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Effects of coefficients of solar reflectivity and infrared emissivity on the temperature and heat flux of horizontal flat roofs of artificially conditioned nonresidential buildings
Energy and Buildings 43 (2011) 440–445
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Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Effects of coefficients of solar reflectivity and infrared emissivity on the temperature and heat flux of horizontal flat roofs of artificially conditioned nonresidential buildings J.P. de Brito Filho ∗ , J.R. Henriquez, J.C.C. Dutra Graduate Program in Mechanical Engineering, Federal University of Pernambuco, Av. Acadêmico Hélio Ramos, S/N CEP 50.740-530, Recife, PE, Brazil
a r t i c l e
i n f o
Article history: Received 23 July 2010 Accepted 3 October 2010 Keywords: Roof material properties Selective coatings Insulation Thermal performance Passive cooling Energy Mass-insulation
a b s t r a c t Nonresidential buildings such as shopping centers, supermarkets and factories are constructions characterized as having large roof surfaces in comparison to their external wall surfaces. When conditioned artificially, these buildings become great consumers of electricity. To reduce this consumption, insulation materials are usually used. Notwithstanding the effectiveness of such a procedure, both the cost and environmental issues (the heat-island effect) have been considered as limiting factors for its usage. In this study, we analyze the effect of the application of selective coatings (with very high reflectance for solar radiation and high emittance for infrared radiation) on the surface temperature of the roof and the heat flux that crosses it. Two roof concepts were considered, namely metal roofs both with and without conventional mass-insulation, i.e. an insulating board on the internal side or between two metal foils. The methodology adopted to solve the proposed problem was based on the heat transfer analysis of a roof composed of multiple layers. External air temperature and solar radiation are considered timevarying. The results obtained show the benefits of selective coatings in terms of reductions in both roof temperature and heat flux and, consequently, alleviation of the urban heat-island effect and reduction of electricity consumption. © 2010 Elsevier B.V. All rights reserved.
1. Introduction The thermophysical properties of walls and roofs can adversely affect the outdoor and the indoor air temperature of a building. For this reason, several works have been carried out in the last decade to develop new materials and construction procedures, aiming to minimize such undesired effects. This study deals with a particular aspect of this problem, namely, the study of the effects of the radiation properties (reflectivity for the solar radiation spectrum and hemispherical emissivity for the infrared region of the thermal radiation spectrum) on the external surface temperature and heat flux that crosses a roof. Heat transfer in walls, windows, roofs, and floors of both residential and nonresidential buildings such as shopping centers, supermarkets and factories has been investigated intensively since the first oil crisis. The investigations deal with the different concepts of external walls [1,2], double glass on windows [3,4], ground heat exchangers [5], building’s orientation [6], green roofs [7,8], thermal-insulation thickness [9], and other aspects. An overview of recent studies concerning new developments in passive cool-
∗ Corresponding author. Tel.: +55 81 21268210; fax: +55 81 21268215. E-mail address: [email protected] (J.P. de Brito Filho). 0378-7788/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2010.10.007
ing techniques is provided in the study by Santamouris et al. [10]. Nonresidential buildings are characterized by having large roof areas compared with their external walls. In such constructions, the roof can be flat or shed, with a slight angle of inclination with reference to the horizontal plane or, alternatively, vaulted. They are exposed to solar radiation much more than the external walls and reach high temperatures during the day because they rapidly absorb the incoming solar radiation. In these cases, to guarantee comfortable temperature levels, passive cooling methods alone, such as natural ventilation and the presence of dense shades from trees, are normally insufficient. Active methods, such as airconditioning systems, are the alternative routes usually adopted to reduce thermal discomfort, particularly in countries with hot climate. However, large roof areas are responsible for large thermal loads and, consequently, for huge air-conditioning costs and elevated peaks of electricity consumption. It is, therefore, relevant to reduce the number of hours or the load to which air-conditioning systems are subject during the day. To reduce heat transfer by conduction, the classical approach consists of applying mass-insulation, i.e. an insulating board on the internal surface of the roof or between two metal foils. Although a thicker mass-insulation layer yields a higher resistance to heat transfer and, consequently, a lower thermal load,
J.P. de Brito Filho et al. / Energy and Buildings 43 (2011) 440–445
Nomenclature h Hh k qs q R t T
heat transfer coefficient (W m−2 K−1 ) monthly average daily global solar radiation (MJ m−2 ) thermal conductivity (W m−1 K−1 ) solar radiation on the plane of the roof (W m−2 ) heat flux through the roof (W m−2 ) thermal resistance (K W−1 ) time (h) temperature (◦ C)
Greek letters ˛ absorptivity of the roof Stefan–Boltzmann constant (W m−2 K−4 ) ı thickness (m) reflectivity of the roof ε hemispherical emissivity of the roof Subscripts a refers to external ambient air ave refers to the monthly average daily c refers to convection e refers to external surface of the roof i refers to inner surface of the roof ir refers to infrared region of the thermal radiation spectrum min refers to monthly average daily minimum max refers to monthly average daily maximum o refers to internal ambient air r refers to radiation s refers to solar radiation
some of its side effects, such as release of heat during the night, are important environmental concerns. Actually, this phenomenon is known as heat-island effect and contributes to make urban regions warmer than their rural surroundings, forming “islands” of higher temperatures in the landscape. For example, in Athens (Greece), it was observed that, for a group of representative buildings, the heat island intensity exceeded 10 K and increased the cooling load by about 100%, while the peak electricity load may have tripled (Santamouris et al. [11]). An alternative to increasing the thickness of mass-insulation is to use selective coatings, which implies a high reflectivity in the solar-radiation spectrum and a large hemispherical emissivity in terms of the infrared radiation emitted by the external surface of the roof [12–19]. Furthermore, the selective coating can decrease the difference in the temperature level of the roof during the day and the night protecting the surface against thermal shock because the temperature on the external surface of the roof with massinsulation only can be quite high during the day and low in the early morning. The displacements in the metal foils caused by thermal shock can produce water infiltration between the foils and consequently damages on the insulation material. In addition, thermal shocks can be responsible for mechanical stress on the mounting screws, accelerating eventually a corrosion process in the region. All these problems increase the roof-maintenance. Another question that must be taken into account is that some insulating materials are flammable and so the cost of fire insurance of the building is higher. Selective coatings also provide other valueadded benefits which are not found in mass-insulation materials such as noise reduction. Besides all these advantages, roofs with selective coatings and thinner mass-insulation layers are lighter and easier to install.
