The addition of insulating layers on vertical walls of buildings is a common practice for providing 10 a higher thermal insulation of the envelope . Workmanship defects, however , might influence the 11 effectiveness of such insulation strategy. Damaged materials , incorrect installation , use of aged or weathered 12 materials might alter the capability of reducing heat transfer through the envelope , whether vertical or 13 sloped. In this work, drawbacks caused by the wrong installation of insulating material and by damaged 14 material are assessed. A specimen wall was investigated by experimental and numerical approaches, the 15 latter carried out by using COMSOL Multiphysics ®. Results are compared and discussed . 16 17 Keyword : Numerical simulation ; Heat transfer; Insulating panel; EPS; COMSOL Multiphysics ®; Guarded 18 Hot Box 19 20 Declarations of interest : none 21 22 1. Introduction 23 High energy consumptions in the building sector (about 32% of total global final energy use ), addressed for a 24 share of 34% to space heating [ 1], are pushing research activities in finding the best solution to avoid , shift 25 and reduce heat waves or losses [2-6]. 26 2 A key role in this scenario is played by the renovation and refurbishment of the built environment [ 7, 8]. 27 Such interventions represent the main opportunity of energy efficiency for urban context that , due to energy 28 policies or to reasons of force majeure, face the challenge of building renovation. The latter is the case of the 29 city of L’Aquila , in central Italy , that in 2009 was hit by a violent earthquake; most of buildings (both private 30 and public) has undergone (or is still undergoing) reconstruction or renovation [ 9, 10] . The natural disaster , 31 therefore, has given the opportunity to intervene on several buildings and to improve the energy efficiency. 32 In this sense, the most rapid and common adopted strategy is the addition of insulating layer (the so called 33 ETICS that sta nds for External Thermal Insulation Composite System). The effectiveness of this solution 34 depends not only on the quality of employed materials , but also on how workm en laid the materials. Each 35 error, damage or omission that occurs during the construction phase might increase the energy performance 36 gap, that is , the difference between predicted and measured energy performance. 37 Several works deal with defects taxonomy , aiming at providing a definition of “defects” and a possible 38 classification , the phase of occurrence (project , construction or management phase) , their major causes and 39 the influences on building thermal performance [ 11-14]. Several kinds of defects are accounted [ 13], like 40 detachments , incorrect installation , discontinuities , gaps and thermal bridging. Incorrect installation is one of 41 the most frequent workmanship defects [14]. Obviously, defects can worsen the capabilities and features of 42 the assets on which occur , and quality defects (like those mentioned before) can impact buildings thermal 43 performance , causing local increase of thermal losses, and leading to higher energy consumption 44 An aid for a better evaluation of building f eatures is provided by software and tools [15-17]. The possibility 45 of investigating building elements by using simulation and computer tools is widening the study of new 46 materials and solutions for the realization or renovation of the built environment. In this sense, calculation 47 codes can reproduce or simulate buildi ng elements energy performances, thus they allow to infer the thermal 48 response of elements under different conditions. 49 Several simulation tools are available, both open source and commercial . Amongst these , COMSOL 50 Multiphysics® is spreading. It is a software platform based on advanced numerical methods that allows the 51 modeling and simulation of physical problems [18]. 52 As shown in recent literature, COMSOL Multiphysics® can be employed for studying several and different 53 building related problems [ 19-25]; numerical result can be validated by comparison with various control 54 3 systems such as thermo -flowmeters, thermocouples (as in the case under analysis) , and thermographic 55 techniques [ 26]. 