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Thermal analysis of roofs with thermal insulation layer and reflective coatings in subtropical and equatorial climate regions in Brazil
Energy and Buildings 84 (2014) 466–474
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Thermal analysis of roofs with thermal insulation layer and reflective coatings in subtropical and equatorial climate regions in Brazil J.P. Brito Filho a,∗ , T.V. Oliveira Santos b a Programa de Pós-graduac¸ão em Engenharia Mecânica, Universidade Federal de Pernambuco, Av. Acadêmico Hélio Ramos, S/N, CEP 50.740-530, Recife, PE, Brazil b Instituto Federal de Educac¸ão, Ciência e Tecnologia, Av. Prof. Luiz Freire, 500, CEP 50.740-540, Recife, PE, Brazil
a r t i c l e
i n f o
Article history: Received 3 April 2014 Received in revised form 22 August 2014 Accepted 23 August 2014 Available online 30 August 2014 Keywords: Cool roof Selective coating Urban heat island Thermal insulation layer
a b s t r a c t This article presents a comparative analysis of the thermal performance of large metal roofs like those found on exhibition halls, airports, and malls located in subtropical and equatorial climates regions in Brazil. The focus of the investigation was the suitability of the use of white paints, selective coatings, and thermal insulation layers in those regions. The survey was based on a model of heat transfer through a roof where solar radiation and ambient air-temperature were studied as functions of time. The results showed that in cities with an equatorial climate, the roof with the thermal insulation layer and selective coating is the best option because it saves more energy and reduces the effects of urban heat island (UHI). Otherwise, in cities with a subtropical climate, the application of white paint on a roof without a thermal insulation layer is the best solution for both a reduction in energy consumption and a decrease in the formation of UHI. © 2014 Elsevier B.V. All rights reserved.
1. Introduction The ambient air-temperature in large cities increases in part from solar radiation being absorbed by the urban construction and by the exposed soil at a higher rate than what is reflected and emitted. This fact raises the average temperature of the city, creating a temperature difference between the urban area and the countryside. For instance, on very hot days some Brazilian’ cities have an average temperature of 12 K warmer than the surrounding areas. This is the urban heat island (UHI) effect. The contribution to UHI from urban construction comes mainly from pavement and building roofs. A building component that deserves more attention is the roof, especially in non-residential construction such as malls, factories, and exhibition halls. These buildings are characterized as having large roof surfaces (e.g. flat roofs) in comparison to their external wall surfaces. Also observe that roof surfaces are always exposed to solar radiation between sunrise and sunset. Therefore, they are responsible for a considerable part of the thermal load of the building and consequently the electrical energy consumption required for cooling. According to Brazil’s Mining and Energy Ministry [1],
∗ Corresponding author. Tel.: +55 81 21267795; fax: +55 81 21268215. E-mail addresses: [email protected], [email protected] (J.P. Brito Filho), [email protected] (T.V.O. Santos). http://dx.doi.org/10.1016/j.enbuild.2014.08.042 0378-7788/© 2014 Elsevier B.V. All rights reserved.
the electrical energy consumption of buildings in 2012 accounted for 26.3% of the total electrical energy used in the country. It is estimated that at least one quarter of this amount is used for cooling. In a previous work, Brito Filho et al. [2] showed that while it is possible to reduce heat gain through roofs by adding an evengreater thermal insulation layer, a more effective and adequate way is to combine a traditional thermal insulation layer with reflective surface coatings. This approach makes it possible to balance two competing effects, namely: cooling energy saving (i.e. lower the heat flux across the roof) and mitigation of UHI (i.e. lower the roof’s external surface temperature). The climatic data used in [2] was for the city of São Paulo (latitude 23◦ 30 S, longitude 46◦ 37 W, and altitude of 792 m). The analysis was based on a model of heat transfer that includes solar radiation and external ambient airtemperature as a function of time, convection and radiation heat transfer, roof thickness, and thermophysical and optical properties of the materials. The dependent variables of the model are the time-dependent outside surface temperature of the roof and the heat flux that crosses it. The applicability of the model equations is for comparison of the thermal performance between roof configuration taking into account their impacts on UHI and heat flux that reach the indoor environment. The objective of the present study is to extend the research [2] in two ways. First, showing the versatility of the mathematical model proposed regarding the analysis of a roof’s thermal behavior. Secondly, applying the model to show the thermal effect of white
J.P. Brito Filho, T.V.O. Santos / Energy and Buildings 84 (2014) 466–474
Nomenclature Latin letters h heat transfer coefficient (W m−2 K−1 ) Hh monthly average daily global solar radiation for a horizontal surface (MJ m−2 ) thermal conductivity (W m−1 K−1 ) k L thickness (m) q heat flux through the roof (W m−2 ) solar radiation on the plane of the roof (W m−2 ) qs R thermal resistance (K W−1 ) t time (h) T temperature (◦ C) v wind speed (m s−1 ) Greek letters absorptivity of the roof ˛ thickness (m) ı ε hemispherical emissivity of the roof reflectivity of the roof Stefan–Boltzmann constant (W m−2 K−4 ) Subscripts external ambient air a ave monthly average daily convection c e external face of the roof (facing the sun) i internal face of the roof (facing the interior ambient) infrared region of the thermal radiation spectrum ir min monthly average daily minimum monthly average daily maximum max o internal ambient air radiation r s solar radiation
paints, selective coatings, and a thermal insulation layer for the first time on the external surface temperature of roofs and the heat flux through them in subtropical and equatorial climates regions in Brazil, and that the effectiveness of a particular roof’s configuration will depend on the site’s climate conditions. In forthcoming research, this model will be extended to include a building electrical energy saving estimation taking into account the roof type and climate region in Brazil. The next section presents a literature review aiming to show case studies that support the findings reported and what is missing that this research intends to fill in. In particular: (a) the two relevant dependent variables of the roof heat transfer problem are the external surface temperature and heat flux because they are responsible for UHI and energy saving, respectively; (b) our model reproduces the qualitative results obtained by other authors, i.e. the effect of thermal insulation, paints, and selective coatings; and (c) the role of climate on roof thermal performance. 2. Literature review Heat transfer in roofs has been investigated in many technological fields due to its importance in the thermal load of a building and the mitigation of the UHI effect. Current technologies of energy conservation and mitigation of UHI range from the use of shading objects such as trees [3], covering roofs with a layer of plants [4–6] and even more sophisticated solutions such as roof ponds [7] and roof water sprayings [8]. Another powerful technology is based on the use of reflective roof coatings. Several articles have reported energy savings and
