Effect of roof and ceiling configuration on energy performance of a metamaterial-based cool roof for low-rise office building in China

Abstract

Cool roofs with higher solar reflectance and emittance can effectively reduce building energy consumption. However, it is still limited to use at night on account of the development of roof materials during the past decades. The newly proposed metamaterial-based cool roof (MCR) greatly improves the possibility of the radiative cooling in the daytime. To study the influence of MCR on the energy consumption for the office building, a small single-floor office was adopted to analyse the cooling performance of MCR by using EnergyPlus. In this study, the optimization analysis was conducted based on the proposed dimensionless thermal resistance (θ_RTR) and roof pitch (Δ). Then the annual electricity saving potential of the office building with MCR was evaluated in details based on the selected cities from all five climate zones in China. The results show that more annual electricity saving can be achieved under the optimized values of θ_R7 = 1.53 and Δ = 20°. Furthermore, more than 15.7% of annual cooling electricity saving can be achieved while the optimized θ_RTR and Δ are applied.

Keywords

Energy consumption Office building Cool roof Thermal resistance of roof and ceiling Roof pitch

Introduction

Approximately 40% of primary energy is used in buildings, and most of them are consumed by air-conditioning systems to achieve the satisfactory indoor built environment.^1–5 As a passive cooling technique, radiative cooling has been demonstrated as an effective way to reduce the energy consumption of buildings by providing the free cooling energy accounts for the heat radiated from the radiative cooling surface to outer space through atmosphere windows (8–13 μm in wavelength).^6–10 Furthermore, the free cooling energy can always be produced once the effective temperature of the sky is lower than the temperature of the radiative cooling surface.^11–13

The most convenient employment of radiative cooling is configured as the cool roof of buildings since the only additional work is to adhere/paint the radiative cooling surface/paints to the original roof.^14–17 The tetrafluoroethylene monomer fluorocarbon coating in a water-borne formula proposed by Mastrapostoli et al.¹⁸ was employed as the cool roof in an industrial building which had a surface area of 1685 m² and a height of 7.58 m. Their study showed that 73% of cooling energy-saving as well as 5% of heating energy penalty are achieved while the roof albedo changes from 0.3 to 0.67 by replacing the original roof with the tetrafluoroethylene monomer fluorocarbon coating. Hossain et al.¹⁹ investigated the cooling efficiency of radiative cooling based on an emitter with anisotropic and conical-shaped structure surface. The results showed that the cooling capacity and temperature of the emitter can reach 116.6 W/m² and 12.2°C below the ambient temperature.

Climate and heat transfer coefficient of roof and ceiling not only have great effects on the energy consumption and thermal comfort of buildings with a cool roof but also contribute significant benefits to the heat island phenomenon.^20–22 To indicate the effects of climate and heat transfer coefficient of the roof on the energy consumption of buildings with a cool roof, a single-floor residential building with a roof area of 100 m² were simulated by Synnefa et al.²³ in 27 cities located at five typical climate zones around the world. They found that the maximum energy-saving potential would vary between 10.7% and 27.0% for different climate zones, while the heat transfer coefficient of the roof is configured as 0.84 W/m² K. The effects of solar reflectance and thermal insulation on the cooling performance of cool roof were considered comprehensively by Piselli et al.²⁴ to obtain the optimum configuration of roof for the buildings located at different climate zones. Their results showed that the maximum cooling benefit can be achieved by employing the cool roof with a high solar reflectance capability (higher than 0.8) and a no/low insulation level (thickness between 0 m and 0.03 m) except for the extremely hot or cold climate zones. To analyse the energy-saving potential for the large-scale application of cool roof in Mediterranean climate zone, the cooling benefit and heating penalty of the cool roof were calculated by Boixo et al.²⁵ with DOE (Department of Energy, U.S.) cool roof calculator for the building located at Andalucía. By comparing the residential building with a dark roof, the application of a medium-coloured roof can save 59 million euros annually in electricity costs and directly avoid the emission of 136,000 metric tons of CO₂ every year. A thermal insulation coating, which was formulated using titanium dioxide pigment with chicken eggshell waste as bio-filler bound together by a polyurethane resin binder, was employed by Yew et al.²⁶ to reduce heat transmission through the roof. Their investigation indicated that the attic temperature can be reduced by 13°C at maximum (from 42.4°C to 29.6°C) by applying the cool roof combined with the thermal insulation coating and moving-air-cavity on an opened attic. Costanzo et al.²⁷ conducted a simulation study based on an existing office building located at southern Italy. The simulation results showed that the annual energy consumption reductions of 11% and 3% would be achieved for buildings in Catania and Rome. However, the adoption of cool paint could induce a slight increase of 3% for the building in Milan which is in the cold climate zone. It also indicated that the adoption of a cool roof in the zones of intense or long winter periods must be considered carefully as an increase in the energy needs for space heating in winter. Although the existing publications have focused on the impact of roof thermal resistance on the building energy consumption, few studies focused on the influence of ceiling thermal resistance especially the coupling effect of roof thermal resistance and ceiling thermal resistance.