56 However, none of the works available in literature, at the best of authors’ knowledge, deals with the 57 employment of COMSOL Multiphysics® for the modeling of the effects of workmanship defects during the 58 installation of materials in buildings , althoug h the issue is quite important . 59 This paper aims to understand how relevant workmanship defects can be on wall thermal performance . 60 61 2. Materials and methods 62 In this paper , the effects on the temperature field caused by defects in insulating panels were assessed both 63 via COMSOL Multiphysics ® and via experimental measuring campaigns. 64 Two expanded polystyrene (EPS) panels were mounted on a specimen wall: a defective and a flawless one. 65 Tests have been carried out in a controlled environment ( i.e. a hot box). Heat flow and temperatures were 66 measured on defects and on the flawless panel. A numerical model was then realized by COMSOL 67 Multiphysics®. Numerical results were, then, validated by comparison with superficial temperatures 68 measured, becoming a helpful tool to quantify possible heat losses on buildings. 69 The paper is structured as follows: section 2 describes the employed methods (the experimental 70 measurements set up, its numerical model, together with the physics of the numerical simulation and the 71 solver mesh). Section 3 reports experimental and numerical data. Section 4, devoted to conclusions, 72 completes the paper. 73 In this section, the set up employed for experimental campaign is described , together with the numerical 74 model , its governing equa tions and mesh spacing used for comparison. The assessment procedure of defects 75 effects that relies on the coupling between laboratory data and numerical modeling is shown in Figure 1. 76 77 4 Figure 1. Adopted procedure . 78 2.1 Test setup 79 This paper presents the numerical model , built with COMSOL Multiphysics® , of heat transfer through 80 defective and flawless insulation employed as ETICS. The model replicates the realized experimental setup. 81 For the purpose , two EPS panels , whose sizes are 48 cm x 198 cm x 8 cm (LxHxW) , were employed: a 82 flawless panel (FP of F igure 2), and a defective one (DP of F igure 2). To replicate a discontinuity of 83 insulation layer , a small piece of the adjacent side of the pane ls was left without adhesive. 84 For choosing the defect dimensions , the following considerations were taken into account : 85 • A defect should be large enough to allow the placing of the flux plate and of the temperature probe in 86 its proximity ; 87 • A defect should be as far as possible from discontinuities since they can cause side effects; 88 • Defects should not interfere with each other. 89 Therefore , following a symmetric criterion , the experimental setup shown in Figure 2 was realized. P1 90 indicates the bonding defect; P2 is a void in the panels, that is , a piece of panel partially hollowed, 91 replicating what occurs for sheaths and wires passage. Sizes of defect P2 ar e 5 cm x 30 cm x 3 cm 92 (LxHxW) , and its layout is show in section A -A’. Point P3 represents a sound area on the flawless panel. 93 94 95 5 a) b) Figure 2. Setup and defects details: a) picture; b) drawing with sizes. 96 The defects length was chosen starting from the assumption proposed in a recent work [ 12] dealing with 97 insulation defect. In [12], monolayer specimen s, whose dimensions were 30 cm x 30 cm, were tested by 98 using a hot plate device, and five defect typologies were investigated , assessing their thermal conductance 99 also according to various aspect ratio s. The set up was conce ived to reduce edge effects on such small 100 samples. 101 In our tests , the experimental setup is based on samples of insulating layers , applied on a wall large enough 102 to reproduce real condition of heat losses that might occur on a building. 103 To guarantee accurate results, a controlled environment was chosen. Therefore, tests were performed in a 104 guarded hot box (GHB) . 