**Determination of the Insulation Solution that Leads to Lower CO2 Emissions during the Construction Phase of a Building**

**María José Bastante-Ceca 1,\* , Alberto Cerezo-Narváez <sup>2</sup> , José-María Piñero-Vilela <sup>2</sup> and Andrés Pastor-Fernández <sup>2</sup>**


Received: 29 March 2019; Accepted: 17 June 2019; Published: 21 June 2019

**Abstract:** The characteristics of the envelope of a building determine, together with other factors, its consumption of energy. Additionally, the climate zone and insulation material may vary the minimum insulation thickness of walls and roofs, making it different, according to cooling down or warming up the home. Spanish legislation establishes different maximum values for energy demand according to different climate area both for heating and for cooling. This paper presents the results of a study that determines the influence of many variables as the climate zone or the orientation, among others, in the optimization of thickness insulation in residential homes in Spain to reduce the CO2 emissions embodied. To do that, 12 representative cities in Spain corresponding to different climate zones, four orientations, two constructive solutions, and four different configurations of the same house have been combined, for three different hypotheses and four insulation materials, resulting in 4608 cases of study. The results show that, under equal conditions on energy demand, the optimal insulation requirements are determined by heating necessities more than by cooling ones. In addition, a higher insulation thickness need does not necessarily mean more CO2 emissions, since it can be compensated with a lower Global Warming Potential characterization factor that is associated to the insulation material. The findings of this study can serve to designers and architects to establish the better combination of the variables that are involved in order to minimize the CO2 emissions embodied during the construction phase of a building, making it more energy efficient.

**Keywords:** energy demand analysis; insulation materials; climate zones; envelope; CO2 emissions

#### **1. Introduction**

Urban growth following the central years of the "real estate bubble 1998–2007" [1] has produced significant change in Spain in terms of building densities, which fell to substantially below 35 dwellings per hectare [2]. Current legislation, far from restricting the expansion of the urban by occupation of the rural space, promotes it by deregulating the use of undeveloped land [3]. Lower urban densities, high losses of non-urban land covers, the depopulation of metropolitan inner cores, and the expansion of transportation infrastructures confirm the generalization of the dispersed urban model, in which the importance of single housings is highlighted [4,5].

The upward trend in energy prices is growing [6], parallel to this disproportionate development of urban society, which makes it necessary to implement measures that are aimed at optimizing demand and promoting energy saving and efficiency [7]. In this respect, dwellings, like all other buildings,

face the challenge of achieving an energy management that allows them to contribute to economic growth, social welfare and sustainability of non-renewable resources, and preservation of the natural environment [8].

Buildings are big consumers of energy and materials and important producers of waste and emissions. Prefabrication presents an opportunity to reduce impacts in the building sector [9]. Among the advantages and benefits that are offered by the prefabricated building systems when compared to conventional construction methods, reductions in cost and time, improved quality, safety, and accuracy in manufacture, speed of installation on-site, and even dismantling and reuse are provided [10,11], as well as customization [12].

Energy consumption in the building sector is gaining increasing interest, as it is directly related to energy economics and sustainable development. The design and the choice of building materials, as well as the energy and thermal systems, evolve very rapidly. In the energy challenge, the building is among the largest consumers of energy in the European Union area [13]. The efficiency and optimization of energy systems remain among the main items that are studied in order to reduce energy consumption and increase system performance. In the area of housing, the cost and optimization of space are the two main reasons that require the decrease of the thickness of walls in new constructions; however, this reduction greatly affects the thermal inertia of the frame and makes it insufficient to effectively damp the oscillations due to the outdoor temperature variation [14]. Under these conditions, the optimization of the thickness insulation plays an important role in reaching a workable compromise between the comfort, the cost of the building, and the consumption of energy (and its corresponding cost during their lifetime).

Spain has generated an intense development of new regulations seeking for better energy performance in buildings in recent years. Thus, it is noteworthy that, as a result of the transposition of Directive 2002/91/CE [15], the Technical Building Code (CTE) is enacted [16], as well as a procedure for energy Certification for Buildings [17] (transposition of Directive 2010/31/EU [18]) and a new Regulation for Thermal Installations in Buildings [19] (transposition of Directive 2012/27/EU [20]).

Many of the potential effects of climate change on the building sector are not well studied, as climate change one of the most important social and environmental concern [21]. At the European level, about 36% of CO2 emissions are related to buildings. For this reason, the European Union (EU) has identified the building sector as one key area for achieving its objectives for greenhouse gas emission reductions [22].

The EU Directive on the Energy Performance of Buildings [18] specifies that, by the end of 2020, all new buildings shall be nearly Zero Energy Building (nZEB). Directive 2012/27/EU establishes a specific mandatory for member states to draw up national plans to increase the number of nZEB. These plans must include the detailed definition of the nZEB concept in such a way that their national, regional, or local conditions are reflected, and a numerical indicator of the primary energy use must be included and expressed in kWh/m<sup>2</sup> per year.

The Basic Document of Energy Saving (DB-HE) of the CTE [23] is the second revision of the original one dated on 2006 in terms of energy saving (the first revision is dated on 2013). The method of calculation of the characteristic parameters of the elements that compose the thermal envelope of the models is carried out according to the Directives of DB-HE of the CTE. This method consists of the calculation of the thermal transmittance of these elements: enclosures that are in contact with external air, enclosures in contact with the ground, interior partitions in contact with non-habitable spaces and hollows, and skylights considering their modified solar factor.

Usually, the lifetime of the buildings easily reach between 50 and 100 years, so the buildings constructed today need to be resilient to future climates, than can be largely different than the one that we experience today [22]. Pérez-Andreau et al. [24] studied the impacts of climate change on heating and cooling energy demand in a residential building in a Mediterranean climate with two different Global Circulation Models for 2050 and 2100. The authors concluded that climate change has a direct effect on energy demand in homes, and suggested that thermal insulation will have great effect on total energy demand.

Previous studies have analyzed the environmental impact of using different insulation materials [25–30], fixing the rest of parameters (orientation, climate zone, compactness, or constructive solution). This is the case of Braulio-Gonzalo and Bovea [25], which compares eleven insulation materials alternatives for a single-family house that was located in the climate zone B3, with a given orientation, and fixing the envelope description and thermal resistance, in order to see the influence of the insulation material and the thickness on energy demand, to accomplish the Spanish Technical Code. On the other hand, Hill et al. [26] make a review of the different insulation materials environmental information published, with the aim of comparing both the embodied energy and the environmental impact in terms of CO2 emissions, independently of the rest of variables or the insulation needs. Additionally, Pargana et al. [27] compare the different insulation materials in order to evaluate their environmental impacts, and the consumption of energy on their production. Again, the authors do not consider the needs of insulation materials or the possibility that, although one type of insulation may have a higher environmental impact during its production, this can be compensated with lower insulation thickness needs, resulting in lower CO2 emissions once placed into the building during its construction phase. Sierra-Pérez et al. [28] analyse different façade-building systems and thermal insulation materials for different climatic conditions, in order to determine their environmental impact. These authors consider five insulation materials, three façade systems, but, as in [25], just consider one climate zone (D), although they perform a sensitivity analysis varying the climate zone, but without varying orientation, compactness, or constructive solutions, variables that also influence the envelope and the insulation thickness needs. The same authors indicate, as one of the weaknesses of their research, that they just consider a unique building façade system in isolation and not as part of an entire building. Asdrubali et al. [29], in line with that indicated for [27], present a report of the state-of-the-art of insulation materials, without going into embodied energy or CO2 emissions that are associated to its construction, or in the different insulation thickness needs according to variables as orientation, climate zone, and so on. Finally, Schiavoni et al. [30] make a review of the different insulation materials that were used for the building sector, presenting a comparative life cycle assessment between the different insulation materials for four different typical configurations of external walls, in order to compare both the embodied energy and global warming potential in terms of CO2 emissions, for the same functional unit. Again, the authors do not consider different insulation thickness needs, depending on the climate zone, the orientation of the building, the constructive solution, and the building model, among others, apart from the insulation material.

In addition, different authors have studied the influence of different electricity-to-emissions conversion factors for three different insulation materials into the calculation of lifecycle emissions [13]. Apart from that, other studies [31] have investigated the building energy demand under different climates, or even including variables, such as the configuration of walls [32], but none of them have considered the influence of all the parameters, taken together.

This paper presents the results of a study that determines the influence of different parameters as the climate zone, the compactness of the building and the orientation, as well as the insulation material and the constructive solution in the optimization of thickness insulation in residential prefabricated houses in order to minimize the CO2 emissions that were embodied during their construction phase.

A series of cases of a single-family semi-detached house is proposed to develop the study. In total, 4608 cases of study have been analyzed, while considering 12 locations according to DB-HE climate zones, four main orientations, two constructive solutions, and four compactnesses, all of them for four insulation materials, under three hypotheses of demand limitation.

The results of this study can help professionals that are involved in the building sector (designers, builders, architects, engineers, and even legislators) to establish the better conditions for minimizing the CO2 emissions from the insulation during the construction phase for an energy demand fixed for cooling and heating in the use phase. Variables that have been taken into account are the climatic zone, the orientation, the constructive solution for fa ade and roof, and the compactness of the building, as well as the insulation material and its thickness.