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the mitigation of the UHI effect that results from the application of reflective coatings on buildings. Sproul et al. [9] reported an economic comparison of white, green, and dark colored flat roofs in the USA using a 50-year life cycle cost analysis. The authors found that relative to dark colored roofs, white roofs provide a 50-year net savings of $25/m2 and green roofs have a negative net savings of $71/m2 . Additionally, the annualized cost premium of white roofs compared to green roofs is small. Santamouris [10] conducted a comprehensive literature review of green and reflective roof technologies to mitigate UHI and improve comfort levels in urban environments, taking into account over 180 published studies. The author reported that when green roofs are applied on a city scale, the average ambient air-temperature is reduced to between 0.3 and 3 K. Otherwise, considering a global increase of the city’s albedo, the expected mean decrease of the average ambient air-temperature is close to 0.3 K per 0.1 rise of the albedo, while the corresponding average decrease of the peak ambient air-temperature is close to 0.9 K. However, when only cool roofs are taking into account, the expected depression rate of the average urban ambient air-temperature varies between 0.1 and 0.33 K per 0.1 increase of the roofs albedo with a mean value close to 0.2 K. Rosado et al. [11] experimentally investigated two similar single family, single story homes (initial albedo of 0.51 and of 0.07) for one year which were built in Fresno, California (USA) aiming to assess the benefits of cool roofs. The authors calculated the cool roof energy savings in the cooling and heating seasons. They reported an annual cooling, heating fuel, and heating fan site energy savings per unit ceiling area of 2.82 kWh/m2 (26%), 1.13 kWh/m2 (4%), and 0.0294 kWh/m2 (3%), respectively. Rosenfeld et al. [12] found that the electricity consumption savings were 40% in a house in Sacramento, California (USA) with the walls and roof painted white. The albedo rose from 0.18 to 0.73. Simpson and McPherson [13] carried out a study in Tucson, Arizona (USA) based on three ¼-scale model buildings. They found that white roofs were up to 20 K cooler than that of gray or silver roofs, and up to 30 K cooler than brown roofs. Additionally, the authors estimate an air-conditioning energy reduction by approximately 5% for the house with a white-colored roof compared to the houses with gray and silver-colored roofs. Parker and Barkaszi Jr. [14] experimentally investigated the cooling energy savings provided by reflective roofing coatings in nine occupied homes in Florida (USA). They verified an air-conditioning energy reduction average of 19% after application of high-reflectivity coating. Akbari et al. [15] also reported a significant peak power and cooling energy savings (up to 52%) and a reduction of the daily peak surface temperature of the roof (33–42 K) from high-reflectivity coatings on six California (USA) buildings. Akbari et al. [16] monitored peak power and cooling energy savings from high-reflectivity coatings on two school bungalows and on one house in Sacramento, California (USA). These authors found that changing the reflectivity of the roof from 0.18 to 0.73 might result in seasonal savings for the house of 2.2 kWh/d and of 3.1 kWh/d for the school bungalows. Romeo and Zinzi [17] documented the results of the application of a cool, white paint with high solar reflectance and thermal emissivity on a 700 m2 roof in an office/laboratory building in Trapani, Sicily (Italy). The authors observed a roof surface temperature reduction of up to 20 K, and a cooling energy demand decrease of 54%. Santamouris et al. [18] observed that for a group of representative buildings in Athens (Greece), the UHI intensity exceeded 10 K and increased the cooling load by about 100%, while the peak electricity load may have tripled. Bretz and Akbari [19] reported that cooling energy savings of 10–70% have been achieved by applying high-albedo coatings to residential buildings in California (USA) and Florida (USA). Kolokotroni et al. [20] analyzed the impact from the application of a reflective paint on a flat roof in a naturally ventilated office building in London (UK). The simulations show that the
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Table 1 Climatic data for the cities of Curitiba and Manaus. Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Curitiba Ta,ave (◦ C) Ta,max (◦ C) Ta,min (◦ C) Hh (MJ m−2 )
19.6 25.6 15.8 5.38
19.9 25.8 16.3 4.63
19.0 24.9 15.4 4.28
16.7 22.3 12.8 3.39
14.6 21.1 10.2 2.89
12.2 18.3 7.8 2.72
12.8 19.4 8.1 2.86
14.0 20.9 9.2 3.3
15.0 21.3 10.8 3.61
16.5 22.6 12.5 4.58
18.2 24.5 14.0 4.97
19.3 25.4 15.4 5.11
Manaus Ta,ave (◦ C) Ta,max (◦ C) Ta,min (◦ C) Hh (MJ m−2 )
26.1 30.5 23.1 4.19
26.0 30.4 23.1 3.97
26.1 30.6 23.2 4.28
26.3 30.7 23.3 4.14
26.3 30.8 23 4.28
26.4 31.0 22.7 4.75
26.5 31.3 23 4.64
27 32.6 23.5 4.94
27.5 32.9 23.7 4.94
27.6 32.8 23.7 5.11
27.3 32.1 23.5 4.42
26.7 31.3 23.3 4.19
cooling demand decreases, the heating demand increases and the total energy savings vary between 1 and 8.5% relative to an albedo of 0.1 for the same conditions. Synnefa et al. [21] conducted an experimental investigation in Athens (Greece) with fourteen reflective commercial paints. The surfaces were monitored over three months in a region where the local temperature stood about 10 K above the temperature of the suburb. The maximum temperature reduction achieved was 4 K during the day and 2 K overnight. As expected, the white paints showed a superior performance in comparison with aluminum pigment and gray paint. Hildebrandt et al. [22] measured a daily energy savings in the range of 17–39% in three high albedo retrofitted roofs in Sacramento, California (USA). Jo et al. [23] documented an outdoor surface temperature difference between conventional and cool roof surfaces of 8–14 K in a building located in Phoenix, Arizona (USA). Akridge [24] observed an energy savings of 28% for a school building in Georgia (USA) after the application of a white acrylic coating on an unpainted galvanized roof. Konopacki et al. [25] monitored air-conditioning electricity use and roof surface temperature of three buildings in California (USA). The roof surface temperature on hot sunny summer afternoons drops from 79.5 to 48.9 ◦ C by increasing the roof albedo on average of 0.20–0.60. Summertime daily average air-conditioning electricity use was reduced by 18%, 13%, and 2% in each building. Parker et al. [26] carried out a series of experiments in eleven homes in Florida (USA) with the roof color changed in midsummer. The average cooling energy savings was 19%. Mastrapostoli et al. [27] analyzed the contribution of a new cool fluorocarbon coating in the reduction of energy demand for cooling. The authors reported a 120% increase of the roof’s albedo from the application of this new cool material with a cooling load reduction of 73%. Xu et al. [28] monitored a building in Hyderabad, Andhra Pradesh (India) before and after a roof whitening of a previously black roof and measured an annual energy savings of 20–22 kWh/m2 , corresponding to a 14–26% drop in cooling energy. The application of white coatings to uncoated concrete roofs resulted in annual savings of 13–14 kWh/m2 of roof area, corresponding to cooling energy savings of 10–19%. To the best of our knowledge, the effectiveness of white paints, selective coatings, and thermal insulation layer use on roofs in equatorial and subtropical climate regions in Brazil were not examined.