105 Panels were glued on the specimen wall of a hot box: the final assembly is shown in Figure 3, together with 106 materials thickness (d) [m] and thermal conductivity ( k) [W/(m ∙K)]. 107 108 6 Figure 3. Wall assembly , showing materials thickness (d) and thermal conductivity ( k). 109 As operating principle , a hot box consists of two chambers whose temperatures can be set by acting on a 110 cooling and a heating system (for the cold and hot side, respectively) , while the wall under investigation is 111 interposed between the chambers. This system allows setting , on the boundaries of the specimen wall , the 112 desired temperatures. 113 In this test, a guarded hot box was employed (Figure 4). It is equipped with a cold chamber (CC) and a hot 114 chamber; t he latter is composed by a small er chamber , called metering box (MB) [27, 28], that allows to 115 better confine heat and to prevent two- or three - dimensional heat losses in the wall cent er. Thus , there is a 116 guard box (GB) that surrounds the metering box. 117 118 119 120 121 122 123 7 a) b) CC: cold chamber (sizes: 300 cm x 300 cm) – galvanized steel sheets (0.1 cm) separated by a layer of expanded polyurethane (10 cm) GB: guard box (sizes: 300 cm x 300 cm) – galvanized steel sheets (0.1 cm) separated by a layer of expanded polyurethane (10 cm) MB: metering box (sizes: 180 cm x 180 cm) – galvanized steel sheets (0.1 cm) separated by a layer of expanded polyurethane (10 cm) 1: grid fans 2: electric resistances 3: fans 4: metering box support 5: metering box railing Figure 4. Drawing of the hot box, with sizes and equipment: a) cold chamber; b) hot chamber. 124 Measurements were carried by clamping the hot chamber to the wall , and by leaving the other side facing the 125 facility that hosts the hot box that, in this way , acts as a cold chamber. The laboratory has an air handling 126 unit to control its temperature. 127 Regarding the test, three heat flow meters were installed, one for each defect plus one for the flawless panel. 128 Therefore, a flux plate and two temperature probes were mounted for each point of Figure 2. 129 Flux plates were placed after applying a thin layer of thermal compound , to enhance heat. 130 Pairs of temperature probes (Pt100 type) were mounted for each point , on the hot and cold wall face , one in 131 correspondence to the other. Moreover, probes on the hot side were placed in proximity of the flux plates. A 132 8 data set consisting of heat flow rate, wall temperature on the hot a nd cold side , air temperature of the hot 133 chamber and of the facility was recorded every 10 min and stored by a DeltaT DL2 logger. The measurement 134 campaign lasted 72 hours. This duration was chosen following on one hand the requirement of ISO 9869 135 [29], that suggests a lasting that is an integer multiple of 24 hours, and on the other hand indication from 136 standard ISO 8990 [ 30], that does not provide a minimum lasting for measurement via hot boxes, but gives 137 an example criterion for the definition of the steady -state condition. 138 Following the remark s given in [29], and considering that measurement campaigns are taken under 139 controlled conditions (Hot Box in a laboratory), errors in temperature measurements are assumed within 5% 140 and errors in conductance meas urements are assumed about 15%. 141 142 143 144 2.2 Description of the n umerical model 145 The numerical model describes a wall , as shown in Figure 3. The back of the wall (indicated by a red 146 thermometer in Figure 3) was placed in contact with the hot -side surface of the hot box. In the numerical 147 model , this was represented by a volume, consisting of an air fluid and reproducing the geometry of the 148 chamber. This choice was needed to avoid the imposition of a surface temperature on the wall in a direct 149 way. By directly assi gning a surface temperature boundary condition, the model would be numerically 150 forced. To obtain a behavior like the real case, a virtual box (consisting of air) with a thickness of 500 mm 151 was dimensioned. 