The originality of the research that is presented in this paper consists in the fact that we have considered different variables that have a substantial influence on the determination of the envelope of the building (climate zone, orientation, compactness, constructive solution, insulation material, and energy demand), in order to determine the insulation thickness needs for each case. This way, for a given climate zone, the builders and designers can select the best combination of the variables in order to minimize the embodied CO2 emissions of the building during its construction phase. Economical aspects are not to be left out of the considerations, since they may affect the final decision. Nevertheless, the difference in cost of implementing the most effective solution in terms of reducing CO2 emissions and its possible compensation with the savings derived from a minor energy consumption during the use phase of the building is out of the scope of this study and it will be the subject of subsequent research. In addition, the energy requirements for the use phase of the building and the possibility to satisfy them with renewable energies (solar thermal and photovoltaic energies, for example) will also be the subject of further researches.

The paper is structured, as follows. Section 2 presents the method used, establishing the three calculation hypotheses and describing the software used, choosing the location from the climate zones and their orientation, defining the characteristics of the building (compactness and constructive solutions), and selecting the insulation material. Section 3 shows the main results that were obtained of the study, including the thickness of the insulation for each climatic zone, orientation, compactness, constructive solution, and demand hypotheses, as well as their emissions. The major findings are also highlighted and contextualized, discussing them with the literature review made. Section 4 concludes the paper, summarizes the contributions, and proposes further research continuations.

#### **2. Method**

#### *2.1. Calculation Procedure and Software Used*

The unified tool LIDER-CALENER (HULC) is used in order to assess the energy demand [33]. HULC is the official energy certification tool in Spain, although other homologated tools can also be employed. This tool includes a graphical interface for a three-dimensional (3D) representation of buildings and it performs an hourly simulation considering a transitional regime, while taking into account thermal coupling between adjacent zones and thermal inertia, thanks to its calculation engine, called S3PAS, following the procedure from the ISO 52016-1:2017 standard [34].

There are three demand hypotheses that have been established for each situation (1536 scenarios from 12 climate zones, four orientations, two constructive solutions, and four compactness), making a total of 4608 case studies:


Hypothesis 1, as shown in Table 1, establishes four different heating demands (a basis of 15 kWh/m<sup>2</sup> per year for climate zones A and B, almost 30 kWh/m<sup>2</sup> for climate zone C, and slightly above 40 and 60 kWh/m<sup>2</sup> for climate zones D and E, respectively, as explained in the next section). Regarding cooling demand, only two requirements are stated (15 kWh/m2 per year for climate zones 1, 2, and 3, and 20 kWh/m<sup>2</sup> for climate zone 4, as explained in the next section).


**Table 1.** Maximum heating and cooling demand per climate zone for legal compliance.

Units in kilowatts hour per square meter per year (kWh/m2y).

Spanish legal requirements, which fix the maximum energy demand, generate a gap in energy consumption that is faced by final users from some climate zones, especially D and E ones. On the contrary, the hypothesis 3, which is based on the requirements of the Passivhaus standard [35], limits the heating and cooling demand to 15 kWh/m2 per year each. Given the fact that letter indicates the severity of the winter, whereas the number indicates the severity of summer, for the same winter severity (as explained in the next section), this constraint is detrimental to users in moderate summers as compared to colder ones. Hypothesis 2 is proposed to mitigate this, while considering a joint demand for heating and cooling, aggregating them up to a limit of 30 kWh/m2 per year.

The procedure has been the following: starting with an initial insulation thickness of 0 mm (both for the façade and for the roof and the ground floor), the energy demand has been calculated and compared to the limits by hypothesis. If the energy demand is under the limits, then an increase in insulation thickness of 5 mm is considered and the process is repeated again. The process continues with an incremental insulation thickness of 5 mm until the limits for each of the hypotheses considered are reached. The incremental insulation thickness of 5 mm has been chosen according to the commercial availability on the market. Other parameters must be taken into account once the insulation thickness for each of the hypotheses considered is fixed, and before the energy demand is determined, according to the characteristics of the building (compactness and constructive solutions), and the other variables considered (orientation, climate zones, block shadows, and so on).

The gains and losses are considered by HULC according to the detailed method of the ISO 52000-1:2017 standard [36], and depend on the type and thickness of insulation, infiltration, orientation, and climate zone, among other variable elements. They also depend on the fenestration, thermal bridges, and ventilation, which remain invariable in this study. Besides, both thermal bridges and ventilation are calculated by the DB-HE of the CTE [22]. Ensuring continuity in the insulation of the constructive elements union solves thermal bridges. In the case of ventilation, the minimum required flow rate is 33 liters per second (intake and extraction), which means 0.27 renovations per hour.

#### *2.2. Climate Zones*

The Köppen Climate Classification is chosen in order to identify the climate zones within mainland Spain. This classification, published in 1900, is still one of the most widely classifications systems used for climate studies in the world. According to this, based on the average monthly values for precipitation and air temperature, the climate zones are characterized by a combination of a letter by the climate severity of winter and a number by the climate severity of summer.

For this study, 12 provinces (represented by their capitals) in mainland Spain have been chosen, whose selection is due to its representativeness from their climate zones by their population. Table 2 shows the selected provinces for the study, as well as the climate zone, the altitude of their capitals, their population, and their percentage over the total population of mainland Spain.


**Table 2.** Characteristics of the cities object of the study [37].

<sup>1</sup> Data at 01/01/2018.

Figure 1 shows the distribution of climate zones for mainland Spain, according to Köppen Climate Classification:

**Figure 1.** Distribution of climate zones in Spain.

#### *2.3. Orientation*

Orientation influences the energy consumption of a building, and the election of an accurate orientation, together with the correct location and landscaping changes, may decrease its energy consumption [38]. For this study, in order to consider different advantage of solar power depending on the orientation of the building due to different shadow, and also to analyze the influence of this parameter on the results of insulation thickness needs, the four cardinal orientations have been selected, following the wind rose: North (N), East (E), South (S), and West (W).

#### *2.4. Characteristics of the Building*

All of the buildings considered for this study belong to the category of semidetached houses, joined in a dwelling unit. Each semidetached building consists of three different floors (ground floor, first floor, and roof floor). It can be noted that the same housing units compose all of the studied models). At the ground floor, we can find the dining room, the kitchen, the living room, one bath, and the pantry, apart from the entrance to the house and the ground floor stairs. At the first floor, we can find three bedrooms, two bathrooms, and the first floor stairs. Finally, at the roof floor, there are

the roof floor stairs and the access to the deck. Each dwelling unit is made up of three shared median walls and a faade one limiting with the public domain. The block presents a number multiple of four houses. For example, Figure 2 shows a 3D simulation for the models considered, in which the block configuration can be observed.

**Figure 2.** Three-dimensional (3D) Simulation of the block configuration from the dwelling unit for Models 1–4.

Four different building configurations are considered in order to determine the influence of the compactness of the building. For the four models involved, the degree of compactness vary from 1.5 for Model 4 to 2.2 to Model 1. The configurations of the four models studied are shown in Figure 3a–d, in which the green color corresponds to the garden zones (from the ground floor) and the blue color to walkable terraces (from the first and the roof floor).

In addition, the surface of the building is the same (insofar as all the models are made up of the exactly same housing units), but its compactness, which establishes the relationship between the outer shell of the building and its volume, changes. Independent of the orientation, climate zone, and configuration of the elements, the four models studied have the same building characteristics regarding their volume, their built area, their roof, and ground area, but with small differences regarding their opaque façade surface area and their glazed façade surface area, which makes its compactness vary, as can be seen in Table 3.

**Figure 3.** (**a**) Configuration of the Model 1; (**b**) Configuration of the Model 2; (**c**) Configuration of the Model 3; and, (**d**) Configuration of the Model 4.

**Table 3.** Characteristics of the building for different models analyzed.


\* Compactness is defined as the 'volume divided by the area exposed to outside air (roof and façades)' ratio.

#### *2.5. Selection of the Insulation Material*

The correct choice of the insulation material is relevant when improving the energy-efficiency of the buildings. Different materials can be used to provide similar functions in buildings but the related energy-use and emissions could vary widely [39]. Most commonly used insulation materials in building industry are fiberglass, stone wool (also known as mineral wool or rock wool), glass wool, cellulose fiber, expanded polystyrene (EPS), extruded polystyrene (XPS), polyisocyanurate (PIR), and polyurethane (PUR) [39,40].

For this study, the four commonly insulation materials used have been chosen. The choice has been made according to the state-of-the-art review, where four types of insulation materials have been identified as the most commercialized for building: derived from petroleum (for example, PUR and PIR), polystyrenes (XPS and EPS), minerals (stone wool, glass wool, etcetera), and natural or ecological ones (expanded cork, wood fibreboard, etcetera). According to this, one insulation material of each type has been chosen for this study: Extruded Polystyrene (XPS), Polyurethane foam (PUR), Stone Wool (SW), and Expanded Cork (EC). Table 4 shows the characteristics of insulation materials considered, from Environmental Product Declarations that will be used to determine CO2 emissions according to their insulation thickness needs.


**Table 4.** Characteristics of the insulation materials.

<sup>1</sup> Data in W/mK. <sup>2</sup> Data in kg/m3. <sup>3</sup> Data in kg CO2/m<sup>3</sup> insulation.

As stated before, two different constructive solutions have been considered for the roof and for the façade wall, whereas the intermediate floor, ground floor, medium walls, and partition walls are the same for both cases. The details for their components and layers are shown in Appendix A, Figures A1–A6.

Table 5 includes the data for thermal transmittance (U-value) of the constructive elements detailed. Some of them have a fixed part (because they are invariable) and the others, a variable part, depending on the thickness and the insulation material, as shown in the Figures A7–A9, located in Appendix A.

**Table 5.** Thermal transmittance (U-value) of different constructive elements.


\* Variable transmittance according to thickness and insulation material.