The roof pitch could also influence the energy consumption of the buildings since the amount of solar radiation that would reach on the roof surface could vary with the roof pitch.^28,29 To indicate the effect of roof pitch on the energy consumption of buildings, Irwan et al.³⁰ evaluated the thermal and energy performance of the test cell building in Malaysia by varying the roof pitch from 10° to 20°. The results showed that the energy consumption can be reduced by 0.79 kWh or 4.13% per day, while the roof pitch is configured at 10° comparing against the roof pitch of 20°. Atalar and Cakan³¹ analysed the effect of roof pitch on the thermal environment of buildings under four different roof inclinations of 0°, 15°, 30° and 45° in Antalya. Numerical predictions showed that the temperature inside the building can be decreased by 2.0–2.5°C when the inclination angle of the roof is increased from 0° to 45°. Mahmoud and Ismaeel³² studied the effect of roof pitch on the energy consumption and carbon emissions of the residential buildings located at three different climate zones in Egypt, including hot humid, moderately humid and hot arid, by varying the roof inclination angle. The results indicated that a larger inclined angle applied can decrease the effect of direct solar intensity and associate solar heat gain. Although the roof pitch has a significant influence on the thermal environment and energy consumption of buildings, most of the existing publications are mainly focused on the effect of traditional roofs rather than the cool roof based on the innovative materials.^33–35 Furthermore, most of the previous studies focused on the cool roof are performed based on nocturnal radiative cooling due to the mismatch of solar radiation and radiative cooling during the daytime.³⁶

Recently, several novel materials show good energy-saving potential for building applications as a cool roof. Raman et al.³⁷ reported a photonic nanostructured coating, in which nearly 40.1 W/m² of cooling power can be achieved, while the solar irradiance is 800–870 W/m² under direct sunlight. The photonic nanostructured coating was integrated on the condenser side of the cooling system by Goldstein et al.³⁸ Their study showed that approximately 21% (14.3 MWh) of electricity consumption can be saved for a two-storey office building located at Las Vegas, USA. A novel scalable-manufactured randomized glass-polymer hybrid metamaterial coated (metamaterial) with silver was developed by Zhai et al.,³⁹ and the experiments showed that approximately 93 W/m² of cooling power can be produced at noon at Arizona, USA while the solar irradiance is higher than 900 W/m². The modelling study for the building located at three locations in the USA (Tucson AZ, Los Angeles, CA and Orlando, FL) showed that 113.0–143.9 kWh/m² of annual cooling electricity can be achieved, while the shingle roof is replaced by the metamaterial.⁴⁰ Recently, a hierarchically porous poly coating was fabricated by Mandal et al.⁴¹ for achieving daytime radiative cooling, and experiments showed that approximately 96 W/m² of cooling power is produced by the hierarchically porous poly coating while the solar intensity is about 750 W/m². The simulation study by applying the hierarchically porous poly coating as the super-cool rooftop on the residential and commercial building with a flat roof was conducted by Baniassadi et al.⁴² The results indicated that the surface temperature of the super-cool rooftop is always lower to the ambient air temperature all year round and the cooling energy-saving can be doubled compared to buildings with typical white roofs. The thermal reflective coating, consists of polyurethane resin, nano titanium dioxide, bio-filler and dispersant, was proposed by Yew et al.,⁴³ and the cool roof system was developed by the combination of the thermal reflective coating, improved moving air cavity solar-powered fans and opened attic inlet. Their investigation showed that the temperatures of the roof and attic can be decreased by approximately 7°C and 15°C compared with the normal metal roof system. Although several recently proposed innovative materials show significant energy-saving potential for its application as a cool roof, most of them are conducted based on the flat roof or the experimental emitter faced to the sky.

