Analysis of Incorporating a Phase Change Material in a Roof for the Thermal Management of School Buildings in Hot-Humid Climates

: Strategies to reduce energy consumption are presently experiencing vigorous development. Phase change materials (PCMs) are novel materials that can reduce indoor temperatures via the change in material phase. Regarding the situation in Taiwan, there is no practical utilization of PCMs in school buildings at present, especially in combination with rooftops. In this paper, we discuss the feasibility and utilization potential of installing PCMs in the rooftops of school buildings. School buildings located in northern and southern Taiwan (Taipei and Kaohsiung) were selected to analyze the energy-saving potential and optimization of indoor thermal comfort by installing PCMs with different properties in rooftops over two time periods, including the air conditioning (AC) and natural ventilation (NV) seasons. Based on the simulation results, the feasible patterns of PCM simultaneity are found to be appropriate for improved indoor comfort and energy saving during the different seasons. Speciﬁcally, the efﬁcient phase change temperature (PCT) for different PCM thicknesses is clariﬁed to be 29 ◦ C. The economic thickness of PCM was clariﬁed to be 20 mm for Taipei and Kaohsiung. Through the recommendations proposed in this study, it is expected that the PCMs may be efﬁciently implemented in school buildings to realize the goal of energy conservation and improve thermal comfort.


Introduction
When considering the heat insulation of buildings, the great amount of heat gain from façades and rooftops cannot be neglected. Previous studies attempted to explore various materials and techniques for improving the heat insulation of building envelopes or structures and discuss opportunities and challenges. Furthermore, researchers have suggested feasible utilization strategies [1,2]. Roofs are exposed to direct sunlight for a long period of time and thereby significantly influence the energy consumption of a building when controlling the resulting indoor temperature, especially in hot climate areas, such as Taiwan. One of the most common measures for reducing roof heat gain is to reduce the overall heat transfer coefficient, i.e., the U-value, by adding insulative materials. Phase change materials (PCMs) allow incidental heat gain to be used to change the phase of the material and thus perform heat storage, and such materials may store a significant amount of thermal energy. PCMs are considered to be an innovative technology and an effective method for improving the thermal mass of buildings, owing to the large thermal capacity within a limited temperature range, which is similar to an isothermal energy tank [3]. Incorporating PCMs into roofs can significantly enhance the heat storage ability of a structure and disperse the heat gains from the peak hours of cooling demand, consequently reducing energy consumption and improving indoor thermal comfort.
Most of the previous studies focused on the use of PCMs have primarily considered walls and have neglected the potential for roofs, even though roofs represent significant heat gain. Although most attention has been paid to the installation of PCMs in walls, the ratio of studies discussing PCMs in roofs to those in walls is approximately 1:3 [4]; however, some studies have used experimental or numerical simulation methods to investigate the energy-saving potential of installing PCMs in roofs or floors to discuss the performance of heating systems [5][6][7]. Studies related to the installation of PCMs can be divided into two types, including reducing energy consumption in air-conditioned buildings and improving thermal comfort in non-air-conditioned buildings. In addition, the most common parameters of PCMs that have been analyzed in previous studies are the phasechange temperature (PCT), thickness, and position of the PCM layer. Kim et al. analyzed the energy consumption of a residential building with a PCM with a specific melting temperature under different air conditioning conditions and suggested suitable PCM properties for various cooling and heating conditions in different seasons [8]. Tokuç et al. [9] evaluated roofs with and without PCMs in terms of the cooling load for the summer season in four weather zones of Turkey. They indicated that the reduction in the cooling load in May was more significant when installing thicker PCM layers. Specifically, a PCM with a thickness of 50 mm reduced the cooling load by 48.2%, 56.6%, 78.7%, and 99.1% in Izmir, Istanbul, Ankara, and Erzurum, respectively.
Regarding studies related to the combination of PCMs and rooftops, Alawadhi and Alqallaf [10] carried out numerical and experimental studies of a roof structure with PCMs. It was found that the heat transferred into the indoor space could be reduced by 39%. Mushtaq et al. [11] experimentally studied the effect of incorporating a PCM with a melting temperature of 37 • C into a roof structure with a cooling system under summer weather conditions in Baghdad, Iraq, and found that a roof structure with a PCM reduced heat transfer by 46.71% when compared to the reference roof structure. Zwanzig et al. [12] evaluated the energy-saving potential of installing a PCM layer at different positions inside the roof structure of residential buildings located in three climatic zones in the USA (Minneapolis, Louisville, and Miami). The results showed that installing a PCM in the interior surface resulted in better energy-saving potential, as the cooling loads were reduced by up to 11.4%, 8.0%, and 4.1%, respectively. Xamán et al. [13] developed alternatives with different PCM types and thicknesses for warm weather conditions in Mexico by applying PCMs on the surfaces of roof components that were closer to the indoor environment.
Previous studies also discussed the application of PCMs for promoting thermal comfort. For instance, Mourid and Alami [14] evaluated the effectiveness of combining PCMs with roof structures to improve the summer thermal comfort in lightweight buildings and investigated the influence of the thickness and position of the PCM layer on its effectiveness. Piselli et al. [15] demonstrated that a combination of cool roofing membranes and PCMs is practical and effective at lowering surface temperatures and can mitigate indoor overheating in peak summer conditions without drawbacks in the cold season. Li et al. [16] conducted an experimental study to explore the influence of the melting temperature and thickness of a PCM on the thermal performance of a glazed roof. The results showed that the peak temperature decreased by approximately 16.3 • C, and the energy consumption reduced by 47.5% when utilizing a PCM with a melting temperature of 32 • C. With an increasing thickness of the PCM layer, the energy consumption and dissatisfaction rate for an indoor thermal environment gradually declined. Parametric analysis of the thermal behavior of PCMs with different melting temperatures, layer thicknesses, and numbers of layers incorporated into building roofs was carried out in the humid tropical weather of Chennai, India, by Reddy et al. [17]. Analysis has also been carried out in the cold northeastern area of China by Dong et al. [18] and over a range of climates across the United States by Kibria et al. [19]. Besides, Yu et al. [20] have numerically investigated the phase transition temperature and thickness of a PCM layer in a roof of typical design under climatic conditions in five regions in China. Their results showed that the optimal thickness of PCM is 30 mm and that the optimum phase transition temperature increases linearly with the increase in average outdoor solar air temperature in summer in different climatic regions. David and Javier [21] analyzed the selection of PCMs for building wallboards and roofs via a comparison between multi-criteria decision methods and building energy simulations. The results demonstrated the importance of environment variables in appropriately assessing the performance of PCMs, and indicated that PCMs have different thermal behaviors depending on the climatic conditions. Accordingly, it is essential to assess an extensive evaluation of the climatic condition before applying this strategy.
The previous studies mentioned above analyzed the energy-saving potential and the effect of improving thermal comfort resulted from the utilization of PCM; however, most of these studies are conducted under a specific season. Different from the previous research, this study aims at suggesting a feasible and economic pattern of PCMs for school buildings that can simultaneously fulfill the conditions during the AC and NV seasons to reduce energy consumption and provide a better thermal comfort condition. In view of the fact that the Taiwanese government intends to complete the installation of airconditioning in 103,000 classrooms across the entire island by the summer of 2022, it is considered that the utilization of PCMs is helpful for raising the effect of energy-saving potential and indoor thermal condition. However, there are no existed practical cases of combining the PCMs and rooftop structure in Taiwanese school buildings. Thus, this study acts as a pioneer study to discuss the effect and feasibility of utilizing PCMs on the rooftop of Taiwanese school buildings and attempts to suggest recommendations for the utilization strategies that the energy-saving potential and indoor thermal comfort are both taken into consideration. The investigated cases in this paper were set to analyze the reducing cooling load during the air-conditioning season and improving the thermal comfort of real classrooms during the ventilation season. Based on the simulation results, it is expected to suggest the appropriate properties of PCMs for Taiwanese school buildings, including thickness and PCT. In addition, a feasible pattern of PCM, which is appropriate to be utilized throughout the entire year, is proposed to fulfill the indoor comfort and energy-saving potential.