#### **3. Results and Discussion**

Sections 3.1–3.5 present the main results of CO2 embodied emissions resulting from different insulation requirement needs according to different variable studied: climate zone, insulation material, orientation, constructive solution, and compactness, for the hypotheses H1, H2, and H3, respectively. Finally, a discussion is made in Section 3.6.

Appendix B includes all the results for calculations of different insulation requirement needs for each of the 4608 cases of study in order to reduce the amount of data and extract just the main results obtained from the study, making it more readable and understandable for the reader.

This way, Tables 6–10 show differences between CO2 emissions in relation to the best possible value for each sequence, according to different variables, in a colour scale varying from blue to red. For each of the hypotheses considered two combinations of different variables have been taken into account: the set up that leads to the lowest CO2 emissions possible, and the set up that leads to the higher CO2 emissions possible, in order to analyse the results from both points of view.

Each sequence will be composed by different options, depending on the variable studied. For example, in the case of insulation materials, the options will be EC, SW, PUR, and XPS (as well as for the orientation will be the wind rose, for the compactness will be the four model studied and for the constructive solution will be the two referred in Appendix A). Besides, there will be as sequences as climate zones, set ups, and hypotheses.

For all of the tables, blue colour means situations where no insulation is needed (and consequently no CO2 emissions derived from insulation is generated). On the other side, grey colour means situations where is not possible to realize this combination of variables due to constructive reasons (and, due to this, the calculation of CO2 emissions is not applicable). Cells with no background colour indicate the reference value of CO2 emissions for each sequence, and the rest of the cells will have a different colour, varying from green to red, depending on their difference with the reference value. In this way, the closer the colour of the cell is to light green, the lesser the difference regarding the minimum value of CO2 emissions; on the other hand, the closer the colour of the cell to dark red, the higher the difference regarding the minimum value of CO2 emissions.

#### *3.1. Influence of the Climate Zone on CO2 Emissions*

The differences in the insulation needs depend first of all on the climate zone, as can be seen in Table A1a,b, Table A2a,b and Table A3a,b, in Appendix B. The results were shown to correspond to the minimum insulation thicknesses needed (in increments of 5 millimeters, from 0 to 200) to satisfy the energy demands defined in the hypotheses H1, H2, and H3, according to the rest of the variables considered. As the optimal insulation thickness needs are determined more by the needs of heating than for cooling, climate zones where winters are not severe (letters A and B), will need less insulation than climate zones where the winters are colder (letters C, D, and E).

While analyzing the results from the point of view of insulation thickness needs, we can observe that, for a given climate zone (this is the case of someone who wants to build a house in a determined place), XPS material results always in minor insulation material thicknesses than for the rest of materials considered, but in major insulation material emissions, as explained in the next section. These differences between insulation materials needs considerably increase with the degree of compactness, being the lesser compactness the higher differences among the insulation thickness needs. Nevertheless, although these needs also depend on the rest of variables (orientation and constructive solution), analyzing the results from the point of view of CO2 emissions, the climatic zone is the main factor to be taken into account, as can be understood when analyzing Table 6, which shows that the emissions increased in cold areas, especially for Hypotheses 2 and 3.

In Appendix B, Table A4a–c, Tables A5a–c and A6a–c present the results of CO2 emissions for Hypotheses H1, H2, and H3, respectively. Expression "n.a" meaning: "not applicable" refers to the situations where the minimum insulation thickness to satisfy energy demand is not possible due to constructive restrictions and, therefore, calculations of CO2 emissions have no sense.


**Table 6.** Increase of emissions according to the climatic zone for the best and worst set ups.

#### *3.2. Influence of the Insulation Material on CO2 Emissions*

If we analyze the results in terms of CO2 emissions, we can observe how, although the recommendations for orientation, compactness, and constructive solution are the same (that is to say, always the combination of North orientation, constructive solution 1, and building Model 1 will result in lower CO2 emissions; on the other side, the combination of West orientation, constructive solution 2, and building Model 4 will result in more CO2 emissions, under equal conditions for the rest of variables), the recommendation for the insulation material changes.

The higher insulation thickness that is required to satisfy an energy demand fixed in the case of expanded cork (instead of the minimum thickness need from the extruded polystyrene), as observed in Table A1a,b, Table A2a,b and Table A3a,b, is compensated with its lower Global Warming Potential (GWP) factor, as a result, giving appreciably less CO2 emissions. This difference increase with the needs of insulation material, so, in order to reduce CO2 emissions during the construction phase, expanded cork is always preferable, if possible.

Table 7 shows the increase of CO2 emissions according to the insulation material, for the different climate zones and hypotheses that were considered. The insulation material that generates lower emissions is always the expanded cork. The second one is the stone wool and the third, the polyurethane. The worst is always the extruded polystyrene. However, thanks to its lower thickness needs, it is the most applicable in the cases in which other materials cannot satisfy the demands that are required.

#### *3.3. Influence of the Orientation on CO2 Emissions*

Regarding the orientation, Table A1a,b, Table A2a,b and Table A3a,b in Appendix B show that West orientation is always the most insulation demanding independent of the climate zone, the compactness, the constructive solution, and the insulation material, being the needs higher as long as the compactness of the building decreases. At the same time, the North orientation is also the least insulation demanding.

Table 8 shows the increase of CO2 emissions according to the orientation, for the different climate zones and hypotheses considered. The orientation that generates lower emissions is always the North. The second one is the East and the third, the South. The worst is always the West orientation. It implies that the North orientation is the most applicable and the West is the orientation in which more cases are not possible. However, sometimes the North and East tie, as well as South and West, due to being included in the same step thickness.


**Table 7.** Increase of emissions according to the insulation material for the best and worst set ups.

Best set up: N (Orientation), Model 1 (Compactness), S1 (Constructive Solution). Worst set up: W (Orientation), Model 4 (Compactness), S2 (Constructive Solution).


**Table 8.** Increase of emissions according to the orientation for the best and worst set ups.

Best set up: Model 1 (Compactness), Expanded Cork (EC) (Insulation Material), S1 (Constructive Solution). Worst set up: Model 4 (Compactness), Extruded Polystyrene (XPS) (Insulation Material), S2 (Constructive Solution).

#### *3.4. Influence of the Constructive Solution on CO2 Emissions*

Constructive solution for the roof and façade wall also has an influence on the CO2 emissions, always being preferable the constructive solution 1, under equal conditions of the rest of variables, since the needs of insulation are lower. It can be noted that the constructive solution 1, as can be checked in the Figures A1a and A4a, presents a more modern solution both for the façade and for the roof (ventilated faade and floating roof) than the traditional ones that are represented in the constructive solution 2 (as shown in Figures A1b and A4b). Table 9 shows the increase of CO2 emissions, according to the constructive solution, for the different climate zones and hypotheses considered.


**Table 9.** Increase of emissions due to the constructive solution for the best and worst set ups.

Best set up: N (Orientation), Model 1 (Compactness), EC (Insulation Material). Worst set up: W (Orientation), Model 4 (Compactness), XPS (Insulation Material).

#### *3.5. Influence of the Compactness on CO2 Emissions*

As observed in Table A2a,b and Table A3a,b in Appendix B, as the compactness of the building diminish, and, depending of the hypotheses considered, it could be possible that the maximum insulation thickness cannot be enough to satisfy the energy demand in those climate zones where the winter is extreme. The situation arrives to that point that, for the hypotheses 3 (Passivhauss Standard), it is not possible to satisfy energy demand in any of the 128 cases that were analyzed for the climate zone E1.

Table 10 shows the increase of CO2 emissions according to the compactness, for the different climate zones and hypotheses considered. Model 1 generates, in all of the climate zones and for the three hypotheses considered, lower emissions than the other configuration models. This can be noted, since it is the reference base to calculate the differences with the rest of the models, except in those cases where it is not possible to build that configuration due to constructive reasons.


**Table 10.** Increase of emissions due to the compactness for the best and worst set ups.

Best set up: N (Orientation), EC (Insulation Material), S1 (Constructive Solution). Worst set up: W (Orientation), XPS (Insulation Material), S2 (Constructive Solution).

#### *3.6. Discussion*

It is useful to present an overview of buildings' thermal balance with respect to energy gains and losses, checking ventilation and infiltration, heat gains, and transmission through the envelope before discussing the results of insulation thicknesses and CO2 emissions. Among the 4608 study cases, two from 4008 applicable cases are shown in Tables 11 and 12 as an example (600 of them are not possible due to constructive limitations in which insulation thicknesses are not enough), corresponding to the Hypothesis 2, from Madrid (D3) and Barcelona (C2).

**Table 11.** Thermal balance. Example 1: Hypothesis 2, Model 1, Constructive solution 1, Climate Zone D3, Orientation North. Thickness 85mm, Insulation Material Expanded Cork.


\* Units in kilowatts hour per square meter per year (kWh/m2y).

**Table 12.** Thermal balance. Example 2: Hypothesis 2, Model 4, Constructive solution 2, Climate Zone C2, Orientation West. Thickness 80mm, Insulation Material XPS.


\* Units in kilowatts hour per square meter per year (kWh/m2y).

In total, we have analyzed 4608 cases of study (1536 cases by hypothesis), corresponding to 12 climatic zones, four main orientations, four models of construction, two constructive solutions, four insulation materials, and three energy demand limitation hypothesis. The results show that just 4008 case studies could really run, from the constructive point of view, given that the 600 remaining cases would require thickness insulation that is incompatible with the constructive characteristics of the building. All of the 600 cases where it was not possible to meet energy demand requirements correspond to the hypothesis H2 (162), and especially to hypothesis H3 (438 cases). However, in many of those cases it would be enough with a small adjustment that allowed a few extra millimeters of insulation in certain cases, in order to achieve compliance with the requirements.