To provide a guiding significance for the application of cool roof based on the novel diurnal radiative cooling materials, the effect of roof and ceiling configurations on the energy performance of a single-floor office building with the metamaterial-based cool roof (MCR) was analysed for buildings located at different cities from all five climate zones in China. A novel dimensionless thermal resistance has been proposed to indicate the coupling influence of roof thermal resistance and ceiling thermal resistance on the cooling performance of MCR. Finally, the impacts of roof pitch on the cooling benefit and heating penalty of MCR were also investigated by using EnergyPlus.

Methodology

Modelling for single-floor office building

A single-floor office building originates from DOE was adopted in this study.⁴⁴ As shown in Figure 1, the office building with a total floor area of 511.16 m² was divided into five thermal zones, including an attic zone, four perimeter zones and a core zone. The perimeter zones and the core zone were conditioned by an air-conditioning and the attic zone was unconditioned. The original roof of the office building with a pitch of approximately 20° is consisted of shingle roof (SR) and thermal insulation layer; however, the shingle roof replaced by the metamaterial³⁹ is considered as MCR.

The modelling work was conducted by using EnergyPlus for the office building located at the selected cites from five climate zones in China, including Harbin (severe cold climate zone), Beijing (cold climate zone), Shanghai (hot-summer and cold-winter climate zone), Guangzhou (hot-summer and warm-winter climate zone) and Kunming (moderate climate zone). The classification of above climate zones was derived for the National Standards of China.^45,46 The specification for the climate zones is also summarized in Table 1, and other details of the office building can be found in Table 2.

Table 1.

Classification of climate zones in China.

Climate zone	Index
Climate zone	Primary index	Subsidiary index
Severe cold climate zone	Average temperature of the coldest month ≤ −10°C	Days ≤ 145 (Days with daily mean temperature ≤ 5°C)
Cold climate zone	Average temperature of the coldest month = 0°C to −10°C	Days = 90 to 145 (Days with daily mean temperature ≤ 5°C)
Hot-summer and cold-winter climate zone	Average temperature of the coldest month = 0°C to 10°C, and average temperature of the hottest month = 25°C to 30°C	Days = 0 to 90 (Days with daily mean temperature ≤ 5°C), and days = 40 to 110 (Days with daily mean temperature ≥ 25°C)
Hot-summer and warm-winter climate zone	Average temperature of the coldest month >10°C, and average temperature of the hottest month = 25°C to 29°C	Days = 100 to 200 (Days with daily mean temperature ≥ 25°C)
Moderate climate zone	Average temperature of the coldest month = 0°C to 13°C, and average temperature of the hottest month = 18°C to 25°C	Days = 0 to 90 (Days with daily mean temperature ≤ 5°C)

Table 2.

Details of the parameters of the single-floor office building.

Parameters	Details
Floor area	511.2 m²
Air conditioning system	Central air-conditioning
Indoor air temperature setting	Cooling: 26°C
	Heating: 18°C
Window-wall ratio	24.4% of south wall
Window-wall ratio	19.8% of other walls
Length×width×height	27.8 m×18.5 m×6.3 m
Thermal emittance	SR: 0.9
Thermal emittance	MCR: 0.93
Solar absorptance	SR: 0.75
Solar absorptance	MCR: 0.04
Thermal resistance	Wall: R14 (2.47 m² K/W)
Window conductivity	0.9 W/m·K
Personnel density	17 m²/person
Equipment power density	6.78 W/m²
Light density	8.5 W/m²
Fresh air volume	30 m³/h per person

Process of heat transfer through MCR

The process of the heat transfer through MCR^47–49 is shown in Figure 2.