Building Prototype and Simulations Procedure
The top-floor classrooms of a typical high-school building ( Figure 1) located in Taiwan are selected as a model for simulation. The setting conditions of the building model are listed in Table 1. Besides, a 2.0 m deep outdoor corridor is used as a horizontal shade on the south side. Regarding the air-conditioning operation and natural ventilation period of this school building model, the air-conditioning is available for use during the weekdays in the hot-humid period from May to October. Based on the regulation, it is allowed to turn on the air-conditioning when the outdoor temperature is higher than 27 • C. Besides, the windows are always closed during the occupancy period and out of the occupancy period at night and on weekends during the AC season. The natural ventilation season is from November to April.
In order to optimize the thermal design for the classroom, including cutting down the cooling load from May to October and improving the thermal environment from November to April, the case studies of installing PCM at the inner side of the existing roof were proposed. Due to the sol-air temperature on the external roof surface varies greatly between day and night, the inner side of the roof was chosen to install the PCM, which is particularly suitable for the application of phase-change energy-storage technology. Moreover, previous studies [22][23][24][25][26] have confirmed that placing PCM on the inner surface of a wall can better regulate the indoor temperature and save more energy than deploying PCM on the outer surface of a wall. The PCM considered in this paper is BioPCM™, which is generally used by other previous studies; besides, the database of the BioPCM™ is complete that can be regarded as a convincing material [27][28][29][30][31][32]. BioPCM™ is nontoxic, non-corrosive, biodegradable, and has a useful life of over 100 years. In addition, BioPCM™ enables users to reduce their carbon footprint and reduce the stress on HVAC Buildings 2021, 11, 248 4 of 17 systems in buildings, data centers, and telecom shelters [33]. In order to investigate the climate and seasonal adaptability of PCM, six types of phase-change temperature (PCT) were considered, including 23 • C (22-25 • C), 25 • C (24-27 • C), 27 • C (26-29 • C), 29 • C (28-31 • C), 31 • C (30-33 • C), and 33 • C (32-35 • C). Furthermore, four different thickness types of PCM layer were set, including 10 mm, 20 mm, 30 mm, and 40 mm. The latent heat of BioPCM is 219 kJ/kg. Figure 2   In order to optimize the thermal design for the classroom, including cutting down the cooling load from May to October and improving the thermal environment from November to April, the case studies of installing PCM at the inner side of the existing roof were proposed. Due to the sol-air temperature on the external roof surface varies greatly between day and night, the inner side of the roof was chosen to install the PCM, which is particularly suitable for the application of phase-change energy-storage technology. Moreover, previous studies [22][23][24][25][26] have confirmed that placing PCM on the inner surface of a wall can better regulate the indoor temperature and save more energy than deploying PCM on the outer surface of a wall. The PCM considered in this paper is BioPCM™, which is generally used by other previous studies; besides, the database of the BioPCM™ is complete that can be regarded as a convincing material [27][28][29][30][31][32]. BioPCM™ is non-toxic, noncorrosive, biodegradable, and has a useful life of over 100 years. In addition, BioPCM™ enables users to reduce their carbon footprint and reduce the stress on HVAC systems in buildings, data centers, and telecom shelters [33]. In order to investigate the climate and seasonal adaptability of PCM, six types of phase-change temperature (PCT) were considered, including 23 °C    The building energy and thermal load simulation software EnergyPlus versi was used in this study to conduct the simulation, and the weather data of a typical The building energy and thermal load simulation software EnergyPlus version 9.4 was used in this study to conduct the simulation, and the weather data of a typical meteorological year (TMY3) of two major cities in Taiwan: Taipei (25.03 • N, 121.50 • E) and Kaohsiung (22.57 • N, 120.30 • E) were used. Specifically, the climatic conditions, including the outdoor temperature, cooling degree hour (CDH), and horizontal solar radiation of each month for the two selected study cities, are shown in Figure 3. Taiwan is located in the sub-tropical zone that the weather features are hot and humid. Referring to Figure 3, it is known that the outdoor temperature in Taipei during winter is much lower than that of Kaohsiung, although Taipei and Kaohsiung are both located in a hot-humid climate zone; as for the outdoor temperature in Kaohsiung, it remains at an extremely high temperature during the entire year. In addition, the heat gains from the rooftop are directly affected by the solar air temperature. As shown in Figure 4, there is a wide range of the variation of daily solar air temperature, which means the utilization potential of PCM in rooftop structure is expectable in both Taipei and Kaohsiung.
each month for the two selected study cities, are shown in Figure 3. Taiwan is located in the sub-tropical zone that the weather features are hot and humid. Referring to Figure 3, it is known that the outdoor temperature in Taipei during winter is much lower than that of Kaohsiung, although Taipei and Kaohsiung are both located in a hot-humid climate zone; as for the outdoor temperature in Kaohsiung, it remains at an extremely high temperature during the entire year. In addition, the heat gains from the rooftop are directly affected by the solar air temperature. As shown in Figure 4, there is a wide range of the variation of daily solar air temperature, which means the utilization potential of PCM in rooftop structure is expectable in both Taipei and Kaohsiung. CDH 27 is a statistic value in the weather data (TMY3). Besides, owing to this value is closed to the standard value that is regulated to turn on the air-conditioning (27-28 °C); therefore, CDH 27 was set for the simulation in this study. All simulations were conducted using the conduction finite difference (CondFD) approach. During the months of May to October, air-conditioning equipment was activated to analyzing the cooling load of the classrooms; during the months of April to November, the thermal conditions of classrooms with natural ventilation opening areas such as windows were simulated (mainly for the operating temperature) through the airflow network model in EnergyPlus. The series of simulations mainly focuses on cases with PCM-installed roofs and night ventilation. Comparing to the traditional reference cases without installing PCM in the roof structure, the cooling load reduction and thermal comfort improvement resulted from the application of PCM in the roofs could be identified.