Table 6 has shown the variability of the emissions that were generated to satisfy a specific heating and cooling demand (hypotheses H1–H3), according to the climate zone in which the building is located. For the H1 scenario, these emissions are doubled in the best scenario and tripled in the worst scenario. However, for hypotheses H2 and H3, the differences increase a lot (almost multiplied by ten times). Subsequently, Tables 7–10 show the contribution of the other factors, once a location is fixed. The compactness and the insulation material also have a major influence on the amount of emissions generated. Next, orientation and the constructive solution for the envelope exert a minor but significance influence.

#### **4. Conclusions**

In general, it is concluded that the optimal insulation thickness are determined more by the needs of heating than for cooling, even in the most severe summer climates needs. On the demand for energy, in the case of H1, values established by CTE result in similar thicknesses independently of the climate zone, and therefore the costs due to insulation during the construction phase are similar. Nevertheless, this will increase the costs of energy during the use phase of the building, punishing the inhabitants of cold spots due to its higher energy demand for heating. On the contrary, while considering the H3, the users of temperate zones are penalized, given that energy demand for cooling in cold areas is very low. Here follows that the intermediate hypothesis, H2, which tries to balance the joint demand during the phase of use of the building, may be the most optimal when regular energy demand limitations, given that these, and therefore, consumption (and their associated costs), they are similar, both in temperate and in cold-zones. For this case, it would be interesting to determine the satisfaction of the energy demand exclusively with renewable energies.

With regard to CO2 emissions, and analyzing the results according to the compactness of the building primarily, it is observed that the model 1, regardless of the climatic zone, the orientation and the scenario, always generates less emissions than the rest of the models, for all cases. In terms of the influence of the orientation, regardless of the climatic zone, compactness of the building, constructive solution, and scenario, the orientation W is always that generates a greater number of emissions. These differences can reach up to 57% for the same climatic zone. This can be taken into account by the designers and builders in order to minimize the emissions from the stages of design and construction of the buildings due to the insulation of the envelope. Additionally, the material has influence on the amount of CO2 emissions, since, as stated before, using expanded cork instead of XPS can reduce the total amount of CO2 emissions during the construction phase of the building, although the needs for this material are higher, due to its lower GWP factor.

It must be recalled that increased consumption means, not only an increase in CO2 emissions during the phase of use of the building, but also an increase of the costs for the users of the same, due to the increase in their electric bills. From this point of view, other future research can be done in order to incorporate a cost analysis to determine the influence of the different variables that are considered into the final cost of the electricity, with the aim of minimizing it. It will be also interesting to analyze, from an eco-efficiency point of view, the costs of fabrication, installation, and maintenance for different materials, which will be material for further research. Other research include the extension of the scope in order to include lighting requirements, and the inclusion of active measures, such as the use of photovoltaic and/or solar thermal energy.

**Author Contributions:** Conceptualization, M.J.B.-C. and A.C.-N.; Methodology, M.J.B.-C. and A.C.-N.; Data Curation, A.C.-N. and J.-M.P.-V.; Formal analysis, A.C.-N. and J.-M.P.-V.; Writing—original draft preparation, M.J.B.-C. and A.C.-N.; Writing—review and editing, M.J.B.-C., A.C.-N. and A.P.-F.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors would like to thank to the "Promotion and Support of the Research Activity Program" of University of Cádiz by their support during this research.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A**

Appendix A includes the constructive description of the different solutions, both variable and permanent, for roofs, ground and intermediate floors, faades, median walls and partitions. The end of the appendix present the thermal transmittance of the variable elements.

**Figure A1.** (**a**) Roof floor components detail for constructive solution 1. (**b**) Roof floor components detail for constructive solution 2.

**Figure A3.** Ground floor components detail.

**Figure A4.** (**a**) Façade wall components detail for constructive solution 1. (**b**) Façade wall components detail for constructive solution 2.

**Figure A5.** Median walls components detail.

**Figure A7.** Thermal transmittance (U-value) according to insulation thickness, for roofs.

**Figure A8.** Thermal transmittance (U-value) according to insulation thickness, for ground floor.

**Figure A9.** Thermal transmittance (U-value) according to insulation thickness, for façade walls.

#### **Appendix B**

Appendix B includes all the results from the 4608 cases studied, both for insulation thickness requirements and for embodied CO2 emissions.


**Table A1.** Insulation thicknesses (in mm), for Hypothesis 1: Legal Minimum Compliance.

**Table A1.** *Cont.*


CZ (Climate Zone); O (Orientation); S (Constructive Solution).


**Table A2.** Insulation thicknesses (in mm), for Hypothesis 2: Joint (heating + cooling) demand ≤ 30.

**Table A2.** *Cont.*


CZ (Climate Zone); O (Orientation); S (Constructive Solution); - Thickness not enough to satisfy demand.


**Table A3.** Insulation thicknesses (in mm), for Hypothesis 3: Both heating and cooling demand ≤ 15.

**Table A3.** *Cont.*


CZ (Climate Zone); O (Orientation); S (Constructive Solution); - Thickness not enough to satisfy demand.

**Table A4.** Emissions of CO2 according to climate zone (CZ), orientation (O), constructive solution (S), building model and insulation material model (in Kg CO2), for H1.



**Table A4.** *Cont.*



**Table A4.** *Cont.*

**Table A5.** Emissions of CO2 according to climate zone (CZ), orientation (O), constructive solution (S), building model and insulation material model (in Kg CO2), for H2.



**Table A5.** *Cont.*

**Table A5.** *Cont.*


**Table A6.** Emissions of CO2 according to climate zone (CZ), orientation (O), constructive solution (S), building model and insulation material model (in Kg CO2), for H3.

**Table A6.** *Cont.*


**Table A6.** *Cont.*


#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Thermal Transmittance of Internal Partition and External Facade LSF Walls: A Parametric Study**

#### **Paulo Santos \* , Gabriela Lemes and Diogo Mateus**

ISISE, Department of Civil Engineering, University of Coimbra, Pólo II, Rua Luís Reis Santos, 3030-788 Coimbra, Portugal

**\*** Correspondence: pfsantos@dec.uc.pt; Tel.: +351-239-797-199

Received: 22 June 2019; Accepted: 10 July 2019; Published: 11 July 2019

**Abstract:** Light steel framed (LSF) construction is becoming widespread as a quick, clean and flexible construction system. However, these LSF elements need to be well designed and protected against undesired thermal bridges caused by the steel high thermal conductivity. To reduce energy consumption in buildings it is necessary to understand how heat transfer happens in all kinds of walls and their configurations, and to adequately reduce the heat loss through them by decreasing its thermal transmittance (*U*-value). In this work, numerical simulations are performed to assess different setups for two kinds of LSF walls: an interior partition wall and an exterior facade wall. Several parameters were evaluated separately to measure their influence on the wall *U*-value, and the addition of other elements was tested (e.g., thermal break strips) with the aim of achieving better thermal performances. The simulation modeling of a LSF interior partition with thermal break strips indicated a 24% *U*-value reduction in comparison with the reference case of using the LSF alone (*U* = 0.449 W/(m2.K)). However, when the clearance between the steel studs was simulated with only 300 mm there was a 29% increase, due to the increase of steel material within the wall structure. For exterior facade walls (*U* = 0.276 W/(m2.K)), the model with 80 mm of expanded polystyrene (EPS) in the exterior thermal insulation composite system (ETICS) reduced the thermal transmittance by 19%. Moreover, when the EPS was removed the *U*-value increased by 79%.

**Keywords:** LSF construction; facade wall; partition wall; thermal transmittance; thermal bridges; parametric study; numerical simulations

#### **1. Introduction**

Buildings account for around 40% of the total energy consumption and about 36% of CO2 emissions in Europe [1]. The main factors of building energy consumption are the properties and design of the building envelope, the operation of building services, the occupants' behavior and the climate/location [2–5]. Most of this energy, ranging from nearly 50% [6] up to 60% [7] depending on climate, design, use type and occupational patterns, is used by air-conditioning systems to achieve thermal comfort inside the buildings. Energy in the form of heat is dissipated to the environment at different rates according to the ventilation and building elements' characteristics (e.g., thermal transmittance *U*-value). The rate of these losses/gains is important because it directly affects the operation and maintenance costs of mechanically ventilated and/or air conditioned buildings [8].

Usually a wall element is composed of several layers, such as internal and external cladding (e.g., cement mortar), one or two supporting panes (e.g., ceramic brick masonry), air cavity, and thermal and acoustic insulation (e.g., expanded polystyrene (EPS) or mineral wool). Typically lightweight steel framed (LSF) walls are made of the following main types of materials [9]: (1) supporting steel frame, which is constituted of cold formed profiles; (2) sheathing panels, such as inner gypsum plasterboard and outer oriented strand board (OSB), and; (3) insulation materials, such as mineral wool filling the air cavity between steel studs (which besides thermal insulation, has also an important acoustic insulation role [10]) and the exterior thermal insulation composite system (ETICS), where the thermal insulation material could be EPS (expanded polystyrene), XPS (extruded polystyrene), mineral wool or other.

The *U*-value of an opaque building element (e.g., facade LSF wall) depends on several factors, such as the thickness of each layer, the number of layers, the thermal conductivity of each layer material, the existence of thermal bridges due to the presence of an inhomogeneous thermal layer (e.g., a steel stud), the existence of air voids in the insulation, and the external and internal surface thermal resistances [11]. Perhaps the most relevant parameters regarding the thermal transmittance of a LSF building element are the level of insulation (i.e., its thickness), material properties (e.g., thermal conductivity) and positioning of insulation, and the amount of steel frame material [7,12].

