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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Fig. 1. Appearance of surfaces in the evaluated conditions: (a) Exposition configuration; (b) Retrofit process; (c) Final samples aspect.

Table 1. Façade system characterisation. Sample ID Composition

Condition

Original 0 year

Insulation slab: EPS (40 mm); Base coat: commercial cementitious mortar; Finishing coat: commercial organic coating composted of mineral filer, resins in aqueous dispersion black pigment (PBk11) and specific additives. Insulation slab: EPS (40 mm); Base coat: commercial cementitious mortar; Finishing coat: commercial organic coating composted of mineral filer, resins in aqueous dispersion black pigment (PBk11) and specific additives; Retrofit layer: commercial NIR black paint with pigment PBk29. Paint renovation Natural aged 3 years

New

Aged

Res

The effects of age and renovation method on the surface temperature were defined considering experimental values for reflectance. In this work, a modular spectrophotometer (FLAME-T and FLAME-NIR Ocean Optics – 200 nm to 1650 nm) with a 30 mm diameter integrating sphere and a Spectralon® reference disc were used to measure the total reflectance ( r ) of the samples in their original state, aged state and renovation. The reflectance was calculated based on the 100 selected ordinates by: = ! ! "" ∑ "($ # ) ! #$" !" (1) where r is the total reflectance of the sample and l is the wavelength weight in nanometres according to ASTM E903 (2020). The measurements were carried out in six different points for each sample. The average was used to calculate the surface temperature. 2.2. Numerical modelling In order to evaluate the thermal effect of reflectance variation for the three conditions studied, the distribution of surface temperature (ST) was calculated considering the steady state condition. For a dry surface under solar radiation, the steady-state surface temperature can be estimated as follows: & % '& # ( = (1 − ) − * ) * − ) * +, ,+ℎ( ) − - ) (2) where T s is the surface temperature (K), T i is the internal temperature (K), R is the thermal resistance of the façade (m 2 K/W), r is the solar reflectance, I is the solar flux incident on the surface (W/m 2 ), ε corresponds to the emittance, T sky is the sky temperature (K), s is the Stefan-Boltzmann constant (5.67x10 -8 W/m 2 K 4 ), h is the external convective heat transfer coefficient and T a is the air temperature (K). • R assumes two conditions, R1 = 3.03 m 2 K/W and R2 = 7.14 m 2 K/W, the maximum and minimum thermal transmittance values according to the Portuguese Regulation on Thermal Properties of the Building Envelope (RCCTE, 2016). • T i is defined as 25 ºC by the RCCTE (2016). • r is the average value calculated from the experimental measurements (New, Aged and Res). For the purposes of this calculation, the following definitions were adopted: • T s should be calculated considering an algorithm to solve a quartic equation.