Table 2 Thermophysical properties of the materials. Materials
ε
k (W m−1 K−1 )
L (m)
Galvanized steel Polyurethane Coating White paint
0.3 × 0.9 0.75
0.3 × 0.9 0.9
45 0.0186 0.00345 –
0.0005 0.05 0.0003 –
and an average annual temperature of 16.48 ◦ C. On the other hand, Manaus is a city with a humid equatorial climate with average annual incident solar radiation of 4.49 kWh m−2 day−1 and average annual temperature of 26.54 ◦ C. Table 1 presents the monthly average (Ta,ave ) and monthly averaged maximum (Ta,max ) and minimum (Ta,min ) external ambient air-temperatures between 1961 and 1990 for both cities [29] in addition to the monthly average daily global solar radiation for a horizontal surface (Hh ) for each month of the year between 1978 and 1990 [30].
3.2. Concepts of roofs investigated Fig. 1 shows the types of horizontal flat roofs investigated. Roof type 1 corresponds to a roof without the thermal insulation layer, while type 2 corresponds to a roof with the thermal insulation layer. The three subtypes distinguish the external surface conditions as follows: (a) surface without treatment (εe,ir = e,s = 0.30); (b) surface painted white (εe,ir = 0.75, e,s = 0.90); and (c) surface with selective coating treatment (εe,ir = e,s = 0.90). In Brazil, one of the most used lightweight metal roofs are composed first of one galvanized steel foil and second of two galvanized steel foils with a polyurethane layer in between. Table 2 shows the thermophysical properties and thicknesses of the roof’s materials. The values in the third row of the table correspond to a white, commercial, ceramic-filled elastomeric coating [31]. In this study, the thickness of white paint was negligible.
3. Mathematical model and simulation process 3.1. Weather data In order to use real-world weather data in the simulations, two Brazilian cities were chosen: Curitiba (latitude 25◦ 25 S, longitude 49◦ 16 W, and altitude of 945 m) is located in a subtropical region, and Manaus (latitude 3◦ 10 S, longitude 60◦ 01 W, and altitude of 100 m) is located very close to the equator. Curitiba presents an average annual solar radiation incidence of 3.97 kWh m−2 day−1
Fig. 1. Types of roofs investigated.
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Fig. 2. Average annual hourly external surface temperature (a) and the average annual hourly heat flux through a roof (b) without the thermal insulation layer as a function of daytime.
3.3. Heat transfer process in the roof The outside surface of the roof is exposed to solar radiation. Part of this incident radiation is reflected and a part is absorbed. The absorbed fraction of the solar radiation is first transferred to the outside environment by convection and radiation, then by conduction through the roof to the internal ambient. The heat reaching the interior surface is then transferred to the internal ambient air by convection and radiation.
infrared radiation of this surface are ˛e,s and εe,ir , respectively. On the other hand, the internal surface of the roof with temperature Ti exposed to the internal ambient air at a temperature T0 , arbitrarily held constant during the day at 22 ◦ C, has an emissivity for infrared radiation εi,ir . The energy-balance equations on the free surfaces of the roof are: ˛e,s qs (t) +
Ta (t) − Te (t) Te (t) − Ti (t) = Re Rroof
(1)
and 3.4. Governing equations The outside surface of the roof at temperature Te is in touch with the outside ambient air at temperature Ta . Both temperatures are time-varying. The surface is exposed to time-varying solar radiation qs as well. The absorptivity for solar radiation and emissivity for
Te (t) − Ti (t) T (t) − T0 = i . Rroof Ri
(2)
The thermal resistances Re , Ri and Rroof are given as: Re =
1 , hce + hre
(3)
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Fig. 3. Average annual daily external surface temperature of the roof without the thermal insulation layer (a) and with the thermal insulation layer (b) as a function of reflectivity.
Ri =
1 hci + hri
and
(4)
ı k
Rroof =
+
ı k
˛e,s qs (t) + hce [Ta (t) − Te (t)] + εe,ir [Ta4 (t) − Te4 (t)]
(coating) +
ı k
where (=5.67 × 10−8 W m−2 K−4 ) is the Stefan–Boltzmann constant, yields:
(metal sheet)
(insulation layer) +
=
ı k
Te (t) − Ti (t) Rroof
(8)
and (metal sheet).
(5)
In Eqs. (3) and (4), hce and hci are the external and internal convection heat transfer coefficients, respectively, and hre and hri the radiation heat transfer coefficients from the surface to the external and internal ambient, respectively. In Eq. (5), ı and k are thickness and thermal conductivity, respectively. Substituting Eqs. (3) and (4) into Eqs. (1) and (2) and taking into account that hre [Te (t) − Ta (t)] = εe,ir [Te4 (t) − Ta4 (t)],
(6)
hri [Ti (t) − T0 ] = εi,ir [Ti4 (t) − T04 ],
(7)
hci [Ti (t) − T0 ] + εi,ir [Ti4 (t) − T04 ] =
Te (t) − Ti (t) . Rroof
(9)
In these equations, the view factor between the roof and the sky is equal to 1 (the roof is horizontally positioned) and for simplicity the sky temperature is assumed equals to the external ambient airtemperature. Therefore, the unknowns are Te and Ti . The convection coefficients of heat transfer were determined by the following correlation [32]: hc = 5.5 + 3.8v,
(10)
where v is the wind speed. This correlation is valid for v ≤ 5 m s−1 and attends to the purpose of this comparative study.
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Fig. 4. Maximum average annual daily external surface temperature of the roof as a function of reflectivity.
The heat flux that reaches the internal ambient can be defined in a straightforward way as: q(t) =
Te (t) − Ti (t) . Rroof
(11)
Summarizing, Eqs. (8) and (9) give the surfaces temperature of the roof and Eq. (11) the heat flux through it. According to the second law of thermodynamics, the internal ambient air-temperature and the heat flux directly affect the energy consumption cooling of the building. 3.5. Simulation process The unknowns Ta (t) and qs (t) in Eqs. (8) and (9) are obtained by carrying out a numerical calculation following these steps: (a) Evaluation of Ta (t) Method: The instantaneous ambient air-temperature for a typical day of a given month is obtained by representing the function Ta (t) as a Fourier series of the second order. For the Fourier series coefficients calculation, we used the procedure described by Lyra [33]. Martins [34] and Brito Filho and Fraidenraich [35] later used this method. Input data: Measured monthly average (Ta,ave ) and monthly averaged maximum (Ta,max ) and minimum (Ta,min ) external ambient air-temperatures. (b) Evaluation of qs (t) Method: The instantaneous irradiance was obtained starting with the hemispherical irradiation following the standard procedures proposed by Collares-Pereira and Rabl [36] and the recommended average day for each month proposed by Klein [37]. Input data: Monthly average daily global solar radiation for a horizontal surface (Hh ), latitude and longitude of Curitiba and Manaus. (c) Evaluation of Rroof Input data: ı and k. (d) Evaluation of Te (t) Input data: Ta (t), qs (t), e,s , εe,ir , hce , hci , T0 and Rroof . (e) Evaluation of q(t) Input data: Te (t), Ti (t) and Rroof .