Selection of Performance Indicators
Through combining PCMs with a building's heating, ventilation, and air-conditioning (HVAC) system, it can utilize low nighttime temperatures to store or release energy and make use of the energy transfer for "peak shaving and valley filling", and thereby providing all or part of the heating or cooling required during the day. In order to take better advantage of PCMs in buildings, it is essential to evaluate the usage efficiency of PCMs based on latent heat. In addition to the usage efficiency of PCMs, other indicators must be considered to evaluate the effectiveness in terms of improving indoor thermal comfort and energy savings. Therefore, three performance indicators, including the daytime heating efficiency coefficient (heat storage), the nighttime cooling efficiency coefficient (heat release), and the effective latent storage, were selected to assess the usage efficiency of a PCM roof in energy storage/releasing and the effectiveness in terms of improving the indoor thermal environment and energy saving. Each of the evaluation indicators is respectively elaborated in the following section.

Usage Efficiency of PCM
There are two main factors that influence the usage efficiency of PCM: operational period and latent storing and releasing capability of heat. Specifically, regarding the operational period, the PCM layer can reach a completely solidified or completely melted CDH 27 is a statistic value in the weather data (TMY3). Besides, owing to this value is closed to the standard value that is regulated to turn on the air-conditioning (27-28 • C); therefore, CDH 27 was set for the simulation in this study. All simulations were conducted using the conduction finite difference (CondFD) approach. During the months of May to October, air-conditioning equipment was activated to analyzing the cooling load of the classrooms; during the months of April to November, the thermal conditions of classrooms with natural ventilation opening areas such as windows were simulated (mainly for the operating temperature) through the airflow network model in EnergyPlus. The series of simulations mainly focuses on cases with PCM-installed roofs and night ventilation. Comparing to the traditional reference cases without installing PCM in the roof structure, the cooling load reduction and thermal comfort improvement resulted from the application of PCM in the roofs could be identified.

Selection of Performance Indicators
Through combining PCMs with a building's heating, ventilation, and air-conditioning (HVAC) system, it can utilize low nighttime temperatures to store or release energy and Buildings 2021, 11, 248 6 of 17 make use of the energy transfer for "peak shaving and valley filling", and thereby providing all or part of the heating or cooling required during the day. In order to take better advantage of PCMs in buildings, it is essential to evaluate the usage efficiency of PCMs based on latent heat. In addition to the usage efficiency of PCMs, other indicators must be considered to evaluate the effectiveness in terms of improving indoor thermal comfort and energy savings. Therefore, three performance indicators, including the daytime heating efficiency coefficient (heat storage), the nighttime cooling efficiency coefficient (heat release), and the effective latent storage, were selected to assess the usage efficiency of a PCM roof in energy storage/releasing and the effectiveness in terms of improving the indoor thermal environment and energy saving. Each of the evaluation indicators is respectively elaborated in the following section.

Usage Efficiency of PCM
There are two main factors that influence the usage efficiency of PCM: operational period and latent storing and releasing capability of heat. Specifically, regarding the operational period, the PCM layer can reach a completely solidified or completely melted stage within a relatively short period of time; in other words, instead of operating all day, the PCM layer must be in a partially melted state for a long period time, which means that it operates effectively in daily cycles. Concerning the latent storing and releasing capability of heat, it is unpopular to utilize the PCM layer with worse performance than storing or releasing a small amount of energy during the daily cycles. Scilicet, the better performance of PCMs is that the heat-storing at night is equivalent to the heat releasing during daytime. Aforementioned, the usage efficiency of a PCM can be analyzed through its latent storing and releasing capability of heat, as well as its operational period within one daily cycle.
Ramakrishnan et al. [28] developed a method to determine the latent storing and releasing capability of heat by combining the factors mentioned above, and thereby providing more accurate predictions of the daytime heating efficiency coefficient (heat storage) and the nighttime cooling efficiency coefficient (heat release) for a PCM, named HE and CE (Equations (1) and (2)). HE and CE are used to respectively describe the operating effectiveness of the PCM during the storing and releasing latent heat period and are separately calculated for the air-conditioning season from May to October and for the natural ventilation season from November to April. Referring to Equations (1) and (2), L C and L DC provide information regarding the potential energy that is effectively stored and released in the PCM layer via the melting and solidification processes. In this paper, the releasing time of heat during the daytime was 600 min (08:00-17:00), and the storing time of heat at nighttime was 840 min (17:00-08:00). Besides, T C and T DC can be used to identify the length of time that the PCM layer is activated during the heat-storage/releasing period; a longer time period in which the PCM layer is activated can provide longer isothermal energy storage.
where L C and L DC are the ratios of latent heat stored/released by the PCM during daytime/nighttime over the total latent heat capacity of the PCM; T C and T DC are the ratios of the actual operating time of the PCM during daytime/nighttime over the storing/releasing time during daytime/nighttime; T C /T DC is the interval between occurrence times of the maximum and the minimum value. The effective latent storage (η) of the PCM layer at a specific moment is calculated by Equation (3). The value of η = 1 means that the PCM layer is completely solidified; η = 0 means that the PCM layer is completely melted.
where ∆H is the phase-change enthalpy value of PCM; H(T i ) and H(T 0 ) are the specific enthalpies of PCM at the temperature T i and the melting onset temperature T 0 , respectively. The node temperature of the PCM can be confirmed from the simulation results of EnergyPlus, and the specific enthalpy can be obtained from the enthalpy-temperature curves in.