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Several articles describing the cooling potential of the application of reflective roofing coatings on buildings have been published. A detailed experimental work was conducted by Park and Barkaszi [16] aiming to investigate cooling energy savings provided by reflective roofing coatings in nine occupied homes in Florida (USA). According to this study, the air-conditioning energy use was reduced on average by 19%, ranging from a minimum of 2% up to a maximum of 43%, after application of high-reflectivity coating to the roofs. In these cases, the peak demand reduction between 5 and 6 p.m. ranged from 12% to 38%, respectively. A similar study, though based on three 1/4-scale model buildings situated in Tucson, AZ (USA), was carried out by Simpson and McPherson [17]. In this work, it was demonstrated 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. Concerning air-conditioning total daily and hourly electricity consumption, a reduction of approximately 5% for the house with white-colored roof compared to the houses with gray and silver-colored roofs was obtained. The effect of roof reflectivity on cooling energy savings was also investigated by Akbari et al. [18]. The authors monitored peak power and cooling energy savings from high-reflectivity coatings in one house and two school bungalows in Sacramento, CA (USA). The investigations showed that changing the reflectivity of the house roof from 0.18 to 0.73 might result in seasonal savings of 2.2 kWh/day. The peak demand was reduced by 0.6 kW. The cooling energy was reduced by 3.1 kWh/day and the peak demand by 0.6 kW in the school bungalows. An extensive outdoor experimental work carried out by Synnefa et al. [19], which involved the testing of 14 selective coatings, showed that the use of reflective coatings can reduce the surface temperature of a white concrete tile, under hot summer conditions, by 4 K during the day and by 2 K in the night. Besides, it can be warmer than the ambient air by 2 K during the day and cooler by 5.9 K in the night. The authors demonstrated that white coatings (acrylic elastomeric coatings) applied on concrete tiles have surface temperatures almost 20 K lower than silver gray reflectivity coatings (aluminum pigmented acrylic coatings).
2. Geometry and material of the roof There is a great variety of roof materials and geometries worldwide, both metallic and nonmetallic. In Brazil, in particular, diverse materials are used: red and white ceramics, fibrocement without asbestos, coated and uncoated galvanized steel and aluminum, aluminum- and zinc-coated metal, thermoacoustic metal (such as green, white, and ceramics in color), and colored cement (light gray, dark gray, red and ochre in color) [15]. In the residential sector, red ceramic roofs of various shapes are the most widely used. Fibrocement roofs are found in the residential sector, usually in low-income households. In contrast, in the commercial and industrial sectors, metallic roofs (normally, uncoated) are preferred, because they have low-cost installation. The two alternative concepts considered in this study are shown in Fig. 1. These configurations will be called Roofs 1 and 2, respectively, throughout the next chapters. The thermophysical properties and thicknesses of both the materials and the coating used in the simulations are presented in Table 1. A list with 14 selective coatings materials (three with very high infrared emissivity and solar reflectivity) can be found in [19]. The thermal conductivity value corresponds to a ceramic filled white elastomeric coating [20]. It is assumed that all thermophysical properties are independent of temperature.
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Fig. 1. The two types of roofs studied.
Fig. 2. Composite roof.
Table 1 Thermophysical properties and thicknesses of the roof materials and the coating.
Coating Galvanized steel Fiberglass wool
e,s (–)
εe,ir (–)
k (W m−1 K)
ı (m)
0.3–0.9 0.3 –
0.3–0.9 0.3 –
0.00345 45 0.038
0.00003 0.0005 0.05
3. Environmental conditions
Fig. 3. Heat transfer model.
The climatic data used in this study are for the city of São Paulo (latitude 23◦ 30 S, longitude 46◦ 37 W, and altitude 792 m), the Brazilian city with the largest industrial complex, stock exchange, and economic production. Of the industrial parks in the state of São Paulo, a major portion (52%) is concentrated in the city of São Paulo and its surroundings, where 27% of the Brazilian population lives. The city of São Paulo is on average 3 K warmer than the surroundings. In a very hot day, this difference can reach 12 K. The monthly average (Hh ) daily global solar radiation for each month of the year [21], in addition to the monthly average and monthly averaged maximum and minimum external ambient air temperatures (Tave , Tmax , Tmin ) [22], are presented in Table 2. The lowest temperature of 11.7 ◦ C occurs in July and the maximum of 28 ◦ C in February. The maximum monthly average daily global solar radiation of the year spans from October to February (around 17 MJ m−2 ). In the following sections, a brief description of the procedure to convert the average ambient temperatures and irradiation data (Table 2) to instantaneous temperature (Ta (t)) and irradiance for an average day of a given month is provided. In scientific literature, standard procedures, such as those in the study by Collares Pereira and Rabl [23], are available to obtain the variation of irradiance time (qs (t)) during the course of a day, starting with the hemispherical irradiation. In this case, because horizontal roofs are considered, the variable qs (t) represents the radiation collected on a horizontal plane. The time variation of the external ambient air temperature is obtained by representing the function Ta (t) as a Fourier series of the second order. Considering that the derivative of the function Ta (t) is zero at the average maximum and minimum temperatures (Tmax , Tmin ) the coefficients of the Fourier series can be obtained [24]. This procedure has to be supplemented by the estimation of the local time when the temperatures are the maximum and the minimum, which is obtained by representation of the daily ambient temperature, as proposed by Spirito and Vitale [25].
