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Impact of Shape Factor on Energy Demand, CO2 Emissions and Energy Cost of Residential Buildings in Cold Oceanic Climates: Case Study of South Chile

Department of Construction Engineering and Management, School of Engineering, Pontificia Universidad Católica de Chile, Santiago 7820436, Chile
UC Energy Research Center, Pontificia Universidad Católica de Chile, Santiago 7820436, Chile
Civil Engineer, Valdivia 5090000, Chile
Author to whom correspondence should be addressed.
Sustainability 2021, 13(17), 9491;
Submission received: 2 July 2021 / Revised: 15 August 2021 / Accepted: 19 August 2021 / Published: 24 August 2021


The increase in energy consumption that occurs in the residential sector implies a higher consumption of natural resources and, therefore, an increase in pollution and a degradation of the ecosystem. An optimal use of materials in the thermal envelope, together with efficient measures in the passive architectural design process, translate into lower energy demands in residential buildings. The objective of this study is to analyse and compare, through simulating different models, the impact of the shape factor on energy demand and CO2 emissions depending on the type of construction solution used in the envelope in a cold oceanic climate in South Chile. Five models with different geometries were considered based on their relationship between exposed surface and volume. Additionally, three construction solutions were chosen so that their thermal transmittance gradually complied with the values required by thermal regulations according to the climatic zone considered. Other parameters were equally established for all simulations so that their comparison was objective. Ninety case studies were obtained. Research has shown that an appropriate design, considering a shape factor suitable below 0.767 for the type of cold oceanic climate, implies a decrease in energy demand, which increased when considering architectural designs in the envelope with high values of thermal resistance.

Graphical Abstract

1. Introduction

Energy consumption is reflected in the gross domestic product (GDP) of a country. There is a close relationship between GDP and the required electrical energy, which increases every year at the country level and is sustained [1]. The world has created a legal framework to respond to the need to provide energy in the context of sustainable development, given the threats [2]. As a first initiative in the regulatory framework, in 1997, 37 industrialised countries and the European Union established the Kyoto Protocol [3]. A building, especially in the operation stage, can be a great potential consumer of energy, and only using measures and strategies in the design stage which involve insignificant increases in construction costs and significant benefits in energy demand (or energy need [4]) and emission reduction can significantly affect its energy consumption [5].
The energy efficiency of a building depends not only on the thermal properties of the materials in the envelope but also on its shape; the orientation and distribution of spaces, windows and closing ratios; interior temperature; the façade colour and protection against solar radiation [6]. All these parameters influence the passive design of a building, depending on the climatic zone in which it is located. The volumetric impact on a building at the design stage produces better efficiency during the life cycle of the home, reducing energy and natural resource consumption [7,8]. To optimise architectural designs for thermal envelopes, it is essential to study the climate of the building area in detail [9,10].
Compactness is a characteristic of the volume of the building; it is used to adjust the exposed envelope, depending on the useful area, as much as possible [11]. This geometric relationship is represented by the shape factor (SFv). Buildings with a high SFv value are less compact, resulting in higher heating energy demands in cold climates with poorly sunny winters [12,13]. The impact of SFv varies considerably for buildings with different properties in the thermal envelope and weather conditions [14]. A study of the impact of different thermal envelopes in buildings showed that more significant benefits are obtained by using materials with better thermal quality in the envelope when there is more exposed surface per m2 of useful surface [15]. However, for a correct architectural design, a multitude of variables such as orientation, wind and lighting, among others, must be taken into account.
Globally, Chile has an essential representation of cities located in cold oceanic climates [16]. In Chile, one of the most significant increases in energy demand occurred between 2008 and 2014, reaching 18.43% in the commercial, public and residential sectors [17]. Most of this increase (53.7%) was renewable energy from biomass. Furthermore, the imported energy sources are primarily crude oil, natural gas and coal, with 51.8%, 17.0% and 31.2%, respectively. This marked dependence on scarce and non-renewable fuels suggests future problems in energy supply [18]. Additionally, the high carbon emissions resulting from using these fossil fuels generate major environmental and health problems, mainly climate change caused by greenhouse gas emissions [19].
In Chile, the Ordenanza General de Urbanismo y Construcciones (OGUC) (General Ordinance of Urbanism and Constructions) has incorporated the Regulación Térmica (RT) (Thermal Regulation) [20] to be able to classify the energy demand of a building through an energy certification programme, taking into account the different climatic zones (Chilean regulations use the synonym thermal zones). In the specific case of Chile, various investigations were carried out to specify the different climatic zones [21,22], including making projections of future climate change [23] and seeing its application in different fields of study, such as heritage [24]. For cold climates, as in southern Chile, compact buildings with good insulation and infiltration control are recommended. However, care should be taken when using a very low SFv, as this can cause ventilation problems and less use of natural light [25].
Considering this background, the objective of this study is to analyse the influence of buildings’ thermal envelope SFv on energy demand and CO2 emissions in oceanic cold climates by simulating different solutions for optimisation. To carry out this main objective, the following specific objectives were developed: (i) Modelling buildings with different SFv; (ii) Applying different architectural designs to the models; (iii) Simulation in different cities in southern Chile; and (iv) Analysing the results. The scope of this study is limited to SFv in climatic zones of southern Chile with different constructive solutions. A multitude of additional variables can be studied in future works for a complete analysis of complex architectural designs.