Evaluation of Thermal Comfort and Energy-Saving Potential
A long-term evaluation of building performance and the criteria for determining the performance should consider the different potential susceptibilities of occupants to overheating [35]. In addition, the thermal evaluation and the design corresponding to the occupants should apply the thermal comfort standard that adapted to occupants' thermal perception [36]. Hence, the adaptive comfort model for students in Taiwan [37] is used to evaluate the thermal environment of classrooms during the natural ventilation season from November to April. Specifically, this model is based on the experimental data of a thermal comfort survey in elementary schools and high schools. The upper limit temperature of thermal comfort (T max ) is defined by Equation (4): where T max is the upper limit temperature of thermal comfort; T om is the monthly moving average or the daily average of the outdoor air temperature for the past 30 days.
Regarding the long-term evaluation of indoor thermal comfort, Annex H of ISO 7730 [38] listed two types of measures for thermal discomfort to simultaneously consider the frequency and level of discomfort severity; besides, all of these two measures use the positive difference between the current operating temperature and the upper limit of thermal comfort range to evaluate the overheating discomfort. Briefly reviewing the two measures, the first measure is the number of hours in which the upper limit of thermal comfort range is exceeded; the second measure is the level of overheating severity that reflects the continuous duration and level of overheating, which is also called weighted overheating hours. The weighted measure indicates the level of thermal dissatisfaction among subjects and takes discomfort to be proportional to the non-linear ratio of the discomfort curve (PD h ) [37]. The two measures are defined by Equations (5) and (6). Eventually, the energy-saving potential of PCM from May to October is defined as the percentage of energy savings based on the cooling load (Equation (7)): where, I is the measures for thermal discomfort; for the first measure, wf 1 (τ) = 1.0; for the second measure, wf 2 (τ) = PD h (τ)/0.2; T op is the operating temperature; PD h is the discomfort curve, defined by Equation (6).

Cooling Load and Thermal Environment with No PCM Roof
The simulation results of monthly cooling loads (CL), the number of overheating hours (I1), and the number of weighted overheating hours (I2), which represent the thermal discomfort level of the classrooms without a PCM in the roof structure in Taipei and Kaohsiung are shown in Figure 5. According to Figure 5, under the weather conditions of CDH 27, it is known that the annual cooling load is 59.0 GJ and the thermal discomfort levels of I1 and I2 are respectively 234 h and 519 h for the top-floor classrooms in Taipei.
Regarding the results of Kaohsiung, the cooling load is 79.8 GJ, and the thermal discomfort levels of I1 and I2 are respectively 344 h and 651 h. Owing to there is a higher CDH 27 and horizontal solar radiation, it is predictable that the cooling load of Kaohsiung will be higher than that of Taipei. For projects aimed at the improvement of roof structures, the ideal outcome is to reduce the cooling load and thermal discomfort in the top-floor classrooms to be the same level as in non-top-floor classrooms at the same time. Therefore, the simulation results of the non-top-floor classrooms, which had the same identical configuration with top-floor classrooms, are also shown in Figure 5 for comparing the difference. Specifically, the differences between the cooling loads and thermal discomfort levels of top-floor and non-top-floor classrooms can be regarded as being caused by the heat transferred from the roof.
The simulation results of monthly cooling loads (CL), the number of overheating hours (I1), and the number of weighted overheating hours (I2), which represent the thermal discomfort level of the classrooms without a PCM in the roof structure in Taipei and Kaohsiung are shown in Figure 5. According to Figure 5, under the weather conditions of CDH 27, it is known that the annual cooling load is 59.0 GJ and the thermal discomfort levels of I1 and I2 are respectively 234 hours and 519 hours for the top-floor classrooms in Taipei. Regarding the results of Kaohsiung, the cooling load is 79.8 GJ, and the thermal discomfort levels of I1 and I2 are respectively 344 hours and 651 hours. Owing to there is a higher CDH 27 and horizontal solar radiation, it is predictable that the cooling load of Kaohsiung will be higher than that of Taipei. For projects aimed at the improvement of roof structures, the ideal outcome is to reduce the cooling load and thermal discomfort in the top-floor classrooms to be the same level as in non-top-floor classrooms at the same time. Therefore, the simulation results of the non-top-floor classrooms, which had the same identical configuration with top-floor classrooms, are also shown in Figure 5 for comparing the difference. Specifically, the differences between the cooling loads and thermal discomfort levels of top-floor and non-top-floor classrooms can be regarded as being caused by the heat transferred from the roof. The contribution of heat transferred from the roof to the cooling loads and thermal discomfort levels of classrooms without PCM in the roof structure is shown in Table 2. The results show that the heat transferred from the roof accounts for 20.4% of the cooling load during the air-conditioning season in Taipei and 19.7% in Kaohsiung. The proportion of the overheating hours (I1) contributed by a roof in the ventilation season is 44.4% in Taipei and 64.2% in Kaohsiung; the proportion of the weighted overheating hours (I2) contributed by the roof is respectively 52.8% and 68.5% in Taipei and Kaohsiung. According to the results mentioned above, the importance and urgency of improving the thermal performance of the roof structure are confirmed.