The roof configuration and mathematical model used to simulate the roof behavior under various conditions follows. 4. Model equations A composite roof consisting of ‘m’ layers, each with thickness ıj and thermal conductivity kj , is shown in Fig. 2. The external surface of layer 1, with temperature Te (t) and exposed to solar radiation qs (t), is assumed to be in contact with the external ambient air, with a time-varying ambient temperature Ta (t). No inertial effects are considered. The absorptivity of that surface for solar radiation is ˛e,s , and the emissivity for infrared radiation is εe,ir . The internal surface of the layer ‘m’ with temperature Ti (t) is assumed to be exposed to the internal ambient air, whose temperature is T0 . Its emissivity for infrared radiation is εi,ir . It is assumed that the internal ambient air temperature, T0 , is determined by an air-conditioning equipment and that it remains constant during the day. Temperature variations allowed by the control system of the equipment are then neglected. Heat transfer between the external surface and the external environment and between the internal surface and the internal ambient air occur by natural convection and infrared radiation. Between the layers, heat transfer occurs by conduction of heat. The heat transfer process that occurs between the external environment, the roof, and the internal environment can be better understood using the resistance model shown in Fig. 3. Solar radiation is collected on the plane of the roof layer in the period between sunset and sunrise. As the surface of the roof is not a black body, part of this incident radiation is reflected and a part is absorbed. The fraction of the incident radiation that is reflected or absorbed depends on the reflectivity of the material and the conditions of this surface. The absorbed fraction of the solar radiation is transferred to the exterior environment by the mechanisms of natural convection and infrared radiation, as well as to the roof
Table 2 Climatic data for the city of São Paulo.
Tave (◦ C) Tmax (◦ C) Tmin (◦ C) Hh (MJ m−2 )
January
February
March
April
May
June
July
August
September
October
November
December
22.1 27.3 18.7 17.1
22.4 28.0 18.8 16.2
21.7 27.2 18.2 14.8
19.7 25.1 16.3 13.1
17.6 23.0 13.8 11.2
16.5 21.8 12.4 10.7
15.8 21.8 11.7 11.2
17.1 23.8 12.8 12.8
17.8 23.9 13.9 13.3
19.0 24.8 15.3 16.2
20.3 25.9 16.6 17.5
21.1 26.3 17.7 17.0
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layers in the direction of the internal ambient, by the mechanism of conduction. The heat reaching the internal surface of the roof, before being delivered to the internal ambient air at temperature T0 , finds two thermal resistances occurring in parallel: a thermal resistance to radiation and the second resistance to convection. An energy balance on the nodes 1 and 2 gives the following equations: Ta (t) − Te (t) Te (t) − Ti (t) + ˛e,s qs (t) = ; and Re Rroof
(1)
Te (t) − Ti (t) T (t) − T0 = i ; Rroof Ri
(2)
where Re =
1 , hre + hce
(3)
Ri =
1 , hri + hci
(4)
and Rroof = R1 + R2 + · · · + Rm = (ı1 /k1 ) + (ı2 /k2 ) + · · · + (ım /km ). (5) The terms hce and hci are the convective heat transfer coefficients, and hre and hri are the radiative heat transfer coefficients for the transfer of heat from the outside layer to the external environment and the inside layer to the internal ambient air, respectively. The radiative heat transfer terms, (hre [Te (t) − Ta (t)]) and (hri [Ti (t) − T0 (t)]), denote the Stefan–Boltzmann equation given by hre [Te (t) − Ta (t)] = εe,ir [Te 4 (t) − Ta 4 (t)], and 4
4
hri [Ti (t) − T0 ] = εi,ir [Ti (t) − T0 ],
(6) (7)
where is the Stefan–Boltzmann constant. Substituting the expression for Re and Ri in Eqs. (1) and (2), it follows that ˛e,s qs (t) + hce [Ta (t) − Te (t)] + εe,ir [Ta 4 (t) − Te 4 (t)] =
Te (t) − Ti (t) , and Rroof
hci [Ti (t) − T0 ] + εi,ir [Ti 4 (t) − T0 4 ] =
(8) Te (t) − Ti (t) . Rroof
(9)
The unknowns of the problem are the temperatures of the external and internal surfaces of the roof. The heat flux that reaches the internal ambient can be determined in a straightforward way. 5. Results and discussion The main data used in the simulations are the thermophysical properties and thicknesses of the materials, the instantaneous external ambient air temperature, and irradiance values. The unknowns of Eqs. (8) and (9) are obtained by carrying out a numerical calculation following these steps:
Fig. 4. (a) Solar radiation on the plane of the roof during the daytime. (b) External ambient air temperature during the daytime.