As given in Figure 2, h_CI,c (W/m²·K) is the convective heat transfer coefficient for the ceiling thermal insulation, h_CI,r (W/m²·K) is the radiative heat transfer coefficient for the ceiling thermal insulation, h_CS (W/m²·K) is the overall heat transfer coefficient for the ceiling, h_CS,c (W/m²·K) is the convective heat transfer coefficient for the ceiling, h_CS,r (W/m²·K) is the radiative heat transfer coefficient for the ceiling, h_RI (W/m²·K) is the overall heat transfer coefficient for the roof thermal insulation, h_RI,c (W/m²·K) is the convective heat transfer coefficient for the roof thermal insulation, h_RI,r (W/m²·K) is the radiative heat transfer coefficient for the roof thermal insulation, h_RS (W/m²·K) is the overall heat transfer coefficient for the roof, h_RS,c (W/m²·K) is the convective heat transfer coefficient for the roof, h_RS,r (W/m²·K) is the radiative heat transfer coefficient for the roof, I_in (W/m²) is the incident radiation, I_out (W/m²) is the outgoing radiation, LWR_in (W/m²) is the incident long wave radiation, LWR_out (W/m²) is the outgoing long wave radiation, L_CT (m) is the thickness of the ceiling, L_RT (m) is the thickness of the roof, SWR_in (W/m²) is the incident short wave radiation, SWR_out (W/m²) is the outgoing short wave radiation, t (s) is time, T_a (K) is the solar-air temperature of the roof, T_att (K) is the temperature of attic, T_CI (K) is the ceiling thermal insulation temperature, T_CS (K) is the ceiling temperature, T_floor (K) is the temperature of the floor, T_i (K) is the indoor air temperature, T_o (K) is the outdoor air temperature, T_RI (K) is the roof thermal insulation temperature, T_RS (K) is the roof temperature, T_sky (K) is the sky temperature.

As shown in Figure 2, the process of heat transfer through MCR is complicated, including incident radiation, outgoing radiation, convection heat transfer and conduction heat transfer. Since the top surface of MCR is exposed to the incident radiation, the net absorbed radiation can be obtained by summing the incident radiation on the MCR (I_in) and the outgoing radiation from the MCR (I_out). The overall heat transfer coefficient for MCR (h_RS) can be calculated by considering the effect of net absorbed radiation and the convection heat transfer on the MCR. The heat gain/loss would be transferred to the attic by the conduction heat transfer.

Method of optimization analysis

As discussed in the ‘Introduction’, both the roof thermal resistance (RTR) and the ceiling thermal resistance (CTR) could affect the cooling performance of buildings with a cool roof. However, the influence of RTR and CTR is coupled with each other. The variation in each of RTR and CTR could impact the cooling benefit and heating penalty of the building with a cool roof, but each of them can vary separately. To indicate the coupling effect of RTR and CTR on the cooling performance of MCR, a dimensionless thermal resistance is considered, as defined by equation (1)

θ_{RTR} = \frac{CTR}{RTR}

(1)

where θ_RTR is the ratio of ceiling thermal resistance to roof thermal resistance.

Optimization analysis becomes more and more popular for designing and evaluating building and energy systems, and the optimization methods of both multi-objective and single-objective have been used for optimizing buildings envelopes.^50–53

The optimization analysis in this study aims to minimize annual HVAC electricity consumption by optimizing the roof configuration, and thus the optimization analysis of the cooling effect for the building with a cool roof was performed by considering θ_RTR, RTR and roof pitch (Δ). The flow chart of the optimization analysis is given in Figure 3.

As shown in Figure 3, the optimization analysis was conducted based on numerical analysis by using EnergyPlus. The typical market available thermal insulations were selected for ceiling application, including R7 (1.26 m² · K/W), R11 (1.93 m² · K/W), R15 (2.64 m² · K/W), R21 (3.69 m² · K/W), R30 (5.28 m² · K/W) and R46 (8.11 m² · K/W). Furthermore, R7, R15 and R30 were selected for the roof insulation. Thus, θ_RTR was determined by the selected thermal insulations of R7 to R46. Furthermore, four roof pitches were employed in this study, including 10°, 20°, 30°, 45°, 60°. The 20° is the original angle of the roof given in the model of the single-floor office building.