Influence of PCM on The Energy Consumption of the Air-Conditioning Season
In this paper, 30 cases of different properties of PCM are set to analyze the parameters which influence thermal performance. Specifically, six kinds of PCTs (23 • C, 25 • C, 27 • C, 29 • C, 31 • C, and 33 • C) and five types of PCM thickness (10-50 mm) were set. Figure 6 shows the energy-saving effects achieved by coupling different PCTs and PCM thicknesses during the AC season from May to October. Both PCT and thickness of PCM significantly influenced the reduction percentage of cooling load during the air-conditioning season. Within the scope of study cases, the energy-saving potential of a PCM layer on the cooling load was 1.2-7.8% in Taipei, which is equivalent to a cutback proportion of 6.3-41.6% cooling load from the roof; and 0.9-6.2% in Kaohsiung, which is equivalent to a cutback proportion of 4.8-33.1% of the cooling load from the roof. Under the circumstance of the same PCM layer thickness during the air-conditioning season, the analysis results of the six selected PCTs show that the energy-saving effect initially increased with the increasing PCT; however, after reaching the peak of energy-saving effect, the energy-saving effect decreases as the PCT increases. In addition, it is important to match the PCT with the outdoor air temperature at night to make the PCM layer completely release the latent heat absorbed and stored during the daytime; meanwhile, it can avoid the heat storage capacity of the PCM layer becoming smaller on the next day. In other words, a higher PCT restricts the heat that can be absorbed and stored by the PCM layer during daytime and lead to a poorer energy-saving effect. Nevertheless, a lower PCT cannot release enough heat at nighttime and results in the poor ability to absorb and store heat. Therefore, it had the same effect of reducing cooling load as higher PCT.
h influence thermal performance. Specifically, six kinds of PCTs (23 °C, 25 °C, 27 °C, , 31 °C, and 33 °C) and five types of PCM thickness (10-50 mm) were set. Figure 6 s the energy-saving effects achieved by coupling different PCTs and PCM thickes during the AC season from May to October. Both PCT and thickness of PCM sigantly influenced the reduction percentage of cooling load during the air-conditioning on. Within the scope of study cases, the energy-saving potential of a PCM layer on the ing load was 1.2-7.8% in Taipei, which is equivalent to a cutback proportion of 6.3cooling load from the roof; and 0.9-6.2% in Kaohsiung, which is equivalent to a ack proportion of 4.8-33.1% of the cooling load from the roof. Under the circumstance e same PCM layer thickness during the air-conditioning season, the analysis results e six selected PCTs show that the energy-saving effect initially increased with the asing PCT; however, after reaching the peak of energy-saving effect, the energy-savffect decreases as the PCT increases. In addition, it is important to match the PCT the outdoor air temperature at night to make the PCM layer completely release the t heat absorbed and stored during the daytime; meanwhile, it can avoid the heat storapacity of the PCM layer becoming smaller on the next day. In other words, a higher restricts the heat that can be absorbed and stored by the PCM layer during daytime lead to a poorer energy-saving effect. Nevertheless, a lower PCT cannot release gh heat at nighttime and results in the poor ability to absorb and store heat. Thereit had the same effect of reducing cooling load as higher PCT. For achieving the maximum energy-saving effect, the feasible PCTs for an air-con tioning season under different thicknesses of PCM are confirmed. Specifically, from aspect of cost and efficiency, there is still an upper limitation that when increasing PCT or thickness may not achieve the corresponding effect in a linear relationship. A cording to the results shown in Table 3, it is worth noting that only the case with a PC thickness of 50 mm showed a better PCT at 27 °C in Taipei, all of the beneficial PCTs o PCM layer in the air-conditioning season occurred at 29 °C both in Taipei or Kaohsiu This result is in accordance with the previous literature reviews [39][40][41], which point that it is not recommended to apply PCM with PCT > 30 °C as passive cooling for bui ings. As shown in Figure 6, when the thickness of the PCM layer in Taipei was 50 mm, energy-saving effect of PCT = 29 °C or the beneficial PCT = 27 °C was almost the same t the differences between these two cases were negligible. Therefore, the beneficial PCT a PCM roof in the air-conditioning season could be regarded as 29 °C. In addition, results also show that though the solar radiation in Kaohsiung was higher than in Taip however, there is no need to apply the PCM layer with higher PCT in Kaohsiung to cre a better energy-saving effect. Figure 6 also shows the expected trends: the energy-saving effect increases with increasing thickness of the PCM layer, and the increasing trend became moderate wh the thickness of the PCM layer decreased. Taking a beneficial PCT as an example, acco ing to the simulation results, when the thickness of the PCM layer increases from 10 m For achieving the maximum energy-saving effect, the feasible PCTs for an airconditioning season under different thicknesses of PCM are confirmed. Specifically, from the aspect of cost and efficiency, there is still an upper limitation that when increasing the PCT or thickness may not achieve the corresponding effect in a linear relationship. According to the results shown in Table 3, it is worth noting that only the case with a PCM thickness of 50 mm showed a better PCT at 27 • C in Taipei, all of the beneficial PCTs of a PCM layer in the air-conditioning season occurred at 29 • C both in Taipei or Kaohsiung. This result is in accordance with the previous literature reviews [39][40][41], which point out that it is not recommended to apply PCM with PCT > 30 • C as passive cooling for buildings. As shown in Figure 6, when the thickness of the PCM layer in Taipei was 50 mm, the energy-saving effect of PCT = 29 • C or the beneficial PCT = 27 • C was almost the same that the differences between these two cases were negligible. Therefore, the beneficial PCT of a PCM roof in the air-conditioning season could be regarded as 29 • C. In addition, the results also show that though the solar radiation in Kaohsiung was higher than in Taipei; however, there is no need to apply the PCM layer with higher PCT in Kaohsiung to create a better energy-saving effect. Figure 6 also shows the expected trends: the energy-saving effect increases with the increasing thickness of the PCM layer, and the increasing trend became moderate when the thickness of the PCM layer decreased. Taking a beneficial PCT as an example, according to the simulation results, when the thickness of the PCM layer increases from 10 mm to 20 mm, the energy-saving effect increased from 5.21% to 6.86% in Taipei, which was an increment of 1.65%; increased from 4.74% to 5.91% in Kaohsiung, with an increment of 1.16%. Regarding the thickness of the PCM layer increases from 40 mm to 50 mm, the energy-saving effect increases from 7.45% to 7.6% in Taipei, for which the increment was 0.15%; as for the results of Kaohsiung, the energy-saving effect increased from 6.17% to 6.22%, for which the increment was barely 0.05%. It is worth noting that the thickness of the two circumstances increased the same by 10 mm, but the increment of the energy-saving effect differs by nearly 11 times and 24 times. It is because of the low thermal conductivity of PCM (0.2 W/m·K) and a thicker PCM layer, the required time for complete melting of PCM is prolonged. If the time required for melting lasts too long, part of the PCM may remain in a solid state at the end of the daytime period of the endothermic process. Under the circumstance of a thicker PCM layer, the full capacity of PCM has not yet been utilized; therefore, the relationship between the energy-saving effect and the thickness of PCM was not linearly related.

