Proper evaluation of the external convective heat transfer for the thermal analysis of cool roofs
Introduction
The solar energy absorbed by the external envelope of buildings produces the rise in their surface temperature by several degrees above the outdoor air temperature, and also an increase in the heat flux incoming through them, especially in summer.
On the building scale, this has several drawbacks: first of all, it highly affects the energy demand for space cooling and the peak cooling load in conditioned buildings, while in non-conditioned spaces it determines a significant worsening of the thermal comfort conditions. Then, the high temperature fluctuations in the roof may cause mechanical stress and increase the surface deterioration.
Furthermore, on a wider scale, this effect produces the rise of the urban air temperature if compared to surrounding rural areas, i.e. the well-known phenomenon called urban heat island effect (UHI), which is extensively discussed in [1].
However, all of these effects can be mitigated by the use of cool materials, i.e. materials characterized by high solar reflectance and high infrared emittance values. Actually, when applied to the external surfaces of roofs in buildings, these materials limit the amount of solar irradiance absorbed by the roof, and increase the rate of heat flux released by irradiation to the environment, especially during nighttime, which significantly lowers the external surface temperature.
Field measurements have already shown the remarkable benefits of the application of a cool material to a roof, in terms of reduction of the external surface temperature, incoming heat flux, indoor air temperature and energy savings (at least in summer). As an example, in the framework of the EU Cool Roofs Project, five buildings have been monitored with the aim of evaluating the actual performance achievable with this technology.
Romeo et al. [2] measured the air temperature and the relative humidity in the rooms, the global solar radiation and the external surface temperature on the roof for a public building in Trapani. They found out that the application of a cool paint with a solar reflectance r = 0.86 results in a reduction of about 20 °C in the peak surface temperature of the roof, thus maintaining it only a few degrees above the outdoor air temperature. This leads to a noticeable reduction in the operative temperature of the rooms (2.3 °C on average), thus improving the thermal comfort of the occupants in absence of air conditioning devices. Furthermore, if using a cooling device, a reduction in the cooling needs of about 54% has to be expected.
Synnefa et al. [3] analyzed a school building in Athens before and after the application of a white paint to the roof (r = 0.89), with results comparable to those obtained for the case study in Trapani. In fact, they registered a reduction in the peak external surface temperature of about 25 °C, and a mean reduction in the indoor air temperature of about 1.5–2 °C; additional simulations also indicated a decrease by 40% in the annual cooling load in the case of conditioned building. Furthermore, the authors observed that daily temperature fluctuations are strongly reduced, so a longer life of the roof finishing layer has to be expected.
Another case study in the Mediterranean area involved a laboratory building in Iraklion [4], where a cool paint with r = 0.89 has been applied. In this study, the measured results allowed the calibration of a dynamic model in TRNSYS environment, which was then used for more detailed analyses. The simulations suggested a potential reduction in the cooling needs by about 25%, but also an increase in the heating energy demand by 43%. However, the overall annual energy demand can be reduced by about 20%.
These results are comparable to those described by the authors of the present paper in a recent work [5] for the application of a white paint (r = 0.85) to an office building in Catania, Southern Italy. In this work, further investigations in terms of primary energy were also carried out, with the conclusion that the convenience of a cool roof on an annual basis may be influenced by the effectiveness of the space heating devices, especially in moderate climates. However, as a general rule, in winter the sun is much lower in the sky, the solar radiation hitting a horizontal surface is less intense and there is a higher probability of having overcast sky. Thus, the negative effect of cool roofs in winter is normally less significant than the advantages in summer [6].
The two last case studies proposed in the framework of the EU Cool Roofs Project show the benefits of using cool materials also in cold climates like that of Poitiers [7] and London [8], where the summer season is milder than in the countries of the Mediterranean basin. Indeed, even if the buildings in countries like France and England show high insulation levels of the envelope, and the solar availability is much lower than in hot countries, cool roofs are still effective for reducing the discomfort due to overheating.
All these case studies – and others that are not involved in the EU Cool Roofs Project, like the project for the construction of low income buildings in Haiti [9] and the monitoring campaign of commercial buildings in California [10] – are mainly based on experimental measurements (roof temperatures, indoor and operative temperatures of the rooms, heat flux incoming through the roof). In some cases, the results of the experimental campaign are also used to calibrate the simulated model of the real building, thus allowing further analyses and comparisons than those strictly related to the measurements.
However, a point that seems to be neglected when dealing with the simulation of a cool roof, even in the calibration stage, is the calculation of the convective heat transfer coefficient on the external surface of the roof. Indeed, roofs also discharge the absorbed heat by convection on their external surface, and the entity of this mechanism is not negligible. Thus, if not addressed correctly, this issue may introduce considerable inaccuracy in the comparison between cool roofs and traditional solutions. This aspect represents the main subject of this paper.
Section snippets
Preliminary analysis
In order to understand the role played by the external convective heat transfer coefficient in the evaluation of the roof surface temperature, a preliminary calculation based on a stationary model has been performed. Under steady-state conditions, that is to say without considering the heat capacitance of the roof, and with reference to Fig. 1, the energy balance on the roof surface can be stated as in Eq. (1), where Tse is the outer surface temperature:
Review of the algorithms available in EnergyPlus™
In this paper EnergyPlus™ was selected as the simulation platform for implementing the building energy model, as it provides a large variety of algorithms for the calculation of the convective heat transfer coefficient. A very interesting review on this topic, that also addresses other simulation programs, has been presented by Mirsadeghi et al. [18].
More specifically, five basic options for the calculation of hc are available in EnergyPlus™:
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SimpleCombined;
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TARP;
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MoWiTT;
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DOE-2;
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Adaptive.
Each
The sample building
In this section, the results of a monitoring campaign carried out on an existing low-rise office building are firstly presented. Here, a cool paint have been applied over a portion of the horizontal roof, which was originally covered with traditional clay tiles; then, the roof external surface temperature was measured during two summer weeks in two zones of the roofs (with and without cool paint). These experimental results were then compared to those obtained through a numerical simulation
Effect on the cooling energy needs
As previously stated, in this section the energy simulations of the sample building are performed over the whole summer period (from the 1st of June to the 30th of September), in order to quantify the potential error induced by the choice of an inappropriate convection algorithm on the cooling energy needs of the building. In this case, the indoor temperature was kept at 26 °C; the weather data are those reported in the database of EnergyPlus™ for the city of Catania.
The results are shown in
Conclusions
The use of the cool roof technology as a passive cooling strategy has received a wide attention in the last years in Europe. The launch of the European Cool Roof Council, on the footsteps of the more consolidated Cool Roof Rating Council in the USA, has led to a series of studies on the viability of this technology, based both on experimental measurements and on evaluations through well-established building energy simulation tools, such as EnergyPlus™.
However, the results presented in this
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