4. Results and analysis This section presents the thermal performance results of the analyzed lightweight roofs. The two dependent variables of the mathematical model Te and q are depicted using two different average values: annual hourly and annual daily. Fig. 2 shows the average annual hourly external surface temperature (a) and the average annual hourly heat flux through a roof (b) without the thermal insulation as a function of time. As it is shown, the effect of applying selective coatings is evident, i.e. a strong reduction of the external surface temperature (a), with implications on UHI, and the heat flux (b), with direct implications on the building thermal load. High reflectivity and emissivity reduce heat gain from the sun and heat conduction through the roof. What deserves special attention is the possibility of a negative heat flux in the morning on certain days. Fig. 3 shows the average annual daily external surface temperature of the roof without the thermal insulation layer (a) and with the thermal insulation layer (b) as a function of its external surface reflectivity. One can see that the thermal insulation layer increases the external surface temperature and thus the contribution to UHI. It is evidenced that for both cities, the higher the reflectivity (i.e. less heat gain from the sun), the lower the external surface temperature. These figures also show that when the emissivity increases maintaining constant reflectivity, the external surface temperature decreases, but not as strongly as by increasing reflectivity while maintaining constant emissivity. Fig. 4 presents the maximum average annual daily external surface temperature of the roof as a function of its external surface reflectivity and validated these results. The results shown in this figure reinforce those shown in Fig. 3. Fig. 5 depicts the average annual daily heat flux that crosses the roof without the thermal insulation layer (a) and with the thermal insulation layer (b) as a function of its external surface reflectivity. It is evident that when a thermal insulation layer is added to the roof, the heat flux is cut down considerably. Thus, the thermal insulation layer is a very efficient way to reduce building heat gain. It is clear that the higher the reflectivity, the lower the heat transferred to the indoor environment. According to the second law of thermodynamics, less electrical energy is needed for cooling. Moreover, these simulations also show that to reduce heat flux, increasing
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J.P. Brito Filho, T.V.O. Santos / Energy and Buildings 84 (2014) 466–474 Table 3 Percentage reduction in the average annual daily values for each roof configuration when compared with the roof without both thermal insulation layer and painting.
Fig. 5. Average annual daily heat flux that crosses the roof without the thermal insulation layer (a) and with the thermal insulation layer (b) as a function of reflectivity.
External surface temperature
Heat flux
Manaus
Curitiba
Manaus
Curitiba
Roof without thermal insulation layer White painted 17.74 Selective coating 22.61
13.71 17.62
50.42 64.27
104.69 134.49
Roof with thermal insulation layer 2.95 White painted 11.26 Selective coating
14.34 21.45
97.42 98.08
100.17 101.17
reflectivity is much more effective than increasing emissivity. Therefore, the use of paints with high reflectivity in cities with equatorial climates such as Manaus is very important. On the other hand, very high reflectivity values in cities with subtropical climates (such as Curitiba), can reverse the heat flux direction across the roof. Fig. 6 shows the maximum average annual daily heat flux that crosses the roof as a function of its external surface reflectivity. As before, the results shown in this figure reinforce those shown in Fig. 5. Table 3 shows the percentage reduction in the average annual daily values of external surface temperature and heat flux for each roof configuration when compared to the roof without both thermal insulation layers and paint (i.e. a roof of galvanized steel). In Manaus (equatorial climates), roofs with both thermal insulation layers and a selective coating is the best option because it contributes to the reduction of UHI and heat gain. In this configuration, the average annual daily external surface temperature has a reduction of 11.26% and the heat flux of 98.08% compared to the case of a simple roof (only galvanized steel sheet). If one cannot apply a selective coating, the application of a white paint reduces the average annual daily external surface temperature by 2.95% and the mean average annual daily heat flux by 97.42%. Otherwise, if a selective coating is applied to a roof without the thermal insulation layer, the average annual daily external surface temperature decreases 22.61% and the mean daily annual heat flux decreases 64.27%. If no thermal insulation layer and selective coatings are applied, a common white paint reduces the average annual daily external surface temperature by 17.74% and the mean daily annual heat flux by 50.42%.
Fig. 6. Maximum average annual daily heat flux that crosses the roof as a function of reflectivity.
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In Curitiba (subtropical climates), white painted roofs with or without the thermal insulation layer have almost the same performance for temperature and heat flux (compare 14.34% with 13.71% and 100.17% with 104.69%, respectively). One can gain a large reduction of the average annual daily external surface temperature using roofs with the thermal insulation layer and selective coating (21.45%). Otherwise, on roofs without the thermal insulation layer, but with selective coating, a large average annual daily heat flux reduction can be achieved (134.49%). 5. Conclusions and future research The main objective of our research is to identify the most adequate type of roof for a number of given climate regions in Brazil, taking into consideration environmental and energy saving benefits. The focus of the investigation reported in the present manuscript is the suitability of using white paints, selective coatings, and thermal insulation layers on large metal roofs in buildings located in subtropical and equatorial climate regions. This manuscript utilizes a heat transfer model aiming to compare the thermal performance of different roofs’ configurations. With this model, the external surface temperature of the roof Te and the heat flux q through it can be determined. The input data are the roof’s geometry and materials, the monthly average daily global solar radiation for a horizontal surface and the monthly average daily, monthly average daily minimum and monthly average daily maximum temperatures for the location. The two dependent variables Te and q are important to evaluate the roof’s contribution to UHI formation, and energy savings for acclimatization, respectively. Roofs with thermal insulation layer are recommended, mainly because they reduce the heat flux that reaches the internal environment, and consequently the building’s thermal load. However, the thermal insulation layer increases at the same time the external surface temperature of the roof, leading to higher air-temperatures in the surroundings and in doing so contributes to form UHI. In equatorial climates regions, this disadvantage can be greatly reduced by adding white paints or selective coatings on the roof external surface. Furthermore, white paints or selective coatings can decrease the difference in the temperature level of the roof during the day and the night protecting the surface against thermal shock. In subtropical climate regions, an alternative to the thermal insulation layer are white paints. Nevertheless, roofs covered with white paints with very high reflectivity or even with low emissivity values or selective coatings can reverse the heat flux direction across it. In further researches, experimental studies will be carried out in Curitiba and Manaus based on reduced scale models building with the selected roof type. Furthermore, a cost benefit analysis will be done to determine the return on investment for the specific cool roof. Based on the acquired knowledge, we will expand the research to other Brazilian climatic zones (tropical zone, semi-arid zone and highland tropical zone). Acknowledgments The authors express their thanks to the Brazilian National Council for Scientific and Technological Development (CNPq) agency for the financial support given to this research (Proc. 48039/2007-0). References [1] Anuário estatístico de energia elétrica, Ministério de Minas e Energia, Brazil, 2013.