Influence of PCM on Thermal Comfort in the Ventilation Season
The roof structure with PCM creates a more comfortable environment during the ventilation season from November to April, which can reduce the number of overheating hours and weighted overheating hours under the situation of classroom operating temperatures exceeding 80% of the acceptable upper limitation. Figure 7 shows the difference in the number of overheating hours (I1) between the baseline case of a roof without PCM and the case of a roof with different kinds of PCM. In Figure 7, the overheating hours (I1) are represented by a dashed line, and the weighted overheating hours (I2) are represented by a solid line. The reduction percentage in the number of overheating hours was 3.7-45.5% in Taipei and 8.1-47.4% in Kaohsiung, which were equivalent to 9-110 h and 28-163 h less than the case of not using PCM. As shown in Figure 7, among all the analyzed cases, the decrements in weighted overheating hours (I2) were higher than those in the number of overheating hours (I1). Figure 8 explains how the PCM layer enhances the level of thermal comfort during the ventilation season. Specifically, it shows the operating temperatures of classrooms using and not using PCM in Taipei from 22-24 April. In this case, a PCM layer with a melting point of 25 • C and a thickness of 40 mm was set for simulation. As revealed in Figure 8, PCM begins to solidify by releasing heat at nighttime, and since the nighttime temperature of the ventilation season is low, most of the PCM layer was solidified by early morning. As the temperature rises during the daytime, the PCM begins to melt and store the heat transferred to the roof as latent heat, preventing it from being transferred into the interior space and thereby inhibiting the rise in indoor operating temperature. Moreover, there was no extremely high temperature during the ventilation season, so the PCM layer would melt slowly and makes the operating temperature during the day close to the comfort upper limit of 29 • C or within the comfort range. On average, the operating temperature during daytime was reduced by 1.0 • C, and the PD h was decreased by 0.11, while the temperature of the hottest noon period (12:00-14:00) was reduced more by 1.8 • C, and the PD h decreased by 0.23. Although in some high-temperature periods at noon, the PCM layer was not able to reduce the operating temperature to a comfortable range or reduce the number of overheating hours, it did reduce the PD h significantly, which would help to improve the comfort level of classrooms. Furthermore, within the three days shown in Figure 8, the length of time periods in which the operating temperature was outside the comfort zone had also been decreased by installing PCM in the roof structure. Under the situation without PCM, the temperature exceeded the comfort zone for 14 h; while under the situation of using PCM, the continuous time was shortened to 8 h. Simultaneously, referring to the result of the previous night of 23 April, it showed that when the temperature was low enough for a complete solidification of the PCM, the greatest improvement in indoor comfort could be achieved.
in the number of overheating hours (I1) between the baseline case of a roof without PCM and the case of a roof with different kinds of PCM. In Figure 7, the overheating hours (I1) are represented by a dashed line, and the weighted overheating hours (I2) are represented by a solid line. The reduction percentage in the number of overheating hours was 3.7-45.5% in Taipei and 8.1-47.4% in Kaohsiung, which were equivalent to 9-110 h and 28-163 h less than the case of not using PCM. As shown in Figure 7, among all the analyzed cases, the decrements in weighted overheating hours (I2) were higher than those in the number of overheating hours (I1).  space and thereby inhibiting the rise in indoor operating temperature. Moreover was no extremely high temperature during the ventilation season, so the PCM would melt slowly and makes the operating temperature during the day close to th fort upper limit of 29 °C or within the comfort range. On average, the operating tem ture during daytime was reduced by 1.0 °C, and the PDh was decreased by 0.11, wh temperature of the hottest noon period (12:00-14:00) was reduced more by 1.8 °C, a PDh decreased by 0.23. Although in some high-temperature periods at noon, th layer was not able to reduce the operating temperature to a comfortable range or the number of overheating hours, it did reduce the PDh significantly, which wou to improve the comfort level of classrooms. Furthermore, within the three days sh Figure 8, the length of time periods in which the operating temperature was outs comfort zone had also been decreased by installing PCM in the roof structure. Un situation without PCM, the temperature exceeded the comfort zone for 14 h; while the situation of using PCM, the continuous time was shortened to 8 h. Simultan referring to the result of the previous night of 23 April, it showed that when the te ature was low enough for a complete solidification of the PCM, the greatest improv in indoor comfort could be achieved.
According to the results shown in Figure 6 and Table 3, it is worth noting t achieving the maximum comfort effect in the ventilation season under different nesses of PCM, it did not matter if the analysis was based on the number of overh hours or the weighted overheating hours, the beneficial PCTs were identical. For in when the thickness of PCM was 10 mm, the beneficial PCTs were 27 °C in Taipei °C in Kaohsiung; when the thickness of PCM was over 20 mm, the beneficial PCT 25 °C in Taipei and 29 °C in Kaohsiung. In addition, the beneficial PCTs for the ven and air-conditioning seasons were identical in Kaohsiung; but in Taipei, the ben PCT for the air-conditioning season was 4 °C higher than that for the ventilation s The main reason for this difference is because the outdoor air temperature of the a ditioning season was higher than that of the ventilation season; ideally, dual-laye roofs with different PCTs would be expected to be selected according to the outd mate features of the ventilation and air-conditioning seasons. Specifically, the oute layer, which possesses a higher melting temperature, would be active in summer, a inner PCM layer, which possesses lower melting temperatures, would be active in Through this measure, the energy-saving effect and indoor thermal comfort of a bu could be improved in both summer and winter [42,43]; however, it may increase co tion costs and construction difficulties.  According to the results shown in Figure 6 and Table 3, it is worth noting that for achieving the maximum comfort effect in the ventilation season under different thicknesses of PCM, it did not matter if the analysis was based on the number of overheating hours or the weighted overheating hours, the beneficial PCTs were identical. For instance, when the thickness of PCM was 10 mm, the beneficial PCTs were 27 • C in Taipei and 31 • C in Kaohsiung; when the thickness of PCM was over 20 mm, the beneficial PCTs were 25 • C in Taipei and 29 • C in Kaohsiung. In addition, the beneficial PCTs for the ventilation and air-conditioning seasons were identical in Kaohsiung; but in Taipei, the beneficial PCT for the air-conditioning season was 4 • C higher than that for the ventilation season. The main reason for this difference is because the outdoor air temperature of the air-conditioning season was higher than that of the ventilation season; ideally, dual-layer PCM roofs with different PCTs would be expected to be selected according to the outdoor climate features of the ventilation and air-conditioning seasons. Specifically, the outer PCM layer, which possesses a higher melting temperature, would be active in summer, and the inner PCM layer, which possesses lower melting temperatures, would be active in winter. Through this measure, the energy-saving effect and indoor thermal comfort of a building could be improved in both summer and winter [42,43]; however, it may increase construction costs and construction difficulties.