To determine the optimum configuration of the roof and ceiling for the building with MCR, the minimum RTR and θ_RTR were adopted as the initial values for the optimization, which were then input to the model built in EnergyPlus. For the first step, the annual total HVAC electricity consumption (ATEC, a sum of annual cooling electricity consumption and annual heating electricity consumption) was calculated for various θ_RTR under a constant RTR. Secondly, the ATEC for other RTRs related to various θ_RTR was obtained by repeating the first step. By comparing the ATEC from the above calculation, the minimum ATEC was determined with specified RTR and θ_RTR. The specified RTR and θ_RTR were determined in the second step and were used as input values combined with the minimum Δ to calculate the ATEC with EnergyPlus. For the fourth step, different ATEC was obtained by varying the Δ under the specified RTR and θ_RTR. By comparing the ATEC from the fourth step, the minimum ATEC was determined under specified RTR, θ_RTR and Δ. Thus, this minimum ATEC was considered as the final result with the optimal RTR, θ_RTR and Δ. The optimization problem developed based on the above method is described by equation (2)

{\begin{cases} \min ATE C_{MCR} = f (R T R_{i}, θ_{RTR, i}, Δ_{i}) \\ s . t . R T R_{i} \in (R7, R30) \\ θ_{RTR, i} \in (0 .24,5 .07) \\ Δ_{i} \in (10^{o}, 60^{o}) \end{cases}

(2)

where ATEC_MCR (kWh) is the ATEC for the building with MCR.

From the objective function in equation (2), this multi-dimensional optimization analysis is designed to find out the optimum combination of RTR, θ_RTR and Δ to minimize annual total HVAC electricity consumption for the building with MCR. This optimization analysis was also carried out to find the optimum roof configuration, including the coupling effect of the roof and ceiling insulation and roof pitch. This optimization problem involves three design parameters (RTR, θ_RTR and Δ), which were selected as the independent continuous variables. The lower and upper bounds for the three variables are defined in equation (2). From the above, the detailed cases by considering the effect of climate zones are given in Table 3.

Table 3.

Detailed cases for the optimization analysis.

Case	RTR	θ _RTR	Δ	City	Roof type
Case 1	R30	1.54	20°	Shanghai	MCR
Case 2	R30	1.00	20°	Shanghai	MCR
Case 3	R30	0.70	20°	Shanghai	MCR
Case 4	R30	0.50	20°	Shanghai	MCR
Case 5	R30	0.36	20°	Shanghai	MCR
Case 6	R30	0.24	20°	Shanghai	MCR
Case 7	R15	3.07	20°	Shanghai	MCR
Case 8	R15	2.00	20°	Shanghai	MCR
Case 9	R15	1.40	20°	Shanghai	MCR
Case 10	R15	1.00	20°	Shanghai	MCR
Case 11	R15	0.73	20°	Shanghai	MCR
Case 12	R15	0.48	20°	Shanghai	MCR
Case 13	R7	5.07	20°	Shanghai	MCR
Case 14	R7	4.19	20°	Shanghai	MCR
Case 15	R7	2.93	20°	Shanghai	MCR
Case 16	R7	2.10	20°	Shanghai	MCR
Case 17	R7	1.53	20°	Shanghai	MCR
Case 18	R7	1.00	20°	Shanghai	MCR
Case 19	R7	1.53	20°	Shanghai	SR
Case 20	R7	1.53	10°	Shanghai	MCR
Case 21	R7	1.53	10°	Shanghai	SR
Case 22	R7	1.53	30°	Shanghai	MCR
Case 23	R7	1.53	30°	Shanghai	SR
Case 24	R7	1.53	45°	Shanghai	MCR
Case 25	R7	1.53	45°	Shanghai	SR
Case 26	R7	1.53	60°	Shanghai	MCR
Case 27	R7	1.53	60°	Shanghai	SR
Case 28	R7	1.53	60°	Harbin	MCR
Case 29	R7	1.53	60°	Harbin	SR
Case 30	R7	1.53	60°	Beijing	MCR
Case 31	R7	1.53	60°	Beijing	SR
Case 32	R7	1.53	60°	Guangzhou	MCR
Case 33	R7	1.53	60°	Guangzhou	SR
Case 34	R7	1.53	60°	Kunming	MCR
Case 35	R7	1.53	60°	Kunming	SR

Results and discussion

Coupling effect of roof and ceiling insulation

Cases 1 to 18 in Table 3 were selected to investigate the coupling effect of roof and ceiling insulations. The annual cooling electricity consumption (ACEC), annual heating electricity consumption (AHEC) and ATEC for these cases are given in Table 4.

Table 4.

Annual electricity consumption for the selected cases.