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Thermal analysis of roofs with thermal insulation layer and reflective coatings in subtropical and equatorial climate regions in Brazil J.P. Brito Filho a,∗ , T.V. Oliveira Santos b a Programa de Pós-graduac¸ão em Engenharia Mecânica, Universidade Federal de Pernambuco, Av. Acadêmico Hélio Ramos, S/N, CEP 50.740-530, Recife, PE, Brazil b Instituto Federal de Educac¸ão, Ciência e Tecnologia, Av. Prof. Luiz Freire, 500, CEP 50.740-540, Recife, PE, Brazil
a r t i c l e
i n f o
Article history: Received 3 April 2014 Received in revised form 22 August 2014 Accepted 23 August 2014 Available online 30 August 2014 Keywords: Cool roof Selective coating Urban heat island Thermal insulation layer
a b s t r a c t This article presents a comparative analysis of the thermal performance of large metal roofs like those found on exhibition halls, airports, and malls located in subtropical and equatorial climates regions in Brazil. The focus of the investigation was the suitability of the use of white paints, selective coatings, and thermal insulation layers in those regions. The survey was based on a model of heat transfer through a roof where solar radiation and ambient air-temperature were studied as functions of time. The results showed that in cities with an equatorial climate, the roof with the thermal insulation layer and selective coating is the best option because it saves more energy and reduces the effects of urban heat island (UHI). Otherwise, in cities with a subtropical climate, the application of white paint on a roof without a thermal insulation layer is the best solution for both a reduction in energy consumption and a decrease in the formation of UHI. © 2014 Elsevier B.V. All rights reserved.
1. Introduction The ambient air-temperature in large cities increases in part from solar radiation being absorbed by the urban construction and by the exposed soil at a higher rate than what is reflected and emitted. This fact raises the average temperature of the city, creating a temperature difference between the urban area and the countryside. For instance, on very hot days some Brazilian’ cities have an average temperature of 12 K warmer than the surrounding areas. This is the urban heat island (UHI) effect. The contribution to UHI from urban construction comes mainly from pavement and building roofs. A building component that deserves more attention is the roof, especially in non-residential construction such as malls, factories, and exhibition halls. These buildings are characterized as having large roof surfaces (e.g. flat roofs) in comparison to their external wall surfaces. Also observe that roof surfaces are always exposed to solar radiation between sunrise and sunset. Therefore, they are responsible for a considerable part of the thermal load of the building and consequently the electrical energy consumption required for cooling. According to Brazil’s Mining and Energy Ministry [1],
∗ Corresponding author. Tel.: +55 81 21267795; fax: +55 81 21268215. E-mail addresses: [email protected], [email protected] (J.P. Brito Filho), [email protected] (T.V.O. Santos). http://dx.doi.org/10.1016/j.enbuild.2014.08.042 0378-7788/© 2014 Elsevier B.V. All rights reserved.
the electrical energy consumption of buildings in 2012 accounted for 26.3% of the total electrical energy used in the country. It is estimated that at least one quarter of this amount is used for cooling. In a previous work, Brito Filho et al. [2] showed that while it is possible to reduce heat gain through roofs by adding an evengreater thermal insulation layer, a more effective and adequate way is to combine a traditional thermal insulation layer with reflective surface coatings. This approach makes it possible to balance two competing effects, namely: cooling energy saving (i.e. lower the heat flux across the roof) and mitigation of UHI (i.e. lower the roof’s external surface temperature). The climatic data used in [2] was for the city of São Paulo (latitude 23◦ 30 S, longitude 46◦ 37 W, and altitude of 792 m). The analysis was based on a model of heat transfer that includes solar radiation and external ambient airtemperature as a function of time, convection and radiation heat transfer, roof thickness, and thermophysical and optical properties of the materials. The dependent variables of the model are the time-dependent outside surface temperature of the roof and the heat flux that crosses it. The applicability of the model equations is for comparison of the thermal performance between roof configuration taking into account their impacts on UHI and heat flux that reach the indoor environment. The objective of the present study is to extend the research [2] in two ways. First, showing the versatility of the mathematical model proposed regarding the analysis of a roof’s thermal behavior. Secondly, applying the model to show the thermal effect of white
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Nomenclature Latin letters h heat transfer coefficient (W m−2 K−1 ) Hh monthly average daily global solar radiation for a horizontal surface (MJ m−2 ) thermal conductivity (W m−1 K−1 ) k L thickness (m) q heat flux through the roof (W m−2 ) solar radiation on the plane of the roof (W m−2 ) qs R thermal resistance (K W−1 ) t time (h) T temperature (◦ C) v wind speed (m s−1 ) Greek letters absorptivity of the roof ˛ thickness (m) ı ε hemispherical emissivity of the roof reflectivity of the roof Stefan–Boltzmann constant (W m−2 K−4 ) Subscripts external ambient air a ave monthly average daily convection c e external face of the roof (facing the sun) i internal face of the roof (facing the interior ambient) infrared region of the thermal radiation spectrum ir min monthly average daily minimum monthly average daily maximum max o internal ambient air radiation r s solar radiation
paints, selective coatings, and a thermal insulation layer for the first time on the external surface temperature of roofs and the heat flux through them in subtropical and equatorial climates regions in Brazil, and that the effectiveness of a particular roof’s configuration will depend on the site’s climate conditions. In forthcoming research, this model will be extended to include a building electrical energy saving estimation taking into account the roof type and climate region in Brazil. The next section presents a literature review aiming to show case studies that support the findings reported and what is missing that this research intends to fill in. In particular: (a) the two relevant dependent variables of the roof heat transfer problem are the external surface temperature and heat flux because they are responsible for UHI and energy saving, respectively; (b) our model reproduces the qualitative results obtained by other authors, i.e. the effect of thermal insulation, paints, and selective coatings; and (c) the role of climate on roof thermal performance. 2. Literature review Heat transfer in roofs has been investigated in many technological fields due to its importance in the thermal load of a building and the mitigation of the UHI effect. Current technologies of energy conservation and mitigation of UHI range from the use of shading objects such as trees [3], covering roofs with a layer of plants [4–6] and even more sophisticated solutions such as roof ponds [7] and roof water sprayings [8]. Another powerful technology is based on the use of reflective roof coatings. Several articles have reported energy savings and
467