2. Materials and Methods

2.1. Shape Factor

As the surface of the building in contact with the outside is more significant, there will be more energy exchanges, which may be beneficial or unfavourable in certain types of climates [25], depending on whether the building seeks to conserve the heat inside it or dissipate it to the environment.
SFv is a simple equation that relates the enveloping surface to the volume (Equation (1)) [26].
S F v = S e V  
where the SFv is directly related to the heating energy demand in a dwelling, Se is the surface area of the exposed envelope and V is the habitable volume. The higher the SFv (for an identical habitable volume), the higher the heating energy demand of the dwelling.

2.2. Climate Data and Climatic Zones

To validate the optimal SFv in buildings in cold oceanic climates, as shown in Figure 1, capitals of the southern zone of Chile were chosen—Concepción, Temuco, Valdivia, Puerto Montt, Coyhaique and Punta Arenas. These cities generally represent the climatic characteristics that affect the buildings. According to the study carried out by Sarricolea et al. [16] on the climatic regionalisation of continental Chile, all capitals studied using the Köppen–Geiger climate classification have climate C with an oceanic or marine influence. Table 1 shows the climatic zone and climatological station of each of the different cities. In Chile, the regulation that regulates the climatic zones of the country is the OGUC [20], which divides the territory into 7 zones—where Zone 1 is the warmest and Zone 7 is the coldest.
Climatological data for the cities were extracted in *.epw format by the software Meteonorm 7 [27]. Table 1 shows the meteorological stations from which the data were obtained, with radiation periods between 1991 and 2010 and temperature periods between 2000 and 2009.

2.3. CO2 Emissions and Energy Costs of Fuels

As shown in Table 2, the theoretical values of CO2 emissions and the lower heating value (LHV) for different fuels were calculated according to data obtained from different official sources [28,29]. Similarly, the cost of using different types of fuels is the price collected from official reports from the Chilean government [30] and other international studies [31,32,33]. For the present study, only the cost of fuel has been taken into account. The cost of equipment installation and maintenance has not been considered. The equipment used were boilers with a thermal efficiency of 90% and an outlet water temperature of 80 °C for heating [19]. For electricity, instead, an electrical system was used.

2.4. Case Studies

To carry out the present study, five buildings with different SFv and three architectural designs in each of the six capitals of the southern regions of Chile were studied, thus obtaining a total of 90 case studies. The buildings and the energy simulations were modelled following the Building Information Modelling (BIM) and Building Performance Analysis (BPA) methodology through Autodesk© software [34] based on the calculation methodology of ISO 52016-1:2017 [4], ISO 52017-1:2017 [35] and ISO 13789:2017 [36]. All models used the same calculation parameters, with 20 m2/person, an 18–22 °C temperature range, 0.5 air renewals/hour, person 1680 Wh daily heat gain and 2.29 Wh/m2 equipment thermal gain. The characteristics of the different case studies are shown below.

