirical [3] & 11.86 & 0.1605 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Dynamic thermal inertia parameters. Figure 13: Comparison of indoor wall face temperature experimental and numerical results. to 15%. Consequently, moisture content must be taken into account to obtain the thermal conductivity values of each layer of porous materials, in this case, Layer 3 (LWMA) and Layer 2 (LWBA25). Transient thermal tests in different thermal flux directions showed significant differences in terms of time lag (1.25 h difference) and decrement factor (23% difference). Thermal inertia values were, therefore, strongly affected by the multilayer wall composition. According to the thermal inertia tests, Layer 3 (LWMA) was appropriate to be exposed to the outdoor conditions. This material had the lowest density, thermal conductivity, thermal diffusivity and heat capacity in the multi-layer wall. With this configuration, a high time lag and low decrement factor were obtained, so the optimal indoor conditions were reached. Thus, materials with lower values in terms of density and thermal properties are recommended to be used at outdoor conditions. Empirical dynamic thermal inertia parameters exhibited lower time lag and higher decrement factor values than the experimental results. In the empirical formulation, the decrement factor is given by the periodic thermal transmittance divided by the static thermal transmittance of layers with homogeneous materials. In this work, lightweight concrete blocks with cavities were not homogeneous. Their dynamic thermal behavior was not calculated accurately by the empirical formulation. Consequently, the ISO-13786 standard [3] provides more restrictive designs than the experimental ones, and further research is required in this field. Numerical simulation  
A bidimensional FEM model, including conduction, convection and radiation, was used to simulate both steady- and transient-state thermal conditions in a multi-layer wall. The average temperature and heat flux of the block in the middle of the wall was used to obtain numerical results for the thermal transmittance, time lag, and decrement factor. Two DOE analyses were performed to determine the most influential parameters and obtain accurate material thermal properties similar to the experimental behavior.