coefficients were obtained using the classical correlation proposed by McAdams [26], which by natural convection gives 5.7 W m−2 K. Further researches on this field can be found in [27]. Details of the calculations of steps 1 and 2 can be found in the presentation by Brito Filho and Fraidenraich [28]. Results obtained for the instantaneous irradiance on the plane of the roof and the external ambient air temperatures between sunrise and sunset on February 16 and July 17 in the city of São Paulo are shown in Fig. 4(a and b), respectively. The heat flux that reaches the internal ambient is shown in Fig. 5, and Fig. 6 depicts the external surface temperature profiles of Roofs 1 and 2 during the daytime, considering the parameters εe,ir and e,s as varying from 0.3 to 0.9. The curves Roof 1 (or Roof 2) with εe,ir = e,s = 0.3 correspond to a roof without any coating. They have
1. Determination of the instantaneous irradiance on the plane of the roof (qs (t)) considering both diffuse and direct monthly average daily solar radiation. 2. Evaluation of the instantaneous external ambient air temperature (Ta (t)) considering the monthly average daily temperature and monthly average daily minimum and maximum temperatures. 3. Calculation of the instantaneous external- and internal-surface temperatures of the roof and the heat flux that crosses it. In addition to the conditions set out in steps 1 and 2, it has been assumed in this analysis that T0 = 22 ◦ C. The convective heat transfer
Fig. 5. Heat fluxes that cross the two types of roofs during the daytime.
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Fig. 6. External surface temperature profiles of the two types of roofs during the daytime.
Fig. 8. Maximum external surface temperature for the two types of roofs as a function of emissivity.
poor reflectivity and emissivity. Furthermore, the curves Roof 1 (or Roof 2) with εe,ir = 0.3 and e,s = 0.9 correspond to a roof with a white painting. They have a high reflectivity and a poor emissivity. It is evident that high reflectivity drastically decreases both the heat flux that reaches the internal ambient (Fig. 5) and the external surface temperature of the roof (Fig. 6). Although Roof 2 presents the lowest heat flux in these cases, what deserves much more attention is the significant effect of the white painting in the case of Roof 1 (less than 50 W m−2 ). It is also clear that mass-insulation decreases the heat flux that reaches the internal ambient. However, massinsulation increases the external surface temperature of the roof. These behaviors are more pronounced in the case of a roof without any coating. Summarizing, considering the viewpoint of heat flux reduction, the roof with the best performance is Roof 2. However, the lowest external surface temperature is reached with Roof 1. The effect of increased reflectivity on the maximum heat flux that reaches the indoor environment and on the maximum external surface temperature for the two types of roofs are shown in Figs. 7 and 8, respectively. A clear relation is found: as reflectivity increases, the maximum heat flux and the maximum external surface temperature decrease. In addition, the rate of reduction of the maximum heat flux with reflectivity is greater for low values of emissivity. It can be understood observing that when the reflectivity increases, the roof absorbs less energy from the sun, making it cooler and less energy is available to return to the exterior environment, or to be transferred to the interior one. Additionally, if the emissivity is low, the maximum external surface temperature
remains high and more energy is available to be transferred to the internal ambient. Fig. 7 shows also that for Roof 1 the maximum heat flux decreases sharply and the difference between the curves for εe,ir = 0.3 and εe,ir = 0.9 is almost imperceptible. On the other hand, for Roof 2 the maximum heat flux decreases slowly and the difference between the two curves are more pronounced. This behavior can be explained as follows: the heat flux that crosses a roof with mass-insulation is less dependent on their reflectivity values than for a roof without mass-insulation, because it has higher thermal resistance. The reflectivity plays a less important role in these cases. As the temperatures of the roof are higher, the emissivity becomes more important in roofs with mass-insulation than in roofs without mass-insulation, where the temperatures are lower.
Fig. 7. Maximum heat flux that crosses the two types of roofs as a function of reflectivity.
6. Final considerations The mathematical model presented in this article allows for a comparison of the thermal behavior of any type of flat and smooth roof of an artificially conditioned building and its applicability is not limited to a particular type of climate. In this article, the mathematical model was used to evaluate the effects of coefficients of solar reflectivity and infrared emissivity on the temperature and heat flux of horizontal flat roofs of nonresidential buildings. Of particular interest was the investigation of these effects on the two most popular metallic roofs (galvanized steel and fiberglass wool between two galvanized steel foils,) used in Brazil. From the results obtained, the following conclusions can be drawn: 1. Roofs with mass-insulation drastically improve the internal ambient conditions of a nonresidential building by reducing the heat flux that reaches the internal environment (Fig. 5). On the other hand it increases the external surface temperature of the roof (Fig. 6) leading to higher air temperatures in the surroundings. This disadvantage can be extremely minimized by applying a white painting with a high reflectivity even if the emissivity is low. 2. Good-quality white paintings present, in addition to high reflectivity, relatively high emissivity. Selective coatings (very high reflectance for solar radiation and high emittance for infrared radiation) show the best results in terms of heat flux (Fig. 7) and external surface temperature reductions (Fig. 8). 3. Roofs with both mass-insulation and good-reflectivity coating improve indoor conditions independent of what happens to the outdoor conditions.