2.4.1. Building Geometry

Table 3 and Figure 2 show the five residential building models (M1, M2, M3, M4 and M5) created. Each model varies from the highest to the lowest SFv. All models have a square plan with an increase of 10 m of façade between them, a 3 m height between floors and a flat roof.
However, it is necessary to clarify that the building models used do not correspond to actual buildings. These models are theoretical, and all the buildings have common characteristics, with the SFv variable to be compared between them. These theoretical models have the same SFv as more common buildings. For example, on the one hand, M3 maintains the same SFv as a two-floor building with a 9.3 × 9.3 m floor dimension. On the other hand, M5 maintains the same SFv as a six-floor building with a 21 × 21 m floor dimension.

2.4.2. Architectural Designs for the Thermal Envelopes

Figure 3 and Table 4 and Table 5 show the three thermal envelope construction solutions (S1, S2 and S3) for the models described in the previous section. The ratio of window and door area will be 26.67% on all models. According to the material used and the thickness of each layer, each solution has different thermal transmittance (U-value).

3. Results

The results obtained in the models for (i) energy demand, (ii) CO2 emissions and (iii) energy cost are shown below.

3.1. Energy Demand

Figure 4 and Figure 5 show that the total annual energy demand varied from 37.20 kWh/m2 in M5, located in the city of Concepción with an S3, to 348.98 kWh/m2 in M1, in Punta Arenas, with an S1. Only 2.38% of the total energy is required to cool the building, considering all the architectural designs and climatic zones. Detailed results of heating and cooling demands, in all models with different architectural designs in the six cities, are shown in Table A1, Table A2, Table A3, Table A4, Table A5 and Table A6 in the Appendix A.
The results show that the city of Concepción (climatic zone 4) was the one that had the lowest required total energy demand under any of the proposed construction solutions and established models. In contrast, Punta Arenas (climatic zone 7) had the highest total energy demand.
Regarding the design characteristics of the envelope in the different construction solutions considered, S1 is the solution with the highest energy demand in all the models and areas studied, due to the high value of thermal transmittance.
Figure 6 shows the impact of SFv on the annual energy demand in each city, depending on the type of construction solution used. The maximum variation in demand (considering M1 and M5 for all cities) was: S1 between 135.30% and 198.70%; S2 between 162.89% and 235.12%; and S3 between 174.29% and 244.71%.

3.2. CO2 Emissions

Due to the large amount of data obtained, only the results of S2 will be shown, since it is the most representative of all, considering, in turn, a representative city of each climatic zone—Concepción (4), Valdivia (5), Puerto Montt (6) and Punta Arenas (7).
Figure 7 shows the CO2 emissions generated due to energy demand. The energy used to cool the buildings was assumed as electric for all models. However, the energy source used for heating was variable, based on the values presented in Table 1. For all climatic zones, the least optimal is the exclusive use of electricity, independent of the SFv of the dwelling. However, using biomass (wood and pellets) produces low emissions, mainly due to the neutral emission factor [19].
A 160.62 to 235.12% increase in CO2 emissions between climatic zones 4 and 7 was observed when using any heating system. In turn, implementing an S1 to an S3 in the thermal envelope reduced CO2 emissions between 22.74% and 56.67% for all energy options.

3.3. Energy Cost

The energy cost of these alternatives is represented in Figure 8. In this figure, the annual cost of heating and cooling the buildings is shown depending on the SFv and the alternative used, expressed in USD/m2, based on the values presented in Table 2. The use of propane gas as fuel for heating is the most expensive option of all in any area studied; on the contrary, the use of pellets is the most economical.
A 160.43 to 236.25% increase in cost between climate zones 4 and 7, when using any heating system, was similar to what happened in emissions. Implementing an S1 to an S3 in the thermal envelope reduces the cost for all energy options between 22.74% and 56.72%.
Propane gas has had a wide variation in cost between 12.52% and 236.25% for all the climatic zones analysed. The rate of decrease in cost varies depending on the climatic zone. In Concepción its cost drop fluctuates from 6.00 to 26.09% between each SFv interval considered; in Punta Arenas, this range was between 4.99% and 17.49%.
The cost of the heating system was reduced between 52.16% and 63.30% using M1 and M5, respectively, when implementing S1, 34.23 to 48.60% with an S2 and 27.82% and 42.65% with an S3.