Efficiency of PCM
The corresponding efficiency coefficients for the PCM roof with the closest feasible PCT for applying to school buildings in Taiwan are listed in Table 4. According to the table, it could be concluded that the efficiency coefficients of CE (daytime heating) and HE (nighttime cooling) tended to be low for the selected PCM layers of various thicknesses in the two seasons. Regarding the air-conditioning season, CE and HE in Taipei, respectively, lay within 0.58-0.39 and 0.50-0.38, and those in Kaohsiung were within 0.45-0.73 and 0.43-0.55. For the ventilation season, CE and HE in Taipei, respectively, lay within 0.33-0.24 and 0.35-0.27, and those in Kaohsiung were within 0.35-0.48 and 0.38-0.53. It is predictable that the CE and HE of both cities in the two seasons were close to each other. In addition, it is worth mentioning that CE in the air-conditioning season was slightly higher than HE, particularly for the thinner PCM layer. This is because during the air-conditioning season, the outer surface temperature of the roof at 7:00-8:00 in the morning led to the PCM to start melting instead of continuously solidifying, offsetting part of the cold energy charged at nighttime. This could also be corroborated by the lower nighttime latent heat-storing ratio (L C ), as compared to the daytime latent heat-releasing ratio (L DC ). The reasons for the low CE and HE could be clarified by observing the latent heat charging ratio and operating time ratio of the PCM layer. Taking the simulation results of Taipei as examples, for various selected thicknesses of PCM, it was found that the nighttime operating time ratio (T C ) and latent heat charging ratio (L C ) from May to October were respectively 0.62-0.74 and 0.21-0.57. Figure 9 reveals the efficiency of PCM for the four days in May. A high T C indicates that the PCM layer was solidifying and releasing heat at night for most of the time. On the other hand, a low L C indicates that the PCM layer had not completely solidified before sunrise; as shown in Figure 9, the latent heat capacity could not be fully utilized. The daytime latent heat-releasing ratio (L DC ) of the PCM layer was usually close to the nighttime value L C , but the daytime operating time ratio lay within 0.44-0.67, which means that they only operated for half of the time during the daytime, even becoming entirely liquid by noon.
According to the analysis mentioned above that the utilization efficiency barely lay within 0.44-0.67, which means that although the roof with PCM significantly improves indoor thermal comfort from November to April, it does not accompany by high efficiency. In the same manner, we also evaluated the operating time ratio (T C ) and latent heatstoring ratio (L DC ) for the operation of the PCM layer through the entire ventilation season (November to April). Unlike the air-conditioning season, the nighttime operating time ratios are not high (0.30-0.42 for Taipei, 0.37-0.54 for Kaohsiung) from November to April. Moreover, as revealed by comparing Figures 9 and 10, on those four days of February, the daytime latent heat discharging ratio (L DC ) of the PCM was 0.0 at 08:00 and did not reach 1.0 until 17:00; besides, the PCM layer even started solidification after 15:00. According to the results, it means that the lack of demand was the main reason for the PCM not operating for the entire day and could not make full utilization of the latent heat effect, and accordingly lead to the poor CE or HE. Overall, the lack of demand during the daytime was the main reason for the low usage efficiency of the PCM layer in the ventilation season. This result was different for the situation during the air-conditioning season as the PCM was not able to completely solidify at nighttime. However, for the better utilization of storage capacity, the PCM must be fully melted during daytime and fully solidified during nighttime; in other words, the PCM must complete its daily phase change cycle to reach greater performance.   Figures 9 and 10, on those four days of F ary, the daytime latent heat discharging ratio (LDC) of the PCM was 0.0 at 08:00 an not reach 1.0 until 17:00; besides, the PCM layer even started solidification after According to the results, it means that the lack of demand was the main reason f PCM not operating for the entire day and could not make full utilization of the laten effect, and accordingly lead to the poor CE or HE. Overall, the lack of demand duri daytime was the main reason for the low usage efficiency of the PCM layer in the v tion season. This result was different for the situation during the air-conditioning s as the PCM was not able to completely solidify at nighttime. However, for the bett lization of storage capacity, the PCM must be fully melted during daytime and fu lidified during nighttime; in other words, the PCM must complete its daily phase c cycle to reach greater performance.

Selection of PCM
After discussing the feasible PCTs, the proper thickness of the PCM layer for a ing a better economic outcome was analyzed in this section. Under the situation advantageous PCT, the relationship between energy-saving effect, thermal comfo well as HE, and the thickness of PCM is shown in Figure 11. According to the re when the thickness was greater than 20 mm, the rates of increase in both energy-sa during the air-conditioning season and thermal comfort enhancement during the ve