152 The temperature boundary condition was imposed on the contour surface of the air box placed opposite to 153 the interface with the analyzed wall. About the contact conditions between the virtual air box and the 154 supporting structure , continuity conditions for t he temperature field have been assigned. For the remaining 155 four contour surfaces representing the thickness of the air box , the condition -n·(-k∇T) was assigned to avoid 156 the constraint of the temperature in the area proximal to the wall . 157 In contact with the concrete structure, the polystyrene panels have been reported. The interface between the 158 latter and the structural part has been modeled using a layer of glue. 159 9 A splitting area has been represented; it was conceived as an imperfection of contact with r espect to the 160 thickness of the polystyrene panels , assuming the lack of adhesive as an inclusion of air. The latter was 161 realized through a cavity having a rectangular section. Furthermore, in the right -hand panel an additional 162 cavity has been created (as i ndicated in Figure 2, by P2) which also defines a lack of material. The cold 163 chamber was represented similarly to the hot chamber. The relative boundary conditions were imposed with 164 the same procedure described for the hot chamber. Figure 5 shows the geometry of the model , while Figure 6 165 represents the elements in relation to the materials being analyzed. 166 167 168 Figure 5. Complete model geometry . 169 170 171 172 173 174 175 176 10 a) b) c) d) e) f) Figure 6. Elements of the model according to the analyzed materials: a) hot chamber (air) , b) structural wall, 177 c) polystyrene , d) glue , e) defects (air inclusions) , and f) cold chamber. 178 179 180 181 11 2.3 Physics of the numerical simulation 182 The model has a set of governing equations consisting of three mathematical relations: the heat transfer in 183 solid [31] which deals with modeling the elements considered to be free of porosity in the model , the heat 184 transfer in porous media [ 32] and, finally , the heat transfer in fluids [33 ] which develops the temperature 185 field in the air fluid . 186 The first relation is represented by the following equation: 187 𝜌𝐶𝑃𝜕𝜕 𝜕𝜕+𝜌𝐶𝑃𝐮∙∇T=∇∙�𝑘�∇T� −𝐪�+𝑄 (1) in which q is the heat flux vector field , i.e., the Fourier’s law of heat conduction. Eq. 1 characterizes the 188 behavior of the components shown in F igure 6b. The mathematical equations related to porous elements are: 189 (𝜌𝐶𝑃)eff𝜕𝜕 𝜕𝜕+𝜌𝐶𝑃𝐮∙∇T=∇∙�𝑘eff�����∇T�+𝑄+𝑄vd+𝑄P (2) �𝜌𝐶𝑝�eff=𝜃P𝜌P𝐶𝑃,𝑃+(1−𝜃P)𝜌𝐶𝑝 (3) 𝑘eff=𝜃P𝑘P+(1−𝜃P)𝑘 (4) 190 where , at the porosity of the polystyrene has been linked a ѲP equal to 0.2 [34, 35]. For the heat transfer in 191 fluids , Eq.2 was used with the density expressed as indicated in Eq. 5 : 192 𝜌=𝑝𝐴 𝑅𝑆𝜕 (5) The variables in Eq. 1 - 5 are described in Table 1. 193 194 195 196 197 198 199 200 12 Table 1. List of variables. 201 C Thermal conductance [W/(m2·K)] q Density of heat flow rate or heat flux [W/m2] ρ Density [kg/m3] CP Specific heat at constant pressure [J/(kg·K)] 𝑘� Thermal conductivity tensor [W/(m·K)] T Temperature [K] Q Heat source [J] (ρC p)eff Effective volumetric heat capacity at constant pressure 𝑘eff����� Effective thermal conductivity tensor [W/(m·K)] CP, P Specific heat at constant pressure for porous materials [J/(kg·K)] ѲP Volume fraction porous materials ρP Density porous materials [kg/m3] kP Thermal conductivity composite materials [W/(m·K)] QVD Heat sources viscous dissipation [W/m3] QP Heat sources pressure work [W/m3] pa Absolute pressure [Pa] RS Specific gas constant [J/(kg∙K)] 202 The terms present in Eq. 5 , i.e., pA [Pa] and R S, are calculated for the air according to the instantaneous 203 temperature conditions. 204 205 2.4 Solver mesh and materials of the numerical simulation 206 The 3D numerical model required a tetrahedral mesh throughout the structure. After the conve rgence 207 analysis of the mesh , it was possible to bring the minimum quality limit to a very low value , i.e., 8.89e-7. The 208 number of elements of the domain is equal to 444539. To obtain this result , a scaling was performed along 209 the X, Y and Z directions of the mesh , according to the absolute reference of the model . Table 2 shows the 210 setting indications of the mesh . 