4. Discussion

In the present study, implementing S2 represents a 19.68 to 48.01% decrease in required power demand compared to S1; and a 22.74 to 56.16% decrease in consumption compared to the S3, depending on the city where the building is located and the SFv. Comparing our results with the study carried out by Danielski et al. [14], similar results are obtained, where the slope between the total energy demand per square meter and the SFv increases when using a construction solution with less thermal resistance in the envelope.
The impact on energy demand from reducing SFv was studied in various investigations. In Italy, different energy models, with form factors between 0.54 and 0.78, were analysed in different cities, reaching 34.09 to 43.14% differences in energy demand [37]. In Lithuania, a 33.77% variation in the required energy was obtained by decreasing the SFv from 1.35 to 1.17 [8]. In Sweden, heating demand was decreased between 18.00% and 20.00% by reducing the SFv from 1.70 to 1.01 in different cities [14].
Additionally, when comparing the energy demand of M1 and M5, 27.82 to 62.95% reductions were reached depending on the city and the construction system considered. The impact of SFv was less in the coldest city, Punta Arenas, where consumption only decreased by 27.82 to 52.16%. In contrast, in Concepción, energy savings fluctuated between 42.57% and 62.95%.
Whenever the SFv decreases, so do the difference in emissions by improving the architectural design. When the SFv is reduced from 1.067 to 0.302: implementing an S1 caused a CO2 decrease between 52.16% and 63.23%; while with an S3, they decrease from 27.82 to 42.64%. With these and similar data from other studies [15], it has been shown that more significant benefits are obtained by improving the thermal resistance of the envelope when there is a higher relation between the exposed surface and the m2 of the surface of the building.
Finally, in Chile there are other studies on the form factor in buildings and its influence on energy demand. For example, Vásquez et al. [38] investigated with the SFv of office buildings in the city of Santiago, Chile. They conclude that the SFv is essential in architectural design along with other variables such as solar radiation, light, wind or the immediate context.

5. Conclusions

This research showed an appropriate design considering a SFv suitable for cold oceanic climates, which implied a decrease in energy demand and CO2 emissions. The main conclusions derived from this research are the following:
  • The architectural designs with high thermal transmittance values may require from 129.44 to 227.67% of the energy demand of the same building after implementing a solution with a low U-value. Energy demand is widely affected by the weather where housing is located; maximum variations between 135.30 and 244.71% exist for the same SFv and architectural design, depending on the city where it is located.
  • CO2 emissions depend directly on the climatic zone where the building is located and the fuel used. For all cities, using biomass in heating systems has the lowest emission and cost values, as opposed to what happens when using electricity for heating. Differences in CO2 emissions from 7.43 to 235.12% can be found between the different climatic zones for the same model. Similarly, the cost of the heating system is reduced by between 31.81 and 32.95% when switching from a fossil fuel, such as propane, to a renewable fuel, such as biomass in the form of pellets.
  • Overall, the impact of SFv, on both energy demand and CO2 emissions, is greater when architectural designs with a high thermal transmittance value are implemented, reducing energy demand between 22.75% and 56.16%, depending on the area located. Based on the analysis, it is highly recommended to design buildings with a SFv below 0.767 for cold oceanic climates, such as in the southern zone of Chile. Among the values shown, energy demand and CO2 emissions tend to stabilise for all the climatic zones and construction solutions studied, with only 9.03% maximum differences in the energy requirement for heating and 10.37% in CO2 emissions.
These results are fully extrapolated to any area with climatic conditions similar to a cold oceanic climate. This study has considered the SFv as the main variable, although for a comprehensive architectural design other variables must be taken into account, such solar exposure, wind orientation and passive design characteristics.