In colder climates to reduce the *U*-value, and consequently the heat transmission losses, the level of thermal insulation is increased to diminish the heating energy demand [13]. While in warmer climates this level of thermal insulation could be reduced, reducing energy consumption for space heating/cooling as well as the embodied energy related with the insulation materials [14]. In these warmer climates the outdoor temperatures are often higher than the indoor temperatures, which could significantly increase the heat gains. Thus, the use of passive cooling strategies, such as natural ventilation [15], phase change materials [16], free cooling [17] and ground ventilation using an earth-to-air heat exchanger [18] becomes more relevant. In order to predict the energy consumption it is usual to perform advanced dynamic simulations of the entire building [19,20] or make use of more simplified approaches [21].

Apart from the level of thermal insulation (i.e., the thickness of thermal insulation layer(s)), in LSF elements, the position in the building element influences the effectiveness of this insulation (i.e., its *U*-value or thermal transmittance), and is thus very relevant [12]. Notice, that the thermal insulation positioning is also relevant to the effective thermal inertia/mass of the building, but this was not evaluated in the present paper, neither in reference [12] work. Moreover, this insulation, mainly the LSF batt insulation (e.g., mineral wool), is relevant not only for thermal purposes but also for acoustic insulation [10]. A typical interior partition and exterior facade LSF wall cross-sections will be studied in this paper, as presented later in Sections 2.1 and 3.1, respectively.

At the design stage there are several ways to compute the *U*-value of a building element [11]. The detailed calculation method based on numerical simulations (e.g., finite element method (FEM)) should be performed using the modeling rules prescribed in standard ISO 10211 [22]. The most simple approach, applicable for homogeneous thermal layers, which may contain air layers up to 300 mm thick, is to consider the thermal resistance of each layer (depending on the thickness of the layer and on the thermal conductivity of the material) and to compute the reciprocal of the sum of all these thermal resistances, including both internal and external surface resistances [23]. Notice that the external thermal surface resistance mainly depends on the wind direction and velocity, as well as on the surface roughness [24].

The standard ISO 6946 [11] also prescribes an approximate method, known as the 'Combined Method', for building elements containing homogenous and inhomogeneous layers, including the effect of metal fasteners, by means of a *U*-value correction term. However, this methodology is not applicable for LSF elements, where the thermal insulation is bridged by metal (cold and hybrid frame construction), making this type of construction even more challenging in order to obtain an accurate and reliable *U*-value [23].

Several researchers devoted their attention to the thermal behavior and energy efficiency of LSF construction [5,9,23,25,26]. Soares et al. [26] performed a scientific bibliographic review about this kind of research. The first main driving research topic identified in the previous cited work was: "the development of single and combined strategies to reduce thermal bridges and to improve the thermal resistance of LSF envelope elements". The present work deals with this suggested main research issue. Recently Santos et al. [23] accomplished a comparison between experimental measurements in LSF walls' thermal transmittance and numerical simulations (2D and 3D FEM models) and analytical approach (ISO 6946 combined method). It was concluded that for the LSF wall with a simpler frame (i.e., only vertical steel studs) the analytical ISO 6946 and the 2D FEM numerical approaches provide quite good accuracy in the *U*-value estimation.

Since the ISO 6946 combined method is not applicable for LSF elements where the thermal insulation is bridged by the steel frames, some researchers developed some alternative analytical methods for this type of structure, such as Gorgolewsky [27] who developed a simplified analytical method for calculating *U*-values in LSF cold and hybrid construction. This method was based on the principles provided by ISO 6946, but adapted to consider the increased thermal effect of the steel frame, increasing the accuracy of the proposed methodology.

Given the high level of heterogeneity regarding the thermal conductivities of the materials composing the LSF elements, namely the steel frame and the thermal insulation, it is very challenging not only to accurately compute its thermal transmittance, but also to perform accurate and reliable measurements, both in-situ and in laboratory [8]. Regarding the experimental approach there are several methods for the thermal characterization of building elements, such as the heat flow meter (HFM) method, the guarded hot plate (GHP) method, the hot box (HB) method (which could be calibrated (CHB) or guarded (GHB)) and the infrared thermography (IRT) method. For LSF elements the most suitable experimental method, given its large heterogeneity in its component materials' thermal conductivity (e.g., steel and thermal insulation), is the hot box apparatus, since the measurements are not local, but instead in a representative wall area [28].

Recently, Atsonios et al. [29] developed two experimental methods for in-situ measurement of the overall thermal transmittance of cold frame LSF walls, namely the representative points method (RPM) and weighted area method (WAM). These methods make use of the analysis of the examined wall using thermal IR images with the recording and processing of indoor/outdoor air temperature and heat flux. Figure 1 displays an infrared thermal image of an LSF wall, where the thermal bridge's effect due to the high thermal conductivity of the vertical steel studs is quite visible. The vertical red lines denote higher surface temperatures due to an increased heat flow in the vicinity of each vertical steel profile, clearly identifying the position of them in the exterior colder surface of the LSF wall.

**Figure 1.** Thermal bridge's effect due to vertical steel studs in a light steel framed (LSF) wall captured in an infrared thermal image [30].

In fact, due to high thermal conductivity of steel in LSF structures, thermal bridges inspired many researchers to investigate the related thermal performance issues. De Angelis and Serra [31] evaluated the thermal insulation performance of metal framed lightweight walls and concluded that the correct evaluation of LSF walls' thermal performance requires more complex and detailed analysis than the ones necessary for traditional reinforced concrete and masonry constructions.

Also in 2014, Santos et al. [30] evaluated the importance of flanking thermal losses of LSF walls using a 3D FEM model validated by comparison with experimental laboratory measurements. They found heat flux variations from −22% (external surface) to +50% (internal surface) when flanking heat loss was set to zero as a reference case for a LSF wall with a thermal transmittance equal to 0.30 W/(m2.K). Later, in 2016, Martins et al. [32] performed a parametric study in order to evaluate the effectiveness of some thermal bridges mitigation strategies in LSF walls, allowing the improvement of thermal performance and reducing energy consumption by air-conditioning systems. A reduction of 8.3% in the *U*-value was found, comparatively to the reference LSF wall, due to these thermal bridges' mitigation strategies. Additionally, the use of new insulation materials (e.g., aerogel and vacuum insulation panels (VIPs)), which were combined with the mitigation approaches, led to a 68% decrease in the *U*-value.

In previous research works there was a lack of research on both interior partitions and exterior facade LSF walls, as well as the thermal performance comparison between them. In this work the thermal transmittance (*U*-value) of LSF walls is evaluated by means of a parametric study related with the wall typology (internal partition and external facade) and its composition. The main objective of this study is to quantify the relevance of several parameters in the *U*-value of LSF partition and facade walls. The evaluated parameters were selected among the most relevant ones and could be easily implemented in practice with used materials available in the market (e.g., recycled rubber, extruded polystyrene (XPS) and aerogel thermal break strips). Moreover, the analyzed LSF wall configurations were newly implemented for this study (i.e., are different from the ones evaluated before by other researchers).

The simulations were performed bi-dimensionally, and the results could be of interest to building developers and researchers, helping them to mitigate thermal bridges and achieving energy savings, whenever an LSF construction system is used. In Portugal (but probably also in other countries) most of the building designers neglect the effect of repetitive thermal bridges due to the steel frame on the thermal transmittance calculations of LSF elements, leading to lower and erroneous *U*-values. Consequently, the real building energy consumption will be higher than the predicted one in these cases and there is a higher probability of building pathologies related with the occurrence of interstitial condensations.

After this introduction, the evaluated interior and exterior LSF walls are presented, including the reference partition and facade LSF walls and the parameters used in the sensitivity analysis are described. Next, the accuracy of the used 2D FEM algorithm is verified by means of a comparison with ISO 10211 [22] test cases and with the analytical approach, defined in ISO 6946 [11], for a simplified model assuming no steel frame and homogeneous layers. Then, the 2D FEM simulations are explained, including the used boundary conditions and how the air layers were addressed in these simulations. After, the obtained results are presented and discussed for the two LSF wall typologies evaluated. Finally, the main conclusions of this work are presented.

#### **2. Characterization of LSF Interior Walls**

#### *2.1. Reference LSF Interior Partition Wall*

The reference interior wall is a configuration of an LSF wall normally used as an internal partition within the same dwelling. As illustrated in Figure 2 and listed in Table 1, this LSF internal partition is constituted by two gypsum plasterboards (12.5 mm thick each) on each side of the steel frame (made with steel studs C90, 90 mm wide, and 0.6 mm of steel sheet thickness) and the air cavity is fully filled with mineral wool batt insulation (90 mm). The distance between vertical profiles for internal reference walls was set on 600 mm. The total thickness of this partition wall is 140 mm.

**Figure 2.** Cross-section of an interior LSF reference partition wall modeled on THERM software.

**Table 1.** Materials, thicknesses (*d*) and thermal conductivities (λ) of the LSF interior reference partition wall.


<sup>1</sup> GPB—gypsum plasterboard.

Notice that, even being an internal partition, this LSF wall can separate a conditioned space from an unconditioned space (e.g., a garage), with lower temperature. Therefore, this internal partition also has thermal requirements. Table 1 also displays the thickness (*d*) of each material layer, as well as the thermal conductivity (λ) of each material. Usually the sheathing panels (e.g., gypsum plasterboard) are fixed to the LSF structure with metallic self-drilling screws. These fixing bolts were not considered in the simulations since its number is very reduced and the related punctual thermal bridge effect on the overall wall *U*-value is very reduced and, thus, could be neglected [12].