211 13 Table 2. Mesh of the numerical model. 212 Parts of model X - direction scale Y - direction scale Z – direction scale Domain element s Plaster 0.05 1 0.05 28506 Glue (panel -wall) 0.5 1 0.5 9897 Glue (panel -panel) 0.5 1 0.5 10973 Defect in panel 1 1 1 88 Panel 0.5 1 0.5 73308 Chamber 1 1 1 321767 213 The convergence analysis was carried out to evaluate the performance of the mesh in terms of optimization 214 of the discretization of D.o.F. (Degrees of Freedom) inherent to the geometry analyzed. A mesh 215 approximates to the best a structure when the D.o.F. (calculated through the nodes) discretize smaller and 216 smaller volumes of the solid of interest. On the contrary, the increase in the number of nodes involves a 217 greater number of corresponding equations and, therefore, a greater computational cost. For this reason, 218 through specific optimization procedures of t he number of nodal elements constituting the mesh, it is 219 necessary evaluate the appropriate dimension of the element approximating the volume under analysis. It has 220 been found from the geometrical characteristics of the model analyzed that for a dimension of the mesh 221 elements equal to 70 [mm], it was possible to observe the lowerest D.o.F. and, therefore, a lower 222 computational cost. Fig ure 7 shows the trend of the D.o.F. evaluated according to the maximum size 223 assumed by the mesh element approximating the r eal geometry. The x -axis shows the maximum sizes of the 224 element for a range from 30 [mm] to 140 [mm]. The choice of this interval took place after the verification of 225 stability of the calculated solutions satisfying the initial conditions. This, per each dimension of the interval 226 previously explained. 227 14 Figure 7. Convergence analysis. 228 In Figure 8, the mesh of the model is shown. 229 230 Figure 8. Mesh of the model: a) hot and cold chamber ; b) wall with panels and defects . 231 232 The model was analyzed with a fully coupled time dependent solver for the physics , while a multigrid 233 approach was implemented for the geometrical model . The latter was solved with a Direct approach. 234 The selected materials in terms of densities assumed are shown in Tab le 3. 235 236 15 Table 3. The selected materials and their densities. 237 Materials Density �𝑘𝑘 𝑚3� Air [ 36] 1.204 Polystyrene [37] 18 Glue [38] 1700 Concrete [39] 2240 Plaster [40] 802.01 238 All the other parameters relating to the thermo -physical characteristics are shown in Fig ure 3 along with the 239 thicknesses. 240 241 242 243 3 Results 244 3.1 Experimental data 245 Data acquired by probes were wall temperature on the hot side Th,w [°C], on the cold side Tc,w [°C], and the 246 density of heat flow rate q [W/m2]. Those data refer to the studied points (namely, P1, P2 and P3), whose 247 location and characteristics are shown in Figure 2. Air temperature in the hot chamber and in the facility that 248 hosted the setup were also recorded , and constituted the input data for the numerical model. Temperature 249 profiles and density of heat flow rate over a 72 -h period are shown in Figure 9a and 9b respectively . 250 251 16 a) b) Figure 9. Profiles of instantaneous values of : a) temperature s; b) heat flux es. Wall temperatures on the hot side have oscillation with maximum amplitude of 0.5 °C , while air temperature 252 in the hot chamber , that is , the driving force of the heat exchange phenomenon, has an oscillating tren d with 253 maximum amplitude of 0.6 °C. 254 Air on the cold side replicates the outdoor oscillation due to the alternating day/night cycle s, and its 255 maximum amplitude is 3.4 °C . Wall temperatures on the cold side have the same oscillating trend , with 256 amplitudes comprise between 4.1 °C (for P2 ) and 4.5 °C (for P1 ). 257 Heat fluxes recorded for the three points are shown in Figure 9b. Trends are similar but appear shift ed each 258 other. Heat fluxes on P1 are higher than those on P2 that are higher than those on P3. It is interesting to 259 17 analyze these results in terms of percentage difference (Figure 10) from P3 that is on a “sound area”. 