Author Contributions

Conceptualisation, M.C.; methodology, M.C. and D.C.; software, D.C.; validation, M.C.; formal analysis, M.C. and D.C.; investigation, M.C. and D.C.; resources, M.C.; data curation, D.C.; writing—original draft preparation, M.C. and D.C.; visualisation, M.C. and D.C.; project administration, M.C.; funding acquisition, M.C. All authors have read and agreed to the published version of the manuscript.


This research was funded by Agencia Nacional de Investigación y Desarrollo (ANID) of Chile, through the projects ANID FONDECYT 11160524 and ANID FONDECYT 1201052.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

Appendix A

Table A1. Energy demand—Concepción.
Table A1. Energy demand—Concepción.
Monthly Energy Demand [kWh/m2]Annual Energy Demand [kWh/m2]
S = solution; M = model; H = heating; C = cooling.
Table A2. Energy demand—Temuco.
Table A2. Energy demand—Temuco.
Monthly Energy Demand [kWh/m2]Annual Energy Demand [kWh/m2]
S = solution; M = model; H = heating; C = cooling.
Table A3. Energy demand—Valdivia.
Table A3. Energy demand—Valdivia.
Monthly Energy Demand [kWh/m2]Annual Energy Demand [kWh/m2]
S = solution; M = model; H = heating; C = cooling.
Table A4. Energy demand—Puerto Montt.
Table A4. Energy demand—Puerto Montt.
Monthly Energy Demand [kWh/m2]Annual Energy Demand [kWh/m2]
S = solution; M = model; H = heating; C = cooling.
Table A5. Energy demand—Coyhaique.
Table A5. Energy demand—Coyhaique.
Monthly Energy Demand [kWh/m2]Annual Energy Demand [kWh/m2]
S = solution; M = model; H = heating; C = cooling.
Table A6. Energy demand—Punta Arenas.
Table A6. Energy demand—Punta Arenas.
Monthly Energy Demand [kWh/m2]Annual Energy Demand [kWh/m2]
S = solution; M = model; H = heating; C = cooling.