#### *2.2. Parameters for the Sensitivity Analysis*

Table 2 displays the parameters that will be evaluated in the sensitivity analysis, as well as the values to be used for each one. These models and parameters (illustrated in Figure 3) are: the thickness of the steel studs (Model I1); the clearance between steel studs (Model I2); the material and thickness of the thermal break (TB) strips (Model I3); the TB strip materials (Model I4), and; the sheathing panel materials (Model I5). The parameters and values used for each one will be briefly explained in the next paragraphs.


**Table 2.** Interior partition LSF wall: models and parameter values to be evaluated.

<sup>1</sup> TB—thermal break; <sup>2</sup> MS-R1—Acousticork (recycled rubber); <sup>3</sup> XPS—extruded polystyrene; <sup>4</sup> CBS—cold break strip (aerogel); <sup>5</sup> GPB—gypsum plasterboard; <sup>6</sup> OSB—oriented strand board.

**Figure 3.** Interior LSF partition cross-sections: (**a**) Models I1 and I2; (**b**) Models I3 and I4; (**c**) Model I5. Layers: -1 gypsum plasterboard (GPB); -2 mineral wool; -3 steel stud C90; -4 air layer; -5 TB strip.

The first parameter to be evaluated was the steel studs thickness used in the wall steel frame (Model I1). The amount of steel inside the wall structure is very relevant because metal has a very high thermal conductivity and its presence in LSF frames create a path that allow the heat to easily cross through the walls, what is known as steel thermal bridges. The reference thickness of the internal partition steel studs is 0.6 mm, which is a usual value for a non-load-bearing partition wall. Steel profiles are also modeled as 1.0, 1.2 and 1.5 mm thick, as this can be found in load-bearing LSF walls (displayed in Table 2 and illustrated in Figure 3a).

The distance between vertical steel studs is another parameter that will be evaluated (Model I2) in order to assess its relevance on the thermal behavior of the LSF internal partitions (Figure 3a). The reference wall has a distance of 600 mm between steel studs (Figure 2), which is the most used clearance given the usual 1.20 m wideness of the sheathing panels. Three more distances will be evaluated in this parametric study, namely 300, 400 and 800 mm (Table 2).

Thermal break is obtained by the insertion of an insulation material (i.e., with a low thermal conductivity), between the steel sections and the innermost layer of the wall, minimizing the heat transfer through the thermal bridges caused by the steel structure and thus, improving/reducing the thermal transmittance (*U*-value) of the wall. In this parametric study three different thicknesses for an aerogel thermal break strip will be evaluated, namely 2.5, 5.0 and 10.0 mm (Model I3 in Figure 3b).

Nowadays, several materials are available to be used as thermal break strips in LSF structures, such as recycled rubber (an environmentally friendly solution), XPS (a cheaper solution) and aerogel (a state-of-the-art insulation material with very low thermal conductivity). In this assessment three different materials were tested as thermal break strips (see Model I4 in Figure 3b), namely: recycled rubber [36], extruded polystyrene (XPS) and cold break strip (CBS) aerogel [37], as displayed in Table 2. The thicknesses of the thermal break strips are 10.0 mm and thermal conductivities are listed in Table 3.


**Table 3.** Thermal conductivities (λ ) of thermal break strips (10.0 mm thick).

<sup>1</sup> XPS—extruded polystyrene; <sup>2</sup> CBS—cold break strip.

To verify the influence of sheathing panel materials (Model I5), several configurations were modeled for the internal walls as shown in Table 2 and displayed in Figure 3c. The sheathing panels in the reference LSF wall are two gypsum plasterboard panels on each side of the steel structure. On the first parameter variation the inner gypsum plasterboard was replaced by one OSB panel in both sides of the LSF structure. On the second parameter variation, both gypsum plasterboards were replaced by two OSB panels on each side. Regarding the third parameter variation, the inner OSB panel was replaced by one XPS panel with the same thickness (12.0 mm), as illustrated in Figure 3c.

#### **3. Characterization of LSF Exterior Walls**

#### *3.1. Reference LSF Exterior Facade Wall*

The reference exterior wall is an LSF wall normally used for facades, which means that it is a wall that must be prepared to handle high gradients of environment temperature. Therefore, it has an extra thermal insulation layer which was placed on its outside surface. In this case, ETICS (external thermal insulation composite system) using EPS (expanded polystyrene) was chosen as the main insulation material (50 mm thick).

The steel structure that forms the wall frame is made of galvanized cold-formed steel studs and, different for internal walls, the thickness of the steel profile sheet is now 1.5 mm; since this kind of wall is very often a load bearing wall, C90 vertical studs were adopted. Similar to the interior LSF walls, the distance between the vertical profiles for the reference wall is 600 mm. The horizontal cross-section that shows all the layers of the reference exterior LSF wall is illustrated in Figure 4 and the specifications and characteristics of internal composition materials are detailed in Table 4.

**Figure 4.** Cross-section of an exterior LSF reference wall modeled on THERM software.


**Table 4.** Materials, thicknesses (*d* ) and thermal conductivities (λ ) of the reference exterior facade wall.

<sup>1</sup> ETICS—external thermal insulation composite system; <sup>2</sup> EPS—expanded polystyrene; <sup>3</sup> OSB—oriented strand board; <sup>4</sup> GPB—gypsum plasterboard.

#### *3.2. Parameters for Sensitivity Analysis*

The parameters and the values that were evaluated in the sensitivity analysis are displayed in Table 5 and illustrated in Figure 5.


**Table 5.** Exterior facade LSF wall: models and parameters values to be evaluated.

<sup>1</sup> TB—thermal Break; <sup>2</sup> MS-R1—Acousticork (recycled rubber); <sup>3</sup> XPS—extruded polystyrene; <sup>4</sup> CBS—cold break strip (aerogel); <sup>5</sup> GPB—gypsum plasterboard; <sup>6</sup> OSB—oriented strand board; <sup>7</sup> XPS—extruded polystyrene; <sup>8</sup> EPS—expanded polystyrene; <sup>9</sup> ETICS—external thermal insulation composite system.

E6 Thickness of EPS <sup>8</sup> ETICS <sup>9</sup> [mm] 50 0.0 30 80

XPS <sup>7</sup> Thickness [mm] - - - 12.0

The thickness of steel studs used on LSF wall steel frame is the first parameter that will be evaluated (Models E1). The reference value was 1.5 mm and the three additional thicknesses assessed were: 0.6, 1.0 and 1.2 mm (Figure 5a).

Similar to interior partition walls, for exterior facade walls the influence of clearance between the vertical steel studs were also quantified (Models E2). The reference LSF wall has 600 mm of distance between studs and the following clearances were also modeled: 300, 400 and 800 mm (Figure 5a).

Regarding the thermal break strips (Figure 5b), their thickness (Models E3) and materials (Models E4) were the same as for interior partition walls (Figure 3b).

To verify the influence of internal sheathing panels, the exterior wall model was tested in different innermost layer configurations, as shown in Table 5 and illustrated in Figure 5c (Models E5). The reference exterior facade wall has one OSB and one gypsum plasterboard panel as the innermost layer. Notice that these OSB panels are very important in load bearing walls because they give extra resistance to horizontal lateral loads [42]. On the first variation (Value 1), the sheathing panels are composed of two OSBs. For the second variation (Value 2), the internal layers are formed by two gypsum plasterboards (GPBs). In the third variation (Value 3) the OSB panel is replaced by one XPS panel with the same thickness (12.0 mm).

ETICS insulation layer thickness has a great influence on the thermal performance of the external walls. Therefore, this parameter influence will be also evaluated (Models E6). The EPS insulation thickness of the reference exterior LSF wall is 50 mm (Table 5). Three more values will be evaluated, namely: 0.0 mm (i.e., no EPS thermal insulation), 30 and 80 mm (Figure 5c).

**Figure 5.** Exterior LSF facade cross-sections: (**a**) Models E1 and E2; (**b**) Models E3 and E4; (**c**) Models E5 and E6. Layers: -1 ETICS finish; -2 EPS; -3 OSB; -4 mineral wool; -5 steel stud C90; -6 gypsum plasterboard (GPB); -7 air layer; -8 TB strip.

#### **4. Verification of 2D FEM Models**

In this section the accuracy of the two-dimensional (2D) finite element method (FEM) models used in these computations is verified. First, the numerical results are compared against the two 2D test cases presented in ISO 10211 [22] and implemented by the authors. Then, the numerical 2D results are compared with the analytical solution provided by ISO 6946 [11] for simplified wall models with homogeneous layers (i.e., without LSF structure).

#### *4.1. ISO 10211 Test Cases*

To verify the accuracy of two-dimensional calculation algorithms, the ISO 10211 [22] Annex C, provides two test cases reference values (case 1 and 2) that was applied to the 2D FEM THERM software [43] to be classified as a steady-state high precision method.

In the first test case a sketch of a half square column with 28 points placed equidistantly inside the column, for which the corresponding temperatures for each point are known, was provided. The difference between the analytical solution given for each point inside the column and the temperature computed by the algorithm should not exceed 0.1 ◦C. For all the 28 points provided, the temperatures calculated by THERM (Figure 6a) were the same, with one exception, but stayed below a 0.1 ◦C difference from the given reference temperature.

**Figure 6.** Temperature distribution obtained by the authors for the 2D test cases of ISO 10211 [22]: (**a**) test case 1; (**b**) test case 2.

For the second case, ISO 10211 requires that the difference between the temperatures calculated by the method being verified and the reference temperatures listed in the standard shall not exceed 0.1 ◦C, and the difference between the heat flow calculated and the reference value shall not exceed 0.1 W/m. The temperatures (Figure 6b) and heat flow calculated by THERM for test case 2 were exactly the same as prescribed by ISO 10211 Annex C. Notice that these results ensure not only the precision of the THERM software algorithm [43], but also the authors' expertise to use it.