260 Percentage difference between heat flux on P1 and P3 is quite regular , having a mean value of 20.5%; 261 percentage difference between heat flux on P2 and P3 is more stable, and has a mean value of 16.1%. 262 263 Figure 10. Heat fluxes percentage differences (compared to values on P3). 264 By employing HFMs , it is possible to evaluate the thermal conductance on measured points for each ith of the 265 n measurements, as the ratio between the heat flux and the difference between superficial temperatures on 266 the hot and cold side , Eq. (6): 267 𝐶𝑖=𝑞𝑖 𝜕ℎ,𝑤,𝑖−𝜕𝑐,𝑤,𝑖 (6) 268 By applying the average method [29], as per Eq. ( 7), it is possible to assess the averaged trend of 269 conductances , distinguished in the following by subscripts that refer to the measured points. 270 𝐶=∑𝑞𝑖𝑛 𝑖=1 ∑ (𝑛 𝑖=1𝜕ℎ,𝑤,𝑖−𝜕𝑐,𝑤,𝑖) (7) 271 Figure 11 and Figure 12 show , respectively , percentage and absolute difference of averaged thermal 272 conductance s, compared to values on P3 (sound area). . Absolute differences have dumped oscillating trends , 273 with maxi mum values marked in the Figure . 274 18 Figure 11. Conductances percentage differences (compared to values on P3). 275 Figure 12. Conductances absolute differences (compared to values on P3). 276 Given the results shown in Figure 11 and Figure 12, the defect type that most affects the insulating capability 277 is the void (P2). Nevertheless, defect P1 is more likely to occur on real wall s. 278 279 280 281 282 19 3.2 Numerical data 283 The numerical model shows for the surfaces in contact with the hot chamber and the cold chamber , the 284 virtual probes useful for the control of the wall surface temperatures. In Figure 13, the probes as they appear 285 in COMSOL Multiphysics® are added . 286 287 a) 20 b) c) 288 Figure 13. Positions of the virtual probes on the wall surface of the cold chamber: a) center of the 289 polystyrene panel (P3), b) center of the defect of gluing ( air P1), c) center of the “ batten ” made of air ( P2). 290 291 In Figure 13, only the virtual probes of the cold chamber are reported because concerning the side of the hot 292 chamber , the probes are only translated with respect to the Y axis up to the contact with the foremost plaster 293 surface. 294 21 295 Figure 14. Trend of the surface temperature field for the elements shown in the figure. 296 297 In Figure 14, the temperature trends of the virtual probes are shown. 298 The curve with the highest temperature values in F igure 14 represents the trend of the temperature field of 299 the hot chamber. The input values of the numerical model are exactly coincident with the measured case. 300 This because the temperature profile used in the hot box was set by the authors. For the temperature profile 301 of the cold chamber , the trend highlighted by the curve with the smaller values is obtained. It is coinc ident 302 with the real case, too. 303 The remaining curves identify the temperature profile trends coming from the virtual probes , for the surfaces 304 near to both the hot and cold chamber . 305 The initial values reported by the virtual probes were retrieved thanks to a first calculation step , i.e. by 306 evaluating the equilibrium temperature of the system in stationary conditions at the initial instant. 307 The values obtained per probe from this analysis were used as initial conditions in the final model. By a 308 comparison of the trends of the curves measured in F igure 9a and those simulated in Figure 14, it is possible 309 to see an agreement in the behavior both in terms of oscillation and values . Also, the alternation in the 310 position of the curves indicating P1 , P2, and P3 is met. On one hand, the temperature profile s of the probes 311 related to the side of the hot chamber are in perfect agreement with the measured case. 312 On the other hand, the temperature profiles of the probes installed on the surface in contact with the cold 313 chamber are oscillating with the same period of temperature set for the cold environment. Where the cold 314 22 chamber has peak s of temperature (at ≈ 600, 2000 and 3400 min), the probe trends inters ect the room 315 temperature curve. 