Case	RTR	θ _RTR	ACEC(kWh)	AHEC(kWh)	ATEC(kWh)
Case 1	R30	1.54	4009.5	107.5	4117
Case 2	R30	1	3971.8	128	4099.8
Case 3	R30	0.7	3935.1	153.1	4088.2
Case 4	R30	0.5	3878.6	201.6	4080.2
Case 5	R30	0.36	3861.6	220.2	4081.8
Case 6	R30	0.24	3816.6	279.3	4095.9
Case 7	R15	3.07	3986.6	111.3	4097.9
Case 8	R15	2	3939.8	134.9	4074.7
Case 9	R15	1.4	3892.3	164.5	4056.8
Case 10	R15	1	3843.1	202.4	4045.5
Case 11	R15	0.73	3798.5	247.7	4046.2
Case 12	R15	0.48	3734.7	325.3	4060
Case 13	R7	5.07	3958.5	116.4	4074.9
Case 14	R7	4.19	3899.8	143.9	4043.7
Case 15	R7	2.93	3841.3	179.5	4020.8
Case 16	R7	2.1	3778	227.9	4005.9
Case 17	R7	1.53	3714.4	287.1	4001.5
Case 18	R7	1	3626.2	397.6	4023.8

As shown in Table 4, the ACEC is reduced with the decreasing of θ_RTR when RTR is constant; however, the AHEC is increased with the decreasing of θ_RTR. This is because both cooling benefit and heating penalty are increased due to the continuous cooling effect of MCR and the decreasing of total thermal resistance of the roof system in the heating season. Thus, the ATEC is not monotonically increasing or decreasing with θ_RTR when RTR is constant. Table 4 also shows that a higher or a lower CTR is not necessary to lead a saving of ATEC even though RTR is constant. To further indicate the effect of the roof and ceiling insulation on the cooling benefit of MCR for the office building application, the relationships between ATEC, RTR and θ_RTR are illustrated in Figure 4.

As shown in Figure 4, RTR has a significant effect on ATEC. The ATEC is reduced by decreasing RTR when CTR (R_ceiling) is constant. By comparing with an office building with RTR of R30, ATEC can be decreased by 42.1 kWh (CTR of R46), 56.1 kWh (CTR of R30), 67.4 kWh (CTR of R21), 74.3 kWh (CTR of R15), 80.3 kWh (CTR of R11) and 72.1 kWh (CTR of R7) when RTR of an office building is replaced by R7. Figure 4 also indicates that approximately 2% of ATEC can be saved at the maximum once RTR is changed from R30 to R7. Furthermore, the price of R7 is also lower than that of R30 which can result in a reduction of the initial cost of the building.

However, the ATEC is decreased and then is increased with the increase of θ_RTR regardless of RTR (Figure 4(b)). The smaller the RTR, the more serious would be the impact. As shown in Figure 4(b), differences between the maximum and minimum ATEC are 36.7 kWh, 52.4 kWh and 73.4 kWh, while RTR is R30, R15 and R7, respectively. Approximately 2% saving of ATEC can be achieved at the maximum even though the RTR is constant. Furthermore, a smaller RTR has more cooling energy-saving potential. Figure 4 also indicates that there is an optimal configuration of θ_RTR (i.e. CTR and RTR) for achieving the lowest ATEC of the office building with MCR. Although the climate condition would have an impact on the ATEC of the office building with MCR due to the different characteristics of cooling and heating loads of the building, the optimal configuration would still exist as similar changes occur on the annual electricity consumption of cooling and heating.

Accordingly, the effect of roof and ceiling insulations on the ATEC of the office building with MCR is coupled and complicated; however, an optimal configuration of θ_RTR exists. Furthermore, the smaller the RTR, the more energy-saving for the office building with MCR. But the determination on the CTR should be careful by considering the climate condition, and the CTR between R11 and R15 would lead to a more cooling benefit for the office building with MCR located at hot-summer and cold-winter climate zone in China.

Influence of roof pitch on energy consumption

The roof pitch could affect the cooling performance of the office building with MCR. To indicate the influence of the roof pitch, the calculated annual electricity consumption of the selected cases from Table 3 is given in Table 5. According to the process of optimization in Figure 3, R7 and θ_R7 were determined as the optimal results of the first step based on the above analysis. Thus, the analysis was conducted based on R7 and θ_R7. To further indicate the cooling benefit of MCR to the office building, the annual electricity consumption of the office building with SR is also presented in Table 5.