the mitigation of the UHI effect that results from the application of reflective coatings on buildings. Sproul et al. [9] reported an economic comparison of white, green, and dark colored flat roofs in the USA using a 50-year life cycle cost analysis. The authors found that relative to dark colored roofs, white roofs provide a 50-year net savings of $25/m2 and green roofs have a negative net savings of $71/m2 . Additionally, the annualized cost premium of white roofs compared to green roofs is small. Santamouris [10] conducted a comprehensive literature review of green and reflective roof technologies to mitigate UHI and improve comfort levels in urban environments, taking into account over 180 published studies. The author reported that when green roofs are applied on a city scale, the average ambient air-temperature is reduced to between 0.3 and 3 K. Otherwise, considering a global increase of the city’s albedo, the expected mean decrease of the average ambient air-temperature is close to 0.3 K per 0.1 rise of the albedo, while the corresponding average decrease of the peak ambient air-temperature is close to 0.9 K. However, when only cool roofs are taking into account, the expected depression rate of the average urban ambient air-temperature varies between 0.1 and 0.33 K per 0.1 increase of the roofs albedo with a mean value close to 0.2 K. Rosado et al. [11] experimentally investigated two similar single family, single story homes (initial albedo of 0.51 and of 0.07) for one year which were built in Fresno, California (USA) aiming to assess the benefits of cool roofs. The authors calculated the cool roof energy savings in the cooling and heating seasons. They reported an annual cooling, heating fuel, and heating fan site energy savings per unit ceiling area of 2.82 kWh/m2 (26%), 1.13 kWh/m2 (4%), and 0.0294 kWh/m2 (3%), respectively. Rosenfeld et al. [12] found that the electricity consumption savings were 40% in a house in Sacramento, California (USA) with the walls and roof painted white. The albedo rose from 0.18 to 0.73. Simpson and McPherson [13] carried out a study in Tucson, Arizona (USA) based on three ¼-scale model buildings. They found that white roofs were up to 20 K cooler than that of gray or silver roofs, and up to 30 K cooler than brown roofs. Additionally, the authors estimate an air-conditioning energy reduction by approximately 5% for the house with a white-colored roof compared to the houses with gray and silver-colored roofs. Parker and Barkaszi Jr. [14] experimentally investigated the cooling energy savings provided by reflective roofing coatings in nine occupied homes in Florida (USA). They verified an air-conditioning energy reduction average of 19% after application of high-reflectivity coating. Akbari et al. [15] also reported a significant peak power and cooling energy savings (up to 52%) and a reduction of the daily peak surface temperature of the roof (33–42 K) from high-reflectivity coatings on six California (USA) buildings. Akbari et al. [16] monitored peak power and cooling energy savings from high-reflectivity coatings on two school bungalows and on one house in Sacramento, California (USA). These authors found that changing the reflectivity of the roof from 0.18 to 0.73 might result in seasonal savings for the house of 2.2 kWh/d and of 3.1 kWh/d for the school bungalows. Romeo and Zinzi [17] documented the results of the application of a cool, white paint with high solar reflectance and thermal emissivity on a 700 m2 roof in an office/laboratory building in Trapani, Sicily (Italy). The authors observed a roof surface temperature reduction of up to 20 K, and a cooling energy demand decrease of 54%. Santamouris et al. [18] observed that for a group of representative buildings in Athens (Greece), the UHI intensity exceeded 10 K and increased the cooling load by about 100%, while the peak electricity load may have tripled. Bretz and Akbari [19] reported that cooling energy savings of 10–70% have been achieved by applying high-albedo coatings to residential buildings in California (USA) and Florida (USA). Kolokotroni et al. [20] analyzed the impact from the application of a reflective paint on a flat roof in a naturally ventilated office building in London (UK). The simulations show that the
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Table 1 Climatic data for the cities of Curitiba and Manaus. Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Curitiba Ta,ave (◦ C) Ta,max (◦ C) Ta,min (◦ C) Hh (MJ m−2 )
19.6 25.6 15.8 5.38
19.9 25.8 16.3 4.63
19.0 24.9 15.4 4.28
16.7 22.3 12.8 3.39
14.6 21.1 10.2 2.89
12.2 18.3 7.8 2.72
12.8 19.4 8.1 2.86
14.0 20.9 9.2 3.3
15.0 21.3 10.8 3.61
16.5 22.6 12.5 4.58
18.2 24.5 14.0 4.97
19.3 25.4 15.4 5.11
Manaus Ta,ave (◦ C) Ta,max (◦ C) Ta,min (◦ C) Hh (MJ m−2 )
26.1 30.5 23.1 4.19
26.0 30.4 23.1 3.97
26.1 30.6 23.2 4.28
26.3 30.7 23.3 4.14
26.3 30.8 23 4.28
26.4 31.0 22.7 4.75
26.5 31.3 23 4.64
27 32.6 23.5 4.94
27.5 32.9 23.7 4.94
27.6 32.8 23.7 5.11
27.3 32.1 23.5 4.42
26.7 31.3 23.3 4.19
cooling demand decreases, the heating demand increases and the total energy savings vary between 1 and 8.5% relative to an albedo of 0.1 for the same conditions. Synnefa et al. [21] conducted an experimental investigation in Athens (Greece) with fourteen reflective commercial paints. The surfaces were monitored over three months in a region where the local temperature stood about 10 K above the temperature of the suburb. The maximum temperature reduction achieved was 4 K during the day and 2 K overnight. As expected, the white paints showed a superior performance in comparison with aluminum pigment and gray paint. Hildebrandt et al. [22] measured a daily energy savings in the range of 17–39% in three high albedo retrofitted roofs in Sacramento, California (USA). Jo et al. [23] documented an outdoor surface temperature difference between conventional and cool roof surfaces of 8–14 K in a building located in Phoenix, Arizona (USA). Akridge [24] observed an energy savings of 28% for a school building in Georgia (USA) after the application of a white acrylic coating on an unpainted galvanized roof. Konopacki et al. [25] monitored air-conditioning electricity use and roof surface temperature of three buildings in California (USA). The roof surface temperature on hot sunny summer afternoons drops from 79.5 to 48.9 ◦ C by increasing the roof albedo on average of 0.20–0.60. Summertime daily average air-conditioning electricity use was reduced by 18%, 13%, and 2% in each building. Parker et al. [26] carried out a series of experiments in eleven homes in Florida (USA) with the roof color changed in midsummer. The average cooling energy savings was 19%. Mastrapostoli et al. [27] analyzed the contribution of a new cool fluorocarbon coating in the reduction of energy demand for cooling. The authors reported a 120% increase of the roof’s albedo from the application of this new cool material with a cooling load reduction of 73%. Xu et al. [28] monitored a building in Hyderabad, Andhra Pradesh (India) before and after a roof whitening of a previously black roof and measured an annual energy savings of 20–22 kWh/m2 , corresponding to a 14–26% drop in cooling energy. The application of white coatings to uncoated concrete roofs resulted in annual savings of 13–14 kWh/m2 of roof area, corresponding to cooling energy savings of 10–19%. To the best of our knowledge, the effectiveness of white paints, selective coatings, and thermal insulation layer use on roofs in equatorial and subtropical climate regions in Brazil were not examined.