316 In Figure 9a, the intersection between the room temperature and the curves indicating the probe temperatures 317 does not occur. If the model is forced by the boundary conditions , it would not have been possible to verify a 318 crossing between the probe trends and the room temperature curve representing the cold chamber. 319 Therefore , this proves that the model is free to evolve despite being placed between two environments at 320 assigned temperature. 321 In Figure 15, the trend of the heat flux evaluated in correspondence with P1 , P2 and P3 is shown. 322 323 Figure 15. Heat flux trend. 324 325 The trend shown in F igure 15 is the simulated heat flux. Comparing the trends with respect to the curve of 326 Figure 9b, the values of the heat flux are of the same order of magnitude. For the simulated case , the 327 maximum peak is ≈ 10.2 [W/m2] with respect to the peak of the measured value of ≈ 11 [W/m2]. Unless this 328 difference , the curves for P1 , P2 and P3 are in the same sequence but with a slight shift of the oscillation 329 with respect to time. 330 The starting from zero for the simulated case is typical of the numerical model. At the initial instant of the 331 calculation , the temperature parameters are assigned as boundary conditions; they assume a non- zero value. 332 No condition was set for the thermal flux; therefore , the system assigned a value equal to zero. Only after the 333 calculation , in the c entral points of the mesh is linked a value of the heat flux. 334 23 From the analysis carried out by COMSOL Multiphysics® , it is possible to see that the model predicts the 335 trends with good agreement with respect to the real case. 336 337 3.3 Results comparison 338 Results from measurements and modeling can differ due to several factors: instrumentation calibration, data 339 acquisition error, boundary condition variation, biased materials characteristics, governing equation, etc. 340 However, to compare a nd discuss results, in terms of thermal conductance, of simulations (S) and of 341 experimental survey (M), the root mean square error (RMSE) , the mean absolute error (MAE) and the mean 342 bias error (MBE) have been employed [41]. Such values have been calculated according to Equat ions ( 8-10), 343 where n is the number of data , and are shown in Table 4. 344 345 𝑅𝑅𝑅𝑅 =�∑(𝑅−𝑅)2 𝑛 1 𝑛 (8) 346 𝑅𝑀𝑅 = ∑ |𝑅−𝑅|𝑛 1 𝑛 (9) 347 𝑅𝑀𝑅= ∑ 𝑅−𝑅𝑛 1 𝑛 (10) 348 Table 4. RMSE, MAE and MBE between simulated and experimental values . 349 C_P1 C_P2 C_P3 RMSE [W/(m2K)] 0.17 0.17 0.06 MAE [W/(m2K)] 0.16 0.15 0.05 MBE [W/(m2K)] -0.16 -0.15 0.02 350 Given the results analysis shown in Table 4, it is possible to infer that there is a good agreement between 351 experimental and numerical results on the flawless point P3, since MBE and MAE are lower than or equal to 352 0.05 W/(m2K). There is an acceptable agreement between results of P2 and P1 (panels defects) , too; in these 353 cases, differences are of the order of 15 -16%. 354 355 24 Conclusions 356 The frequent recourse to the employment of ETICS for the reduction of building thermal losses implies the 357 need for the evaluation of workmanship defects during its installation. A few works in literature deal with 358 this issue , and none has been carried out of specimen wall. This paper aims at filling this gap , and it deals 359 with the evaluation of the effects of defects on insulating capabilities of EPS panels. 360 Particularly , workmanship defects have been reproduced on twin panels glued on a specimen wall belonging 361 to a guarded hot box (GHB). The use of a GHB allowed the temperature setting on one side of the wall (hot 362 side) , while the other side was kept in contact with the air of the facility that hosts the GHB , equipped with 363 an air handling unit. The set up aims at mimicking what might occur on real wal l refurbished with the 364 addition of an external insulating panel in case of panel corruption. Two kinds of defects were reproduced: 365 (i) the lack of continuity of the insulation layer , caused for instance by the absence of adhesive/glue between 366 two adjacent panels (namely , defect P1) ; (ii) a partial void on panel , caused for instance by sheaths and wires 367 passage (namely , defect P2) . 