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Figure 1. Location map of Chile.
Figure 1. Location map of Chile.
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Figure 2. Graphic detail of SFv models.
Figure 2. Graphic detail of SFv models.
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Figure 3. Graphic detail of the architectural designs.
Figure 3. Graphic detail of the architectural designs.
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Figure 4. Annual energy demand of the models. Concepción, Temuco and Valdivia.
Figure 4. Annual energy demand of the models. Concepción, Temuco and Valdivia.
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Figure 5. Annual energy demand of the models. Puerto Montt, Coyhaique and Punta Arenas.
Figure 5. Annual energy demand of the models. Puerto Montt, Coyhaique and Punta Arenas.
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Figure 6. Annual energy demand versus SFv.
Figure 6. Annual energy demand versus SFv.
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Figure 7. Annual emissions depending on the fuel used.
Figure 7. Annual emissions depending on the fuel used.
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Figure 8. Annual energy cost depending on the fuel used.
Figure 8. Annual energy cost depending on the fuel used.
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Table 1. Climatic zones and meteorological station of the regional capitals of southern Chile.
Table 1. Climatic zones and meteorological station of the regional capitals of southern Chile.
CityRegionMeteorological Station DataClimatic Zone OGUCTemperature —Summer [°C]Temperature—Winter [°C]Annual Global Radiation [kWh/m2]
ConcepciónBio-BioGlobal station416.2 ± 0.711.1 ± 0.31729.1 ± 26.4
TemucoAraucaníaManquehe515.7 ± 0.79.7 ± 0.61552.8 ± 47.5
ValdiviaLos RíosPichoy515.4 ± 0.810.0 ± 0.41509.5 ± 55.9
Puerto MonttLos LagosEl Tepu613.7 ± 0.59.0 ± 0.21335.9 ± 72.9
CoyhaiqueAysén del General Carlos Ibáñez del CampoTeniente V712.4 ± 1.05.4 ± 0.91343.2 ± 76.5
Punta ArenasMagallanes y la
Antártida Chilena
Global station710.0 ± 0.64.8 ± 0.81101.3 ± 29.9
Table 2. Emissions, LHV and cost of different fuels.
Table 2. Emissions, LHV and cost of different fuels.
FuelCO2 Emissions [kgCO2/kWh]LHVCost [USD/kWh]
Electricity (Chile)0.346-0.107
Natural gas0.2049.771 kWh/m30.095
Propane gas0.25413.131 kWh/m30.192
Biomass (wood)Neutral2.759 kWh/kg0.083
Biomass (pellet)Neutral5.010 kWh/kg0.061
Gasoil0.28711.939 kWh/kg0.082
Table 3. SFv of the models.
Table 3. SFv of the models.
ModelFloor Dimensions
[m × m]
Floor Space
Number of FloorsVolume [m3]Exposed Surface [m2]SFv
M110 × 1010013003201.067
M220 × 204001120010400.867
M340 × 4016001480036800.767
M430 × 309002540025200.467
M550 × 502500322,50068000.302
Table 4. Characteristics of the envelope materials.
Table 4. Characteristics of the envelope materials.
Materiale [m]λ [W/(m × K)]R [(m2 × K)/W]
S1Interior wood lining—Insigne pine 1/2 × 4″0.0130.1040.122
Unventilated vertical air chamber0.1000.7140.140
Exterior wood lining—Tinglado dry pine 5 × 3/4″0.0190.1040.183
U = 1.625 [W/(m2 × K)]0.132
S2Cement mortar0.0251.4000.018
Craft brick—285 × 143 × 90 mm—Stonework 20 mm0.1430.6640.215
Cement mortar0.0251.4000.018
Expanded polyethylene with EIFS system—d = 20 kg/m30.0300.0380.781
U = 0.832 [W/(m2 × K)]0.223
S3Thermal stucco0.0250.2200.114
Reinforced concrete0.2001.6300.123
Expanded polyethylene with EIFS system—d = 20 kg/m30.1000.0382.604
U = 0.332 [W/(m2 × K)]0.325
S1Plasterboard—d = 700 kg/m30.0130.2600.048
Wooden beam—Insigne pine 3 × 4″0.1020.1040.977
Non-ventilated vertical air chamber0.1000.7690.130
Fibrocement roof—d = 920 kg/m30.0100.2200.045
U = 0.746 [W/(m2 × K)]0.224
S2Plasterboard—d = 700 kg/m30.0130.2600.048
Wooden beam—Insigne pine 3 × 4″0.1020.1040.977
Expanded polyethylene with EIFS system—d = 20 kg/m30.0600.0381.563
Fibrocement roof—d = 920 kg/m30.0100.2200.045
U = 0.361 [W/(m2 × K)]0.184
S3Plasterboard—d = 700 kg/m30.0130.2600.048
Reinforced concrete slab0.1201.6300.074
Expanded polyethylene with EIFS system—d = 20 kg/m30.1500.0383.906
Fibrocement roof—d = 920 kg/m30.0100.2200.045
U = 0.237 [W/(m2 × K)]0.293
Table 5. Doors and windows.
Table 5. Doors and windows.
MaterialU [W/(m2 × K)]Visual
DoorsHollow wood2.326
S3WindowsLow emission double-glazed2.2150.760.65
DoorsWooden frame—Double-glazed—Glaze against door1.936
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Carpio, M.; Carrasco, D. Impact of Shape Factor on Energy Demand, CO2 Emissions and Energy Cost of Residential Buildings in Cold Oceanic Climates: Case Study of South Chile. Sustainability 2021, 13, 9491.

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Carpio M, Carrasco D. Impact of Shape Factor on Energy Demand, CO2 Emissions and Energy Cost of Residential Buildings in Cold Oceanic Climates: Case Study of South Chile. Sustainability. 2021; 13(17):9491.

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Carpio, Manuel, and David Carrasco. 2021. "Impact of Shape Factor on Energy Demand, CO2 Emissions and Energy Cost of Residential Buildings in Cold Oceanic Climates: Case Study of South Chile" Sustainability 13, no. 17: 9491.

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