#### *4.2. ISO 6946 Analytical Approach*

Another way to check the reliability of 2D FEM models is to compare the numerical results obtained with a simplified model of the same wall composed only for homogeneous layers (i.e., without the steel frame). For those walls with homogeneous layers, analytical solutions are available in ISO 6946 [11] and easy to calculate based on the thickness of each layer and on the material thermal conductivities. The input values (i.e., materials, layer thicknesses and thermal conductivities) were presented before in Table 1 (reference LSF interior partition wall) and Table 4 (reference LSF exterior facade wall). Regarding surface thermal resistances, the used values were obtained in ISO 6946 [11] for horizontal heat flow, namely 0.13 and 0.04 m2.K/W for internal (*Rsi*) and external surfaces (*Rse*), respectively.

The obtained thermal transmittance values for the analytical [11] and numerical approach (2D FEM) are displayed in Table 6. These results once again ensure the authors' skills in using THERM software for modeling [43], as well as its high accuracy.


**Table 6.** Thermal transmittances obtained for simplified wall models with homogeneous layers.

#### **5. Two-Dimensional FEM Simulations**

#### *5.1. Boundary Conditions*

As a mandatory entry to perform a numerical modeling simulation, it is necessary to define the boundary conditions to be applied on the LSF walls. Regarding temperatures, the interior temperature was set at 20 ◦C (a usual winter indoor comfort set-point temperature) and the exterior temperature was 0 ◦C (a usual design outdoor temperature for the winter season in mild climates such as in Portugal). An additional temperature of 10 ◦C was set for the partition walls 'exterior' unconditioned space; this value was considered an intermediate temperature between the adopted indoor (20 ◦C) and outdoor (0 ◦C) temperatures. Notice, that the obtained *U*-values do not depend on the chosen temperature difference between the interior and exterior environments, since this value is computed for a unitary temperature difference (i.e., per degree Celsius (◦C) or, according to international standard units, per Kelvin (K).

Regarding surface thermal resistances, the values set on ISO 6946 [11] for horizontal heat flow were used (i.e., 0.13 and 0.04 m2.K/W for internal (*Rsi*) and external resistance (*Rse*), respectively). Notice that for the interior partition walls, internal surface resistances were used in both sides of the partition (i.e., 0.13 m2.K/W).

#### *5.2. Modeling Air Layers*

The air layers inside the walls were modeled with a solid-equivalent thermal conductivity. The thermal resistance for these unventilated air-gaps were obtained in the ISO 6946 [11]. Knowing the thickness of the air-gap and dividing by its tabulated thermal resistance, the solid-equivalent thermal conductivity used in the 2D FEM numerical simulations was obtained, as displayed in Table 7.

**Table 7.** Thermal resistance and solid-equivalent thermal conductivity of air layers.


<sup>1</sup>*d*air—thickness of air layer; <sup>2</sup> *R*air—thermal resistance of air layer (from ISO 6946); <sup>3</sup> λeq—solid-equivalent thermal conductivity.

#### **6. Results and Discussion**

#### *6.1. Interior LSF Partition Walls*

Table 8 displays the obtained thermal transmittances values for interior LSF partition walls, as well as the differences in relation to the reference LSF partition wall. To facilitate the quick analysis, the same results are illustrated graphically in Figure 7.


**Table 8.** Thermal transmittance obtained for interior LSF partition walls.

<sup>1</sup> TB—thermal Break; <sup>2</sup> MS-R1—Acousticork (rubber); <sup>3</sup> XPS—extruded polystyrene; <sup>4</sup> CBS—cold break strip (aerogel); <sup>5</sup> GPB—gypsum plasterboard; <sup>6</sup> OSB—oriented strand board.

Comparing the obtained thermal transmittance value for the interior reference partition wall without steel frame (Table 6, 0.321 W/(m2.K)) and the calculated value for the reference interior LSF partition wall (Table 8, 0.449 W/(m2.K)) it is possible to verify that the LSF metallic structure increases the thermal transmittance value by about 40% (i.e., +0.128 W/(m2.K)). Notice that this large increase in the *U*-value is due to the high thermal conductivity of steel (see Table 1)—even for a very small steel thickness (only 0.6 mm)—and due to the fact that all thermal insulation (mineral wool) is bridged by the steel studs (i.e., it is not continuous).

The thickness of steel studs (Model I1) was the first parameter to be assessed (Table 8). As expected, given the higher amount of steel, when increasing the thickness from 0.6 mm (reference value) up to 1.0, 1.2 and 1.5 mm, there was an increase in the *U*-value of 5.6%, 7.3% and 9.4%, respectively.

The second parameter evaluated (Table 8) was the distance between the vertical studs (Model I2), with the reference value equal to 600 mm. The decrease of this distance to 300 and 400 mm brought an increase in the wall *U*-value of 29.2% and 14.7%, respectively. This was expected given the increased amount of steel per unit area of the LSF wall. On the other hand, the increase of this distance from 600 mm up to 800 mm brought a wall *U*-value decrease of about 6.5%.

The existence of a thermal break (TB) strip (Model I3) increases the insulation of the steel structure and consequently decreases the thermal transmittance of the wall, as expected (Table 8). This *U*-value reduction was 7.6%, 12.7% and 16.7% for an aerogel TB strip with a thickness of 2.5, 5.0 and 10.0 mm, respectively.

**Figure 7.** Thermal transmittances obtained for interior LSF partition walls.

The influence of the TB strip material (10 mm thick) was also evaluated (Model I4). Using recycled rubber (MS-R1) as a thermal break material, the *U*-value reduction was about 6.2% compared with the reference wall model without the TB strip (Table 8). For an XPS TB strip, the *U*-value decreased 11.8% and when using a material with a lower thermal conductivity (CBS aerogel) the wall thermal transmittance dropped even more (−16.7%). The former material (aerogel) provided the best results but is still quite an expensive material in comparison with the other two (recycled rubber and XPS).

Three variations according to what was previously presented for Model I5 (Table 2) were proposed for the configurations of sheathing panels. All three modeled variations for sheathing panels show better results than the reference interior LSF wall, because gypsum plasterboard has the highest thermal conductivity value, providing the uppermost *U*-value for the reference interior LSF partition wall (Table 8). The *U*-value reduction varied from 6.7% for GPB and OSB panels up to 24.7% for GPB and XPS panels. The largest reduction was expected given the very reduced thermal conductivity of XPS material (0.037 W/(m.K)) in comparison with others [i.e., GPB (0.175 W/(m.K)) and OSB (0.100 W/(m.K))].

Looking now to the extreme values obtained (see highlighted values in Table 8 and Figure 7), the highest thermal transmittance increase (+29.2%) was achieved for the Model I2V1, corresponding to a minimum clearance between steel studs (i.e., 300 mm). The lowest thermal transmittance decrease (−24.7%) was achieved for the Model I5V3, corresponding to GPB and XPS sheathing panels. These extreme *U*-values verify the great relevance of steel inside the LSF wall (Models I2), as well as the importance of providing a continuous thermal insulation layer (Model I5V3), even with a small thickness (only 12.0 mm in each side). Additionally, this XPS sheathing layer has also the advantage of being an affordable solution when compared with more expensive material (e.g., the aerogel TB strips (Models I3)).

In order to visualize and compare the temperature and heat flux distribution for these models, Figure 8 graphically displays this information. The temperature distribution in both LSF wall cross-sections is very similar (Figure 8a), and the influence of the steel stud in the temperature distribution is visible, given the high thermal conductivity from steel and consequently the thermal bridge effect. Analyzing the heat flux images (Figure 8b), the strong concentration of the heat flux around the steel stud is clear. Moreover, there are higher heat flux values for Model I2V1 (i.e., the wall with 300 mm clearance between studs), in comparison to the other model.

**Figure 8.** Temperature (**a**) and heat flux (**b**) color distribution for internal LSF wall models with the highest *U*-value increase (300 mm vertical stud distance) and decrease (XPS + GPB sheathing panels).

#### *6.2. Exterior LSF Facade Walls*

On Table 9 are shown the thermal transmittance values obtained for exterior LSF facade walls, as well as the differences between each parameter *U*-value and the reference LSF exterior wall *U*-value. For a better visualization and easier analysis for all modeled parameters, the graphic presented in Figure 9 plotted the obtained *U*-values and percentage differences.

**Figure 9.** Thermal transmittances obtained for exterior LSF facade walls.


**Table 9.** Thermal transmittances obtained for exterior LSF facade walls.

<sup>1</sup> TB—thermal break; <sup>2</sup> MS-R1—Acousticork (rubber); <sup>3</sup> XPS—extruded polystyrene; <sup>4</sup> CBS—cold break strip (aerogel); <sup>5</sup> GPB—gypsum plasterboard; <sup>6</sup> OSB—oriented strand board; <sup>7</sup> EPS—expanded polystyrene: <sup>8</sup> ETICS—external thermal insulation composite system.

To evaluate the influence of the steel structure the *U*-value for the exterior wall with homogeneous layers was compared (i.e., without steel frame, from Table 6, 0.227 W/(m2.K)) with the *U*-value computed for the complete reference exterior wall (from Table 9, 0.276 W/(m2.K)). The thermal transmittance increase due to the steel frame was 0.049 W/(m2.K) (i.e., +22%, or even only 18% for the 0.6 mm thick (Model E1V1)). Notice that this increment in the *U*-value is much lower when compared with the interior partition wall: +0.128 W/(m2.K) or +40%. This reduced relevance of the steel structure in the exterior partition wall, even having a steel thickness almost triple from the interior wall (1.5 mm instead of 0.6 mm), could be justified by the continuous thermal insulation in the ETICS (hybrid LSF structure), while in the interior partition wall all the thermal insulation is bridged by the steel frames (cold LSF structure).