J.P. de Brito Filho et al. / Energy and Buildings 43 (2011) 440–445
4. Roofs without mass-insulation and with a good-reflectivity coating improve outdoor conditions independent of the consequences to the indoor conditions. 5. Roofs with mass-insulation and coatings with very high reflectivity and emissivity improve both outdoor and indoor conditions. In these considerations one has to consider that the problem of reducing the levels of the temperature of the roofs of buildings is of interest to every country. In regions with hot climate almost throughout the year, such as Brazil, the second problem of interest is reducing the heat flux that reaches the internal ambient. However, in cold climate countries, this interest can occur only during warmer summer months. This subject will be investigated in a following research project. Acknowledgment The authors sincerely express their thanks to CNPq/Proc. 480390/2007-0 for the financial support given to this research. References [1] R. Lindberg, A. Binamu, M. Teikari, Five-year data of measured weather, energy consumption, and time-dependent temperature variations within different exterior wall structures, Energy and Buildings 36 (6) (2004) 495–501. [2] Ö.A. Dombayci, M. Gölcü, Y. Pancar, Optimization of insulation thickness for external walls using different energy-source, Applied Energy 83 (9) (2006) 921–928. [3] K.A.R. Ismail, J.R. Henríquez, Two dimensional model for the double glass naturally ventilated window, Journal of Heat and Mass Transfer 48 (3–4) (2005) 461–475. [4] Z. Yang, X.H. Li, Y.F. Hu, Study on solar radiation and energy efficiency of building glass system, Applied Thermal Engineering 26 (8–9) (2006) 956–961. [5] N. Kyriakis, A. Michopoulos, K. Pattas, On the maximum thermal load of heat exchangers, Energy and Buildings 38 (1) (2006) 25–29. [6] T. Mingfang, Solar control for buildings, Building and Environment 37 (7) (2002) 659–664. [7] E.P. Del Barrio, Analysis of the green roofs cooling potential in buildings, Energy and Buildings 27 (2) (1998) 179–193. [8] R.M. Lazzarin, F. Castellotti, F. Busato, Experimental measurements and numerical modeling of a green roof, Energy and Buildings 37 (12) (2005) 1260–1267.
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Contents lists available at ScienceDirect
Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Effects of coefficients of solar reflectivity and infrared emissivity on the temperature and heat flux of horizontal flat roofs of artificially conditioned nonresidential buildings J.P. de Brito Filho ∗ , J.R. Henriquez, J.C.C. Dutra Graduate Program in Mechanical Engineering, Federal University of Pernambuco, Av. Acadêmico Hélio Ramos, S/N CEP 50.740-530, Recife, PE, Brazil
a r t i c l e
i n f o
Article history: Received 23 July 2010 Accepted 3 October 2010 Keywords: Roof material properties Selective coatings Insulation Thermal performance Passive cooling Energy Mass-insulation
a b s t r a c t Nonresidential buildings such as shopping centers, supermarkets and factories are constructions characterized as having large roof surfaces in comparison to their external wall surfaces. When conditioned artificially, these buildings become great consumers of electricity. To reduce this consumption, insulation materials are usually used. Notwithstanding the effectiveness of such a procedure, both the cost and environmental issues (the heat-island effect) have been considered as limiting factors for its usage. In this study, we analyze the effect of the application of selective coatings (with very high reflectance for solar radiation and high emittance for infrared radiation) on the surface temperature of the roof and the heat flux that crosses it. Two roof concepts were considered, namely metal roofs both with and without conventional mass-insulation, i.e. an insulating board on the internal side or between two metal foils. The methodology adopted to solve the proposed problem was based on the heat transfer analysis of a roof composed of multiple layers. External air temperature and solar radiation are considered timevarying. The results obtained show the benefits of selective coatings in terms of reductions in both roof temperature and heat flux and, consequently, alleviation of the urban heat-island effect and reduction of electricity consumption. © 2010 Elsevier B.V. All rights reserved.
1. Introduction The thermophysical properties of walls and roofs can adversely affect the outdoor and the indoor air temperature of a building. For this reason, several works have been carried out in the last decade to develop new materials and construction procedures, aiming to minimize such undesired effects. This study deals with a particular aspect of this problem, namely, the study of the effects of the radiation properties (reflectivity for the solar radiation spectrum and hemispherical emissivity for the infrared region of the thermal radiation spectrum) on the external surface temperature and heat flux that crosses a roof. Heat transfer in walls, windows, roofs, and floors of both residential and nonresidential buildings such as shopping centers, supermarkets and factories has been investigated intensively since the first oil crisis. The investigations deal with the different concepts of external walls [1,2], double glass on windows [3,4], ground heat exchangers [5], building’s orientation [6], green roofs [7,8], thermal-insulation thickness [9], and other aspects. An overview of recent studies concerning new developments in passive cool-
∗ Corresponding author. Tel.: +55 81 21268210; fax: +55 81 21268215. E-mail address: [email protected] (J.P. de Brito Filho). 0378-7788/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2010.10.007
ing techniques is provided in the study by Santamouris et al. [10]. Nonresidential buildings are characterized by having large roof areas compared with their external walls. In such constructions, the roof can be flat or shed, with a slight angle of inclination with reference to the horizontal plane or, alternatively, vaulted. They are exposed to solar radiation much more than the external walls and reach high temperatures during the day because they rapidly absorb the incoming solar radiation. In these cases, to guarantee comfortable temperature levels, passive cooling methods alone, such as natural ventilation and the presence of dense shades from trees, are normally insufficient. Active methods, such as airconditioning systems, are the alternative routes usually adopted to reduce thermal discomfort, particularly in countries with hot climate. However, large roof areas are responsible for large thermal loads and, consequently, for huge air-conditioning costs and elevated peaks of electricity consumption. It is, therefore, relevant to reduce the number of hours or the load to which air-conditioning systems are subject during the day. To reduce heat transfer by conduction, the classical approach consists of applying mass-insulation, i.e. an insulating board on the internal surface of the roof or between two metal foils. Although a thicker mass-insulation layer yields a higher resistance to heat transfer and, consequently, a lower thermal load,