Selection of PCM
After discussing the feasible PCTs, the proper thickness of the PCM layer for achieving a better economic outcome was analyzed in this section. Under the situation of the advantageous PCT, the relationship between energy-saving effect, thermal comfort, as well as HE, and the thickness of PCM is shown in Figure 11. According to the results, when the thickness was greater than 20 mm, the rates of increase in both energy-savings during the air-conditioning season and thermal comfort enhancement during the ventilation season became significantly more moderate as the PCM layer became thicker. Simultaneously, the decreasing rate of HE became rapid. Therefore, it was more economical to select the PCM with a thickness of 20 mm. tion season became significantly more moderate as the PCM layer became thicker. Simultaneously, the decreasing rate of HE became rapid. Therefore, it was more economical to select the PCM with a thickness of 20 mm. As revealed in the analysis above, the beneficial PCT during the air-conditioning season in Taipei was 4 °C higher than the PCT during the ventilation season. Under the thermal management approach of schools in Taiwan, the feasible selection of PCM roofs must simultaneously consider the energy consumption during the air-conditioning season and the annual benefit of thermal comfort during the ventilation season. The issue of whether to prioritize thermal comfort during the ventilation season or to prioritize energy consumption during the air-conditioning season may not alter by the 4 °C temperature difference when selecting a feasible PCT. Under the economic PCM thickness of 20 mm, the benefits of a PCT of 25 °C or 29 °C in the air-conditioning season and the ventilation season can be observed according to Table 5. Specifically, when 29 °C is selected as the feasible PCT, only an additional 29 h of overheating and 22 h of weighted overheating hours are added in the ventilation season, which does not significantly increase the level of thermal discomfort. Besides, it can achieve an additional 2.5 GJ (3.7%) energy-saving potential of cooling load compared with selecting 25 °C as the beneficial PCT. Even if the air conditioner is turned on for an additional 22 h during the ventilation season, the percentage of increasing cooling load is much less than 3.7%. Thus, we can confirm that the most economical PCM layer in Taipei was PCT = 29 °C and a thickness of 20 mm, which was the same as that in Kaohsiung.

Conclusions
Owing to the undergoing policy of broadly installing the air-conditioning in school buildings in Taiwan, it is essential to draw up energy-saving strategies that not only reduce energy consumption but create better indoor comfort. This paper selected the school buildings located in Taipei and Kaohsiung as target buildings to discuss their cooling load in air-conditioning season and thermal discomfort in natural ventilation season under the circumstance of installing PCM on rooftops. In order to confirm that combining the rooftop structure and PCM brings benefits to building energy-saving, this study firstly revealed the importance of heat insulation from the rooftop by simulating the incoming heat As revealed in the analysis above, the beneficial PCT during the air-conditioning season in Taipei was 4 • C higher than the PCT during the ventilation season. Under the thermal management approach of schools in Taiwan, the feasible selection of PCM roofs must simultaneously consider the energy consumption during the air-conditioning season and the annual benefit of thermal comfort during the ventilation season. The issue of whether to prioritize thermal comfort during the ventilation season or to prioritize energy consumption during the air-conditioning season may not alter by the 4 • C temperature difference when selecting a feasible PCT. Under the economic PCM thickness of 20 mm, the benefits of a PCT of 25 • C or 29 • C in the air-conditioning season and the ventilation season can be observed according to Table 5. Specifically, when 29 • C is selected as the feasible PCT, only an additional 29 h of overheating and 22 h of weighted overheating hours are added in the ventilation season, which does not significantly increase the level of thermal discomfort. Besides, it can achieve an additional 2.5 GJ (3.7%) energy-saving potential of cooling load compared with selecting 25 • C as the beneficial PCT. Even if the air conditioner is turned on for an additional 22 h during the ventilation season, the percentage of increasing cooling load is much less than 3.7%. Thus, we can confirm that the most economical PCM layer in Taipei was PCT = 29 • C and a thickness of 20 mm, which was the same as that in Kaohsiung.

Conclusions
Owing to the undergoing policy of broadly installing the air-conditioning in school buildings in Taiwan, it is essential to draw up energy-saving strategies that not only reduce energy consumption but create better indoor comfort. This paper selected the school buildings located in Taipei and Kaohsiung as target buildings to discuss their cooling load in air-conditioning season and thermal discomfort in natural ventilation season under the circumstance of installing PCM on rooftops. In order to confirm that combining the rooftop structure and PCM brings benefits to building energy-saving, this study firstly revealed the importance of heat insulation from the rooftop by simulating the incoming heat from the rooftop. Secondly, thirty cases of different setting parameters of PCM, including thickness and PCT, were set to simulate their energy-saving effect and thermal discomfort. Eventually, the recommended feasible utilization patterns of PCM for better indoor comfort and energy-saving potential was proposed.
According to the simulation results of incoming heat from a rooftop in AC season, it is known that the ratio of cooling load resulting from the rooftop is significant and cannot be ignored. Regarding the NV season, the ratio of overheating hours resulting from the rooftop should not be overlooked either. As aforementioned, the urgency of heat insulation from the rooftop could be confirmed. The investigated cases of different PCT and thicknesses of PCM show that the features of PCM make noticeable influences on the reducing potential of cooling load. Specifically, regarding the relationship between different PCT and energysaving effects in the AC season, when the thickness of PCM is fixed, it is worth noting that the energy-saving effect increases as the PCT increase. However, when reaching the peak of the energy-saving effect, the energy-saving effect decreased as the PCT increased. Furthermore, based on the simulation results, for achieving the maximum energy-saving potential, the beneficial PCT for all different thicknesses of PCM was clarified as 29 • C. Additionally, this study also analyzed the relationship between the thickness of PCM and the energy-saving effect. The results show that the energy-saving effect increased as the thickness of the PCM increased, whereas the increasing trend becomes moderate when the thickness of PCM keeps increasing. Briefly, the relationship between the energy-saving effect and the thickness of PCM was not linear.
Concerning the relationship between PCM and thermal discomfort in the NV season, the results showed that installing the PCM on the rooftop apparently cut down the weighted overheating hours in both Taipei and Kaohsiung. Furthermore, the feasible PCT under the conditions of different thicknesses of PCM was suggested. In addition, it is worth noting that the beneficial PCT in AC season and NV season was the same value in Kaohsiung; as for Taipei, the beneficial PCT in the air-conditioning season was 4 • C higher than in the NV season. After confirming the feasible PCT, the most economical thickness of PCM for improving the energy-saving effect and thermal comfort is clarified as 20 mm.
According to the aforementioned, this study suggests the feasible selection of PCM, including its thickness and PCT for the school buildings during different seasons. In addition, based on the simulation conducted respectively in the AC season and NV season, the feasible pattern of PCM through the year is proposed to fulfill the whole year indoor comfort and energy-saving potential. Through the recommendations proposed in this study, it is expected to efficiently utilize the PCM in school buildings to reduce the additional energy consumption and eventually realize the goal of energy conservation.