368 Sizes and location of defects were properly chosen , according to previous literature experiences. 369 Three reference points (one fo r each defect plus one on a “sound area” –point P3) were selected for the 370 measuring campaign , based on the heat flow meter method. Therefore , three heat flux plates and six surface 371 temperature probes were installed on the reference points, to evaluate the effects of defects on the thermal 372 conductance of the wall. 373 Moreover , two probes monitored and logged the air temperature on the hot and cold side of the wall. These 374 data constituted the input (as boundary conditions) of the numerical model de veloped by the authors using 375 COMSOL Multiphysics ®. The model faithfully represents the wall , the panels , and the two defects and, 376 moreover , has virtual probes for the temperature and flux evaluation in correspondence to the reference 377 points. Model’s governing equations also consider the porosity of the insulating panels. 378 Experimental results were compared with the numerical responses gathered by the finite element analysis. 379 The following outcomes can be pointed out from the results : 380 • Wall temperatures on the hot side have the same oscillating trend of the air temperature , the latter 381 being conditioned by the heating system of the GHB. Temperature of P1 is higher (0.88 °C on 382 25 average) of that of P3 , that differ s by 0.62 °C (on average) from that of P2. This implies that the air 383 cavity of P2 lowers the wall temperature on the cold side; 384 • Wall temperatures on the cold side have the same oscillating trend of the air temperature, the latter 385 being conditioned by the ai r handling unit of the laboratory. Temperature s of P1 , P2 and P3 on the 386 cold side are quite similar, as shown in F igure 9a). This implies that the effects of defects on 387 temperatures on the cold side are smoothened. Moreover , wall temperatures on the cold s ide seem to 388 differ more when the three peaks are reached; 389 • By comparing instantaneous values of heat flux measured on the flawless point and on the two 390 defects , it can be pointed out that flux on P1 and on P2 differ on average by 20.5% and 16.1% 391 respectivel y from flux on P3. That is , the heat flux that crosses the wall with a bonding defect i s one - 392 fifth bigger than that crossing the sound area; 393 • The defect type that much worsens the insulating capability is the void (P2) . Nevertheless, defect P1 394 is more likely to occur on real wall s; 395 • The finite element model proposed fully represents the heat exchange phenomena occurred during 396 the measuring campaign. This is due on one hand on the proper choice of the governing equations , 397 that include the evaluation of ma terials porosity , on the other hand on the accurate modeling of 398 materials properties , to which the model seemed quite sensitive; 399 • The initial values reported by the virtual probes were retrieved thanks to a first calculation step. This 400 was needed to evaluat e the equilibrium temperature of the system in stationary conditions at the 401 initial instant. The values obtained by using probes from this analysis were used as initial conditions 402 in the final model; 403 • Comparing measured and modeled temperatures trends , it is possible to see an agreement in the 404 behavior both in terms of oscillation and values. Also, the alternation in the position of the curves 405 indicating P1, P2 , and P3 is met; 406 • The numerical model , with its proper equations , is free to evolve despite bein g placed between two 407 environments (hot and cold chamber) at assigned temperature . 408 409 410 26 Acknowledgments 411 The authors thank Mr. Giovanni Pasqualoni (University of L’Aquila) for the support during the experimental 412 measurements in the “G. Parolini” Laboratory. 413 414 Funding : 415 This research did not receive any specific grant from funding agencies in the public, commercial, or not -for- 416 profit sectors. 417 418