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Nomenclature h Hh k qs q R t T
heat transfer coefficient (W m−2 K−1 ) monthly average daily global solar radiation (MJ m−2 ) thermal conductivity (W m−1 K−1 ) solar radiation on the plane of the roof (W m−2 ) heat flux through the roof (W m−2 ) thermal resistance (K W−1 ) time (h) temperature (◦ C)
Greek letters ˛ absorptivity of the roof Stefan–Boltzmann constant (W m−2 K−4 ) ı thickness (m) reflectivity of the roof ε hemispherical emissivity of the roof Subscripts a refers to external ambient air ave refers to the monthly average daily c refers to convection e refers to external surface of the roof i refers to inner surface of the roof ir refers to infrared region of the thermal radiation spectrum min refers to monthly average daily minimum max refers to monthly average daily maximum o refers to internal ambient air r refers to radiation s refers to solar radiation
some of its side effects, such as release of heat during the night, are important environmental concerns. Actually, this phenomenon is known as heat-island effect and contributes to make urban regions warmer than their rural surroundings, forming “islands” of higher temperatures in the landscape. For example, in Athens (Greece), it was observed that, for a group of representative buildings, the heat island intensity exceeded 10 K and increased the cooling load by about 100%, while the peak electricity load may have tripled (Santamouris et al. [11]). An alternative to increasing the thickness of mass-insulation is to use selective coatings, which implies a high reflectivity in the solar-radiation spectrum and a large hemispherical emissivity in terms of the infrared radiation emitted by the external surface of the roof [12–19]. Furthermore, the selective coating can decrease the difference in the temperature level of the roof during the day and the night protecting the surface against thermal shock because the temperature on the external surface of the roof with massinsulation only can be quite high during the day and low in the early morning. The displacements in the metal foils caused by thermal shock can produce water infiltration between the foils and consequently damages on the insulation material. In addition, thermal shocks can be responsible for mechanical stress on the mounting screws, accelerating eventually a corrosion process in the region. All these problems increase the roof-maintenance. Another question that must be taken into account is that some insulating materials are flammable and so the cost of fire insurance of the building is higher. Selective coatings also provide other valueadded benefits which are not found in mass-insulation materials such as noise reduction. Besides all these advantages, roofs with selective coatings and thinner mass-insulation layers are lighter and easier to install.
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Several articles describing the cooling potential of the application of reflective roofing coatings on buildings have been published. A detailed experimental work was conducted by Park and Barkaszi [16] aiming to investigate cooling energy savings provided by reflective roofing coatings in nine occupied homes in Florida (USA). According to this study, the air-conditioning energy use was reduced on average by 19%, ranging from a minimum of 2% up to a maximum of 43%, after application of high-reflectivity coating to the roofs. In these cases, the peak demand reduction between 5 and 6 p.m. ranged from 12% to 38%, respectively. A similar study, though based on three 1/4-scale model buildings situated in Tucson, AZ (USA), was carried out by Simpson and McPherson [17]. In this work, it was demonstrated 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. Concerning air-conditioning total daily and hourly electricity consumption, a reduction of approximately 5% for the house with white-colored roof compared to the houses with gray and silver-colored roofs was obtained. The effect of roof reflectivity on cooling energy savings was also investigated by Akbari et al. [18]. The authors monitored peak power and cooling energy savings from high-reflectivity coatings in one house and two school bungalows in Sacramento, CA (USA). The investigations showed that changing the reflectivity of the house roof from 0.18 to 0.73 might result in seasonal savings of 2.2 kWh/day. The peak demand was reduced by 0.6 kW. The cooling energy was reduced by 3.1 kWh/day and the peak demand by 0.6 kW in the school bungalows. An extensive outdoor experimental work carried out by Synnefa et al. [19], which involved the testing of 14 selective coatings, showed that the use of reflective coatings can reduce the surface temperature of a white concrete tile, under hot summer conditions, by 4 K during the day and by 2 K in the night. Besides, it can be warmer than the ambient air by 2 K during the day and cooler by 5.9 K in the night. The authors demonstrated that white coatings (acrylic elastomeric coatings) applied on concrete tiles have surface temperatures almost 20 K lower than silver gray reflectivity coatings (aluminum pigmented acrylic coatings).
2. Geometry and material of the roof There is a great variety of roof materials and geometries worldwide, both metallic and nonmetallic. In Brazil, in particular, diverse materials are used: red and white ceramics, fibrocement without asbestos, coated and uncoated galvanized steel and aluminum, aluminum- and zinc-coated metal, thermoacoustic metal (such as green, white, and ceramics in color), and colored cement (light gray, dark gray, red and ochre in color) [15]. In the residential sector, red ceramic roofs of various shapes are the most widely used. Fibrocement roofs are found in the residential sector, usually in low-income households. In contrast, in the commercial and industrial sectors, metallic roofs (normally, uncoated) are preferred, because they have low-cost installation. The two alternative concepts considered in this study are shown in Fig. 1. These configurations will be called Roofs 1 and 2, respectively, throughout the next chapters. The thermophysical properties and thicknesses of both the materials and the coating used in the simulations are presented in Table 1. A list with 14 selective coatings materials (three with very high infrared emissivity and solar reflectivity) can be found in [19]. The thermal conductivity value corresponds to a ceramic filled white elastomeric coating [20]. It is assumed that all thermophysical properties are independent of temperature.
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Fig. 1. The two types of roofs studied.
Fig. 2. Composite roof.
Table 1 Thermophysical properties and thicknesses of the roof materials and the coating.
Coating Galvanized steel Fiberglass wool
e,s (–)
εe,ir (–)
k (W m−1 K)
ı (m)
0.3–0.9 0.3 –
0.3–0.9 0.3 –
0.00345 45 0.038
0.00003 0.0005 0.05
3. Environmental conditions
Fig. 3. Heat transfer model.