Looking to the importance of the steel studs thickness in this exterior facade wall (Model E1), when this thickness is reduced from 1.5 mm to 0.6 mm there is a decrease of only 3.3% in the thermal transmittance (Table 9), while in the interior partition wall the corresponding value when there is an increase in the steel thickness from 0.6 mm up to 1.5 mm is +9.4% (Table 8). This again confirms the higher relevance of the steel structure in the interior partition wall.

The second evaluated parameter is the clearance between the vertical studs (Model E2), where the reference value is 600 mm. When decreasing the distance between the studs—300 and 400 mm—the wall *U*-value increases 17.0% and 8.3%, respectively. In contrast, when the studs where placed farther apart (800 mm) the *U*-value decreases 4.7%. As explained before, those thermal transmittance variations are closely linked with the amount of steel inside each wall configuration.

The results of the thickness variation for the CBS aerogel thermal break strip on exterior facade walls were computed using Model E3 (Table 9). As expected, by increasing the TB thickness to 2.5, 5.0 and 10.0 mm, there was a decrease of the wall *U*-value by 4.7%, 7.6% and 10.1%, respectively. Confronting these results with similar ones for the interior partition wall (7.6%, 12.7% and 16.7% in Table 8), it can be seen that the decrease in *U*-values is now considerably lower. This could be justified by the reduced importance of the steel frame in the exterior walls and consequently the effect of the TB strips is also reduced.

Evaluating the effectiveness of different materials for the 10 mm thick TB strip (Model E4), as expected, the aerogel (CBS) strip allowed the biggest reduction on wall thermal transmittance (10.1%), followed by the XPS strip (reduction of 7.2%) and recycled rubber (MS-R1) with a 4.0% decrease on the *U*-value.

Model E5 (Table 9) shows the results of changing the innermost sheathing panels material. Three different configurations were assessed. The first was composed by two panels of GPB and presented a *U*-value increase of 2.2%. The second configuration used two panels of OSB and it obtained a *U*-value reduction of 1.8% in comparison with the reference value. For the last variation, the internal layers were composed of a GPB panel and an XPS panel, having the most significant results (i.e., a reduction of 7.2%). Notice, that this last *U*-value reduction is significantly lower when compared with the one computed for the interior partition wall (−24.7%). Again, this is related with lower relevance of the steel frame thermal bridge transmission due to the existence of the ETICS continuous thermal insulation in the exterior facade wall. Therefore, the relevance of an extra continuous thermal insulation layer is also reduced.

Model E6 evaluates the influence of the EPS thickness in the ETICS. The exterior reference facade wall has 50 mm of EPS, compared with three additional values of 0, 30 and 80 mm. Clearly this was the most relevant evaluated parameter, leading to an increase of 79% in the *U*-value (Model E6V1) when there is no exterior thermal insulation and a reduction of 19.2% when the EPS thickness was increased to 80 mm (Model E6V3).

Figure 10 displays the color temperature and heat flux distribution for these two models with the most extreme *U*-value variation. Regarding the temperature distribution (Figure 10a), the influence of the continuous thermal insulation on Model E6V3 (hybrid LSF structure), with a warmer steel frame temperature in comparison with Model E6V1 (cold frame LSF structure) is very visible. Looking at the heat flux distribution (Figure 10b), as expected, the values for Model E6V1 are visually higher than Model E6V3, given the continuous thermal insulation layer in this second model.

**Figure 10.** Temperature (**a**) and heat flux (**b**) color distribution for exterior LSF wall models with the highest *U*-value increase (0 mm EPS ETICS) and decrease (80 mm EPS ETICS).

#### **7. Conclusions**

In this work, a sensitivity analysis regarding the thermal transmittance (*U*-value) was performed for two different types of lightweight steel framed (LSF) walls: interior partition and exterior facade. The numerical results were obtained by using 2D finite element method (FEM) models. The accuracy of these models was verified by comparison with ISO 10211 test cases and with ISO 6946 analytical approach.

The assessed parameters were: (1) thickness of steel studs; (2) clearance between studs; (3) thermal break strips thickness and (4) material; (5) configuration of internal sheathings panels, and; (6) thickness of EPS external thermal insulation composite system (ETICS), only for the external facade wall. The results of this parametric study were compared to a reference interior partition LSF wall, with a *U*-value equal to 0.449 W/(m2.K) and to a reference exterior facade LSF wall, with a *U*-value equal to 0.276 W/(m2.K). Regarding the obtained results, notice that the percentages of *U*-value change are high, but the absolute differences are rather small in most cases.

The interior partition LSF wall showed higher *U*-values and a greater influence of the internal steel structure on the wall thermal transmittance. This was expected given the high thermal conductivity of steel and the absence of a continuous thermal insulation on interior partition walls potentiates the thermal bridges' effects on the LSF structure, resulting in higher *U*-values. Nevertheless, higher heat flux through the interior walls enables other evaluated parameters to have a greater influence on wall thermal transmittance (e.g., clearance between steel studs (up to +29.2%) and XPS sheathing panel (down to −24.7%)).

The thickness augment of the metallic structure increased the thermal transmittance of the interior wall up to +9.4% (1.5 mm thick). The use of thermal break (TB) strips reduced the *U*-value of the interior wall down to −16.7% (10 mm thick aerogel strip). The use of different materials in the TB strip was also assessed. The *U*-value reduction depends on the thermal conductivity of the material used in the TB strip: −6.2% for recycled rubber, −11.8% for XPS and −16.7% for aerogel.

For the exterior facade LSF walls, the existence of an ETICS continuous thermal insulation on the outer side reduces the heat flux through the wall, particularly through the steel frame, resulting in a lower wall *U*-value and decreasing the importance of other evaluated parameters. In fact, the major and the minor *U*-value increment changed the thickness of the EPS insulation ETICS layer (i.e., an augment of +79.0% when there is no EPS (0.0 mm thick) and a decrease of −19.2% for 80 mm EPS thickness). Notice that the reference wall has 50 mm of EPS ETICS.

Decreasing the steel thickness (1.5 mm) to 0.6 mm reduced the *U*-value to only −3.3% (−0.009 W/(m2.K)). Notice that in the interior partition wall the absolute *<sup>U</sup>*-value increased, when the steel thickness changed from 0.6 mm up to 1.5 mm, and was more than four times higher (i.e., +0.042 W/(m2.K), showing the lower importance of the steel structure in this exterior facade LSF wall.

When changing the distance between the vertical studs from 600 mm to half (300 mm) and doubling the amount of steel, the *U*-value increased only +17.0% (+0.047 W/(m2.K)). Notice that in the interior partition wall the absolute *U*-value increase was almost the triple (i.e., +0.131 W/(m2.K)).

The use of aerogel thermal break strips with different thicknesses (up to 10 mm) reduced the *<sup>U</sup>*-value down to <sup>−</sup>10.1% (−0.028 W/(m2.K)). Notice that in the interior wall this absolute *<sup>U</sup>*-value reduction was more than double (i.e., <sup>−</sup>0.075 W/(m2.K)). Using a 10 mm thick TB strip with different materials (rubber, XPS and aerogel) decreased the *<sup>U</sup>*-value to about <sup>−</sup>4.0% (−0.011 W/(m2.K)), <sup>−</sup>7.2% (−0.020 W/(m2.K)) and <sup>−</sup>10.1% (−0.028 W/(m2.K)), respectively. Notice that in the interior wall these *<sup>U</sup>*-value reductions were quite higher: <sup>−</sup>6.2% (−0.028 W/(m2.K)), <sup>−</sup>11.8% (−0.053 W/(m2.K)) and <sup>−</sup>16.7% (−0.075 W/(m2.K)), respectively.

The use of different inner sheathing panels (GPB, OSB and XPS) led to a *U*-value variation down to <sup>−</sup>7.2% (−0.020 W/(m2.K)) for the XPS/GPB panels. Notice that in the interior LSF wall this absolute *<sup>U</sup>*-value reduction was much more relevant [i.e., more than five times higher (−0.111 W/(m2.K))]. This was due not only to the absence of any continuous thermal insulation in the reference interior LSF wall, but also to the fact that in this case the two wall sides were updated with an XPS sheathing panel

(one in each side), while in the exterior facade only the inner wall surface was updated with an XPS sheathing panel.

For further related research work, the authors intend to perform laboratorial experimental measurements in similar interior and exterior LSF walls. These measurements will be useful to ensure the reliability of the numerical simulations and validate the numerical models. In order to consider and evaluate the relevance of some three-dimensional (3D) effects in the thermal performance of these interior and exterior LSF walls, the authors also intend to perform some 3D FEM simulations in a complementary future research work. Another predicted future work is to evaluate the cost-benefit of these thermal performance improvement measures and the provided energy efficiency benefits for an LSF building.

**Author Contributions:** All the authors participated equally to this work.

**Funding:** This work was financed by FEDER funds through the Competitivity Factors Operational Programme—COMPETE and by national funds through FCT—Foundation for Science and Technology within the scope of the project POCI-01-0145-FEDER-032061.

**Acknowledgments:** The authors also want to thank the support provided by the following companies: Pertecno, Gyptec Ibérica, Volcalis, Sotinco, Kronospan, Hukseflux and Hilti.

**Conflicts of Interest:** The authors declare no conflicts of interest.

#### **References**


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*Article*