Table 2 Thermophysical properties of the materials. Materials
ε
k (W m−1 K−1 )
L (m)
Galvanized steel Polyurethane Coating White paint
0.3 × 0.9 0.75
0.3 × 0.9 0.9
45 0.0186 0.00345 –
0.0005 0.05 0.0003 –
and an average annual temperature of 16.48 ◦ C. On the other hand, Manaus is a city with a humid equatorial climate with average annual incident solar radiation of 4.49 kWh m−2 day−1 and average annual temperature of 26.54 ◦ C. Table 1 presents the monthly average (Ta,ave ) and monthly averaged maximum (Ta,max ) and minimum (Ta,min ) external ambient air-temperatures between 1961 and 1990 for both cities [29] in addition to the monthly average daily global solar radiation for a horizontal surface (Hh ) for each month of the year between 1978 and 1990 [30].
3.2. Concepts of roofs investigated Fig. 1 shows the types of horizontal flat roofs investigated. Roof type 1 corresponds to a roof without the thermal insulation layer, while type 2 corresponds to a roof with the thermal insulation layer. The three subtypes distinguish the external surface conditions as follows: (a) surface without treatment (εe,ir = e,s = 0.30); (b) surface painted white (εe,ir = 0.75, e,s = 0.90); and (c) surface with selective coating treatment (εe,ir = e,s = 0.90). In Brazil, one of the most used lightweight metal roofs are composed first of one galvanized steel foil and second of two galvanized steel foils with a polyurethane layer in between. Table 2 shows the thermophysical properties and thicknesses of the roof’s materials. The values in the third row of the table correspond to a white, commercial, ceramic-filled elastomeric coating [31]. In this study, the thickness of white paint was negligible.
3. Mathematical model and simulation process 3.1. Weather data In order to use real-world weather data in the simulations, two Brazilian cities were chosen: Curitiba (latitude 25◦ 25 S, longitude 49◦ 16 W, and altitude of 945 m) is located in a subtropical region, and Manaus (latitude 3◦ 10 S, longitude 60◦ 01 W, and altitude of 100 m) is located very close to the equator. Curitiba presents an average annual solar radiation incidence of 3.97 kWh m−2 day−1
Fig. 1. Types of roofs investigated.
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Fig. 2. Average annual hourly external surface temperature (a) and the average annual hourly heat flux through a roof (b) without the thermal insulation layer as a function of daytime.
3.3. Heat transfer process in the roof The outside surface of the roof is exposed to solar radiation. Part of this incident radiation is reflected and a part is absorbed. The absorbed fraction of the solar radiation is first transferred to the outside environment by convection and radiation, then by conduction through the roof to the internal ambient. The heat reaching the interior surface is then transferred to the internal ambient air by convection and radiation.
infrared radiation of this surface are ˛e,s and εe,ir , respectively. On the other hand, the internal surface of the roof with temperature Ti exposed to the internal ambient air at a temperature T0 , arbitrarily held constant during the day at 22 ◦ C, has an emissivity for infrared radiation εi,ir . The energy-balance equations on the free surfaces of the roof are: ˛e,s qs (t) +
Ta (t) − Te (t) Te (t) − Ti (t) = Re Rroof
(1)
and 3.4. Governing equations The outside surface of the roof at temperature Te is in touch with the outside ambient air at temperature Ta . Both temperatures are time-varying. The surface is exposed to time-varying solar radiation qs as well. The absorptivity for solar radiation and emissivity for
Te (t) − Ti (t) T (t) − T0 = i . Rroof Ri
(2)
The thermal resistances Re , Ri and Rroof are given as: Re =
1 , hce + hre
(3)
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Fig. 3. Average annual daily external surface temperature of the roof without the thermal insulation layer (a) and with the thermal insulation layer (b) as a function of reflectivity.
Ri =
1 hci + hri
and
(4)
ı k
Rroof =
+
ı k
˛e,s qs (t) + hce [Ta (t) − Te (t)] + εe,ir [Ta4 (t) − Te4 (t)]
(coating) +
ı k
where (=5.67 × 10−8 W m−2 K−4 ) is the Stefan–Boltzmann constant, yields:
(metal sheet)
(insulation layer) +
=
ı k
Te (t) − Ti (t) Rroof
(8)
and (metal sheet).
(5)
In Eqs. (3) and (4), hce and hci are the external and internal convection heat transfer coefficients, respectively, and hre and hri the radiation heat transfer coefficients from the surface to the external and internal ambient, respectively. In Eq. (5), ı and k are thickness and thermal conductivity, respectively. Substituting Eqs. (3) and (4) into Eqs. (1) and (2) and taking into account that hre [Te (t) − Ta (t)] = εe,ir [Te4 (t) − Ta4 (t)],
(6)
hri [Ti (t) − T0 ] = εi,ir [Ti4 (t) − T04 ],
(7)
hci [Ti (t) − T0 ] + εi,ir [Ti4 (t) − T04 ] =
Te (t) − Ti (t) . Rroof
(9)
In these equations, the view factor between the roof and the sky is equal to 1 (the roof is horizontally positioned) and for simplicity the sky temperature is assumed equals to the external ambient airtemperature. Therefore, the unknowns are Te and Ti . The convection coefficients of heat transfer were determined by the following correlation [32]: hc = 5.5 + 3.8v,
(10)
where v is the wind speed. This correlation is valid for v ≤ 5 m s−1 and attends to the purpose of this comparative study.
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471
Fig. 4. Maximum average annual daily external surface temperature of the roof as a function of reflectivity.
The heat flux that reaches the internal ambient can be defined in a straightforward way as: q(t) =
Te (t) − Ti (t) . Rroof
(11)
Summarizing, Eqs. (8) and (9) give the surfaces temperature of the roof and Eq. (11) the heat flux through it. According to the second law of thermodynamics, the internal ambient air-temperature and the heat flux directly affect the energy consumption cooling of the building. 3.5. Simulation process The unknowns Ta (t) and qs (t) in Eqs. (8) and (9) are obtained by carrying out a numerical calculation following these steps: (a) Evaluation of Ta (t) Method: The instantaneous ambient air-temperature for a typical day of a given month is obtained by representing the function Ta (t) as a Fourier series of the second order. For the Fourier series coefficients calculation, we used the procedure described by Lyra [33]. Martins [34] and Brito Filho and Fraidenraich [35] later used this method. Input data: Measured monthly average (Ta,ave ) and monthly averaged maximum (Ta,max ) and minimum (Ta,min ) external ambient air-temperatures. (b) Evaluation of qs (t) Method: The instantaneous irradiance was obtained starting with the hemispherical irradiation following the standard procedures proposed by Collares-Pereira and Rabl [36] and the recommended average day for each month proposed by Klein [37]. Input data: Monthly average daily global solar radiation for a horizontal surface (Hh ), latitude and longitude of Curitiba and Manaus. (c) Evaluation of Rroof Input data: ı and k. (d) Evaluation of Te (t) Input data: Ta (t), qs (t), e,s , εe,ir , hce , hci , T0 and Rroof . (e) Evaluation of q(t) Input data: Te (t), Ti (t) and Rroof .