The climatic data used in this study are for the city of São Paulo (latitude 23◦ 30 S, longitude 46◦ 37 W, and altitude 792 m), the Brazilian city with the largest industrial complex, stock exchange, and economic production. Of the industrial parks in the state of São Paulo, a major portion (52%) is concentrated in the city of São Paulo and its surroundings, where 27% of the Brazilian population lives. The city of São Paulo is on average 3 K warmer than the surroundings. In a very hot day, this difference can reach 12 K. The monthly average (Hh ) daily global solar radiation for each month of the year [21], in addition to the monthly average and monthly averaged maximum and minimum external ambient air temperatures (Tave , Tmax , Tmin ) [22], are presented in Table 2. The lowest temperature of 11.7 ◦ C occurs in July and the maximum of 28 ◦ C in February. The maximum monthly average daily global solar radiation of the year spans from October to February (around 17 MJ m−2 ). In the following sections, a brief description of the procedure to convert the average ambient temperatures and irradiation data (Table 2) to instantaneous temperature (Ta (t)) and irradiance for an average day of a given month is provided. In scientific literature, standard procedures, such as those in the study by Collares Pereira and Rabl [23], are available to obtain the variation of irradiance time (qs (t)) during the course of a day, starting with the hemispherical irradiation. In this case, because horizontal roofs are considered, the variable qs (t) represents the radiation collected on a horizontal plane. The time variation of the external ambient air temperature is obtained by representing the function Ta (t) as a Fourier series of the second order. Considering that the derivative of the function Ta (t) is zero at the average maximum and minimum temperatures (Tmax , Tmin ) the coefficients of the Fourier series can be obtained [24]. This procedure has to be supplemented by the estimation of the local time when the temperatures are the maximum and the minimum, which is obtained by representation of the daily ambient temperature, as proposed by Spirito and Vitale [25].
The roof configuration and mathematical model used to simulate the roof behavior under various conditions follows. 4. Model equations A composite roof consisting of ‘m’ layers, each with thickness ıj and thermal conductivity kj , is shown in Fig. 2. The external surface of layer 1, with temperature Te (t) and exposed to solar radiation qs (t), is assumed to be in contact with the external ambient air, with a time-varying ambient temperature Ta (t). No inertial effects are considered. The absorptivity of that surface for solar radiation is ˛e,s , and the emissivity for infrared radiation is εe,ir . The internal surface of the layer ‘m’ with temperature Ti (t) is assumed to be exposed to the internal ambient air, whose temperature is T0 . Its emissivity for infrared radiation is εi,ir . It is assumed that the internal ambient air temperature, T0 , is determined by an air-conditioning equipment and that it remains constant during the day. Temperature variations allowed by the control system of the equipment are then neglected. Heat transfer between the external surface and the external environment and between the internal surface and the internal ambient air occur by natural convection and infrared radiation. Between the layers, heat transfer occurs by conduction of heat. The heat transfer process that occurs between the external environment, the roof, and the internal environment can be better understood using the resistance model shown in Fig. 3. Solar radiation is collected on the plane of the roof layer in the period between sunset and sunrise. As the surface of the roof is not a black body, part of this incident radiation is reflected and a part is absorbed. The fraction of the incident radiation that is reflected or absorbed depends on the reflectivity of the material and the conditions of this surface. The absorbed fraction of the solar radiation is transferred to the exterior environment by the mechanisms of natural convection and infrared radiation, as well as to the roof
Table 2 Climatic data for the city of São Paulo.
Tave (◦ C) Tmax (◦ C) Tmin (◦ C) Hh (MJ m−2 )
January
February
March
April
May
June
July
August
September
October
November
December
22.1 27.3 18.7 17.1
22.4 28.0 18.8 16.2
21.7 27.2 18.2 14.8
19.7 25.1 16.3 13.1
17.6 23.0 13.8 11.2
16.5 21.8 12.4 10.7
15.8 21.8 11.7 11.2
17.1 23.8 12.8 12.8
17.8 23.9 13.9 13.3
19.0 24.8 15.3 16.2
20.3 25.9 16.6 17.5
21.1 26.3 17.7 17.0
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layers in the direction of the internal ambient, by the mechanism of conduction. The heat reaching the internal surface of the roof, before being delivered to the internal ambient air at temperature T0 , finds two thermal resistances occurring in parallel: a thermal resistance to radiation and the second resistance to convection. An energy balance on the nodes 1 and 2 gives the following equations: Ta (t) − Te (t) Te (t) − Ti (t) + ˛e,s qs (t) = ; and Re Rroof
(1)
Te (t) − Ti (t) T (t) − T0 = i ; Rroof Ri
(2)
where Re =
1 , hre + hce
(3)
Ri =
1 , hri + hci
(4)
and Rroof = R1 + R2 + · · · + Rm = (ı1 /k1 ) + (ı2 /k2 ) + · · · + (ım /km ). (5) The terms hce and hci are the convective heat transfer coefficients, and hre and hri are the radiative heat transfer coefficients for the transfer of heat from the outside layer to the external environment and the inside layer to the internal ambient air, respectively. The radiative heat transfer terms, (hre [Te (t) − Ta (t)]) and (hri [Ti (t) − T0 (t)]), denote the Stefan–Boltzmann equation given by hre [Te (t) − Ta (t)] = εe,ir [Te 4 (t) − Ta 4 (t)], and 4
4
hri [Ti (t) − T0 ] = εi,ir [Ti (t) − T0 ],
(6) (7)
where is the Stefan–Boltzmann constant. Substituting the expression for Re and Ri in Eqs. (1) and (2), it follows that ˛e,s qs (t) + hce [Ta (t) − Te (t)] + εe,ir [Ta 4 (t) − Te 4 (t)] =
Te (t) − Ti (t) , and Rroof
hci [Ti (t) − T0 ] + εi,ir [Ti 4 (t) − T0 4 ] =
(8) Te (t) − Ti (t) . Rroof
(9)
The unknowns of the problem are the temperatures of the external and internal surfaces of the roof. The heat flux that reaches the internal ambient can be determined in a straightforward way. 5. Results and discussion The main data used in the simulations are the thermophysical properties and thicknesses of the materials, the instantaneous external ambient air temperature, and irradiance values. The unknowns of Eqs. (8) and (9) are obtained by carrying out a numerical calculation following these steps:
Fig. 4. (a) Solar radiation on the plane of the roof during the daytime. (b) External ambient air temperature during the daytime.
