PSI - Issue 55

Andréa R. Souza et al. / Procedia Structural Integrity 55 (2024) 143–150 Andrea R. Souza et al / Structural Integrity Procedia 00 (2019) 000–000

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3.2. Calculation algorithm The ST is calculated by a quartic equation for which an algorithm had to be developed to solve the equation 2. In this study, a root algorithm was created in the free software R. The algorithm is based on the equations described in Akbari et al. (1996) and Costanzo et al. (2014). The numerical values calculated by the R algorithm were validated by comparison with the values simulated by WufiPro®. Hence, to evaluate the effects of the three reflectance conditions (New, Aged, and Rest), the ST was calculated considering a fixed emissivity value (0.90), two thermal resistance values (R1 and R2), four Portuguese climates (Csa, Cfa, Cfb and Csa) and six envelope orientation expositions (Horizontal, Vertical/west-east-south-north).The advantage of the algorithm is that it allows the calculation of ST in a steady state with annual distribution, considering any climatic data or characterisation of the material in an accessible form. The result of the algorithm is a file with comma-separated values (.csv) that can be processed in any analysis software. The algorithm can be requested by contacting the authors. 3.3. Estimated surface temperature The surface temperature (ST) of External Thermal Insulation Composite Systems (ETICS) is significantly affected by both radiative properties and thermal resistance. Fig. 2 presents the boxplot distribution of average annual surface temperature, considering three different reflectance values (Table 3) and the two thermal resistance (R1 = 3.03 m 2 K/W and R2 = 7.14 m 2 K/W, item 2.2) Error! Reference source not found. .

Fig. 2. Influence of materials properties annual average values: (a) Reflectance; (b) Thermal resistance.

The ST for the restore conditions (green boxplot, Fig. 2a) and the higher R-value (light blue boxplot, Fig. 2b) have lower dispersion than the other conditions. Meanwhile, in all cases, the ST shows a symmetrical distribution with some outliers, which can be attributed to the influence of the environmental distribution over the year, in particular the fluctuations in air temperature. In Fig. 2a, the annual average surface temperature of the aged condition (red boxplot) is 5% higher than the retrofitted conditions (green boxplot), where the lower reflectance resulting in a TS of 20.41 ºC against 19.37 ºC for the restored reflectance. When compare the aged condition (red boxplot) to the original condition (yellow boxplot), the surface temperature increases by 1.5%. Fig. 2b highlights the impact of changes in thermal resistance, showing that as thermal resistance change from 3.303 m 2 K/W to 7.14 m 2 K/W, surface temperature increases by 3% from 19.68 ºC to 20.27 ºC. This observation suggests that, considering material properties, enhancing reflectance can be more effective in reducing surface temperature than improving the thermal resistance of the building envelope. Fig. 3 presents the boxplot distribution of average annual surface temperature, considering the environmental variables of climate zone and envelope orientation. Fig. 3a shows the effects of climate classification on surface temperature using the radiation and air temperature. The different climate zones exhibit varying surface temperature distribution. For instance, climate zone Cfa displays a higher average ST of 21.62 ºC and an average annual cumulative horizontal radiation of 1764 Wh/m 2 , whereas climate zone Csb presents a ST of 19.14 ºC and an average annual cumulative horizontal radiation of 1648 Wh/m 2 .