4. Results and analysis This section presents the thermal performance results of the analyzed lightweight roofs. The two dependent variables of the mathematical model Te and q are depicted using two different average values: annual hourly and annual daily. Fig. 2 shows the average annual hourly external surface temperature (a) and the average annual hourly heat flux through a roof (b) without the thermal insulation as a function of time. As it is shown, the effect of applying selective coatings is evident, i.e. a strong reduction of the external surface temperature (a), with implications on UHI, and the heat flux (b), with direct implications on the building thermal load. High reflectivity and emissivity reduce heat gain from the sun and heat conduction through the roof. What deserves special attention is the possibility of a negative heat flux in the morning on certain days. Fig. 3 shows the average annual daily external surface temperature of the roof without the thermal insulation layer (a) and with the thermal insulation layer (b) as a function of its external surface reflectivity. One can see that the thermal insulation layer increases the external surface temperature and thus the contribution to UHI. It is evidenced that for both cities, the higher the reflectivity (i.e. less heat gain from the sun), the lower the external surface temperature. These figures also show that when the emissivity increases maintaining constant reflectivity, the external surface temperature decreases, but not as strongly as by increasing reflectivity while maintaining constant emissivity. Fig. 4 presents the maximum average annual daily external surface temperature of the roof as a function of its external surface reflectivity and validated these results. The results shown in this figure reinforce those shown in Fig. 3. Fig. 5 depicts the average annual daily heat flux that crosses the roof without the thermal insulation layer (a) and with the thermal insulation layer (b) as a function of its external surface reflectivity. It is evident that when a thermal insulation layer is added to the roof, the heat flux is cut down considerably. Thus, the thermal insulation layer is a very efficient way to reduce building heat gain. It is clear that the higher the reflectivity, the lower the heat transferred to the indoor environment. According to the second law of thermodynamics, less electrical energy is needed for cooling. Moreover, these simulations also show that to reduce heat flux, increasing
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J.P. Brito Filho, T.V.O. Santos / Energy and Buildings 84 (2014) 466–474 Table 3 Percentage reduction in the average annual daily values for each roof configuration when compared with the roof without both thermal insulation layer and painting.
Fig. 5. Average annual daily heat flux that crosses the roof without the thermal insulation layer (a) and with the thermal insulation layer (b) as a function of reflectivity.
External surface temperature
Heat flux
Manaus
Curitiba
Manaus
Curitiba
Roof without thermal insulation layer White painted 17.74 Selective coating 22.61
13.71 17.62
50.42 64.27
104.69 134.49
Roof with thermal insulation layer 2.95 White painted 11.26 Selective coating
14.34 21.45
97.42 98.08
100.17 101.17
reflectivity is much more effective than increasing emissivity. Therefore, the use of paints with high reflectivity in cities with equatorial climates such as Manaus is very important. On the other hand, very high reflectivity values in cities with subtropical climates (such as Curitiba), can reverse the heat flux direction across the roof. Fig. 6 shows the maximum average annual daily heat flux that crosses the roof as a function of its external surface reflectivity. As before, the results shown in this figure reinforce those shown in Fig. 5. Table 3 shows the percentage reduction in the average annual daily values of external surface temperature and heat flux for each roof configuration when compared to the roof without both thermal insulation layers and paint (i.e. a roof of galvanized steel). In Manaus (equatorial climates), roofs with both thermal insulation layers and a selective coating is the best option because it contributes to the reduction of UHI and heat gain. In this configuration, the average annual daily external surface temperature has a reduction of 11.26% and the heat flux of 98.08% compared to the case of a simple roof (only galvanized steel sheet). If one cannot apply a selective coating, the application of a white paint reduces the average annual daily external surface temperature by 2.95% and the mean average annual daily heat flux by 97.42%. Otherwise, if a selective coating is applied to a roof without the thermal insulation layer, the average annual daily external surface temperature decreases 22.61% and the mean daily annual heat flux decreases 64.27%. If no thermal insulation layer and selective coatings are applied, a common white paint reduces the average annual daily external surface temperature by 17.74% and the mean daily annual heat flux by 50.42%.
Fig. 6. Maximum average annual daily heat flux that crosses the roof as a function of reflectivity.
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In Curitiba (subtropical climates), white painted roofs with or without the thermal insulation layer have almost the same performance for temperature and heat flux (compare 14.34% with 13.71% and 100.17% with 104.69%, respectively). One can gain a large reduction of the average annual daily external surface temperature using roofs with the thermal insulation layer and selective coating (21.45%). Otherwise, on roofs without the thermal insulation layer, but with selective coating, a large average annual daily heat flux reduction can be achieved (134.49%). 5. Conclusions and future research The main objective of our research is to identify the most adequate type of roof for a number of given climate regions in Brazil, taking into consideration environmental and energy saving benefits. The focus of the investigation reported in the present manuscript is the suitability of using white paints, selective coatings, and thermal insulation layers on large metal roofs in buildings located in subtropical and equatorial climate regions. This manuscript utilizes a heat transfer model aiming to compare the thermal performance of different roofs’ configurations. With this model, the external surface temperature of the roof Te and the heat flux q through it can be determined. The input data are the roof’s geometry and materials, the monthly average daily global solar radiation for a horizontal surface and the monthly average daily, monthly average daily minimum and monthly average daily maximum temperatures for the location. The two dependent variables Te and q are important to evaluate the roof’s contribution to UHI formation, and energy savings for acclimatization, respectively. Roofs with thermal insulation layer are recommended, mainly because they reduce the heat flux that reaches the internal environment, and consequently the building’s thermal load. However, the thermal insulation layer increases at the same time the external surface temperature of the roof, leading to higher air-temperatures in the surroundings and in doing so contributes to form UHI. In equatorial climates regions, this disadvantage can be greatly reduced by adding white paints or selective coatings on the roof external surface. Furthermore, white paints or selective coatings can decrease the difference in the temperature level of the roof during the day and the night protecting the surface against thermal shock. In subtropical climate regions, an alternative to the thermal insulation layer are white paints. Nevertheless, roofs covered with white paints with very high reflectivity or even with low emissivity values or selective coatings can reverse the heat flux direction across it. In further researches, experimental studies will be carried out in Curitiba and Manaus based on reduced scale models building with the selected roof type. Furthermore, a cost benefit analysis will be done to determine the return on investment for the specific cool roof. Based on the acquired knowledge, we will expand the research to other Brazilian climatic zones (tropical zone, semi-arid zone and highland tropical zone). Acknowledgments The authors express their thanks to the Brazilian National Council for Scientific and Technological Development (CNPq) agency for the financial support given to this research (Proc. 48039/2007-0). References [1] Anuário estatístico de energia elétrica, Ministério de Minas e Energia, Brazil, 2013.
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