coefficients were obtained using the classical correlation proposed by McAdams [26], which by natural convection gives 5.7 W m−2 K. Further researches on this field can be found in [27]. Details of the calculations of steps 1 and 2 can be found in the presentation by Brito Filho and Fraidenraich [28]. Results obtained for the instantaneous irradiance on the plane of the roof and the external ambient air temperatures between sunrise and sunset on February 16 and July 17 in the city of São Paulo are shown in Fig. 4(a and b), respectively. The heat flux that reaches the internal ambient is shown in Fig. 5, and Fig. 6 depicts the external surface temperature profiles of Roofs 1 and 2 during the daytime, considering the parameters εe,ir and e,s as varying from 0.3 to 0.9. The curves Roof 1 (or Roof 2) with εe,ir = e,s = 0.3 correspond to a roof without any coating. They have
1. Determination of the instantaneous irradiance on the plane of the roof (qs (t)) considering both diffuse and direct monthly average daily solar radiation. 2. Evaluation of the instantaneous external ambient air temperature (Ta (t)) considering the monthly average daily temperature and monthly average daily minimum and maximum temperatures. 3. Calculation of the instantaneous external- and internal-surface temperatures of the roof and the heat flux that crosses it. In addition to the conditions set out in steps 1 and 2, it has been assumed in this analysis that T0 = 22 ◦ C. The convective heat transfer
Fig. 5. Heat fluxes that cross the two types of roofs during the daytime.
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Fig. 6. External surface temperature profiles of the two types of roofs during the daytime.
Fig. 8. Maximum external surface temperature for the two types of roofs as a function of emissivity.
poor reflectivity and emissivity. Furthermore, the curves Roof 1 (or Roof 2) with εe,ir = 0.3 and e,s = 0.9 correspond to a roof with a white painting. They have a high reflectivity and a poor emissivity. It is evident that high reflectivity drastically decreases both the heat flux that reaches the internal ambient (Fig. 5) and the external surface temperature of the roof (Fig. 6). Although Roof 2 presents the lowest heat flux in these cases, what deserves much more attention is the significant effect of the white painting in the case of Roof 1 (less than 50 W m−2 ). It is also clear that mass-insulation decreases the heat flux that reaches the internal ambient. However, massinsulation increases the external surface temperature of the roof. These behaviors are more pronounced in the case of a roof without any coating. Summarizing, considering the viewpoint of heat flux reduction, the roof with the best performance is Roof 2. However, the lowest external surface temperature is reached with Roof 1. The effect of increased reflectivity on the maximum heat flux that reaches the indoor environment and on the maximum external surface temperature for the two types of roofs are shown in Figs. 7 and 8, respectively. A clear relation is found: as reflectivity increases, the maximum heat flux and the maximum external surface temperature decrease. In addition, the rate of reduction of the maximum heat flux with reflectivity is greater for low values of emissivity. It can be understood observing that when the reflectivity increases, the roof absorbs less energy from the sun, making it cooler and less energy is available to return to the exterior environment, or to be transferred to the interior one. Additionally, if the emissivity is low, the maximum external surface temperature
remains high and more energy is available to be transferred to the internal ambient. Fig. 7 shows also that for Roof 1 the maximum heat flux decreases sharply and the difference between the curves for εe,ir = 0.3 and εe,ir = 0.9 is almost imperceptible. On the other hand, for Roof 2 the maximum heat flux decreases slowly and the difference between the two curves are more pronounced. This behavior can be explained as follows: the heat flux that crosses a roof with mass-insulation is less dependent on their reflectivity values than for a roof without mass-insulation, because it has higher thermal resistance. The reflectivity plays a less important role in these cases. As the temperatures of the roof are higher, the emissivity becomes more important in roofs with mass-insulation than in roofs without mass-insulation, where the temperatures are lower.
Fig. 7. Maximum heat flux that crosses the two types of roofs as a function of reflectivity.
6. Final considerations The mathematical model presented in this article allows for a comparison of the thermal behavior of any type of flat and smooth roof of an artificially conditioned building and its applicability is not limited to a particular type of climate. In this article, the mathematical model was used to evaluate the effects of coefficients of solar reflectivity and infrared emissivity on the temperature and heat flux of horizontal flat roofs of nonresidential buildings. Of particular interest was the investigation of these effects on the two most popular metallic roofs (galvanized steel and fiberglass wool between two galvanized steel foils,) used in Brazil. From the results obtained, the following conclusions can be drawn: 1. Roofs with mass-insulation drastically improve the internal ambient conditions of a nonresidential building by reducing the heat flux that reaches the internal environment (Fig. 5). On the other hand it increases the external surface temperature of the roof (Fig. 6) leading to higher air temperatures in the surroundings. This disadvantage can be extremely minimized by applying a white painting with a high reflectivity even if the emissivity is low. 2. Good-quality white paintings present, in addition to high reflectivity, relatively high emissivity. Selective coatings (very high reflectance for solar radiation and high emittance for infrared radiation) show the best results in terms of heat flux (Fig. 7) and external surface temperature reductions (Fig. 8). 3. Roofs with both mass-insulation and good-reflectivity coating improve indoor conditions independent of what happens to the outdoor conditions.
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