Table 5.

Annual electricity consumption for the office building with different roof pitch.

Case	Δ	θ _R7	Roof type	ACEC(kWh)	AHEC(kWh)	ATEC(kWh)
Case 20	10°	1.53	MCR	3724.3	283.4	4007.7
Case 17	20°			3714.4	287.1	4001.5
Case 22	30°			3713.7	288.5	4002.2
Case 24	45°			3713.6	290.5	4004.1
Case 26	60°			3712.3	293.4	4005.7
Case 21	10°		SR	4452.2	178.9	4631.1
Case 19	20°			4456.4	179.6	4636.0
Case 23	30°			4445.1	181.6	4626.7
Case 25	45°			4433.7	183.9	4617.6
Case 27	60°			4426.4	187.1	4613.5

As shown in Table 5, the ACEC and ATEC of the office building with SR are increased and then decreased. The minimum ACEC and ATEC are 4426.4 kWh and 4613.5 kWh when Δ is 60°. However, the AHEC is continuously increased with the increasing of roof pitch. The minimum AHEC is 178.9 kWh when the Δ is 10°. For the office building with MCR, the changes in the annual electricity consumption are almost opposite to the building with SR due to the cooling benefit from MCR. The ACEC and AHEC are decreased and increased respectively with the increasing of roof pitch. The minimum ACEC is 3712.3 kWh when Δ is 60°, and the minimum AHEC of 283.4 kWh is achieved when Δ is 10°. However, the ATEC continuously increases once the roof pitch is higher than 20°. The minimum ATEC is 4001.5 kWh when Δ is 20°. By comparing with an office building with SR, the ATEC is significantly reduced by replacing the roof with MCR. As shown in Figure 5, the decreasing of the minimum ATEC can be higher than 13%.

From the enlarged view of the ATEC for MCR in Figure 5, the trend is close to an exponential curve. Thus, the relationship between the ATEC and roof pitch for the building with MCR located at hot-summer and cold-winter climate zone in China can be expressed by equation (3)

ATEC = 3998.76 + 0.12 θ_{RTR} + 150.79 \times {0.74}^{θ_{RTR}} (R^{2} = 0.999)

(3)

In summary, the roof pitch has a significant effect on the annual electricity consumption of the office building with MCR, and the effect is almost opposite to the building with SR. Furthermore, an optimal roof pitch is existed to minimize the ATEC of the office building with MCR according to the relationship between ATEC and θ_RTR. Take the office building located at hot-summer and cold-winter climate zone in China as an example, more than 13% of the ATEC can be achieved by considering the variation of roof pitch.

Analysis of energy consumption for building with MCR in different climate zones

The annual electricity consumption would be different for the office building with MCR located at different climate zones. Thus, five typical cities from five climate zones in China, including Harbin (severe cold climate zone), Beijing (cold climate zone), Shanghai (hot-summer and cold-winter climate zone), Guangzhou (hot-summer and warm-winter climate zone) and Kunming (moderate climate zone), were selected for comparing the effect of climate. According to the process of optimization, θ_R7 = 1.53 and Δ = 20° were determined as the optimized roof configuration. Then ACEC, AHEC and ATEC of the selected cases from Table 3 are given in Table 6 and Figure 6 for both office buildings with MCR and SR.

Table 6.

Annual electricity consumption for the building in different climate zones.

Case	Δ	θ _R7	Roof type	City	ACEC(kWh)	AHEC(kWh)	ATEC(kWh)
Case 28	20°	1.53	MCR	Harbin	1861.4	19671.3	21532.7
Case 20			MCR	Beijing	2949.3	2196.6	5145.9
Case 26			MCR	Shanghai	3712.3	288.5	4000.8
Case 32			MCR	Guangzhou	5418.1	0	5418.1
Case 34			MCR	Kunming	2332.3	36.0	2368.3
Case 29			SR	Harbin	2297.9	17846.5	20144.4
Case 31			SR	Beijing	3554.5	1592.0	5146.5
Case 27			SR	Shanghai	4426.4	187.1	4613.6
Case 33			SR	Guangzhou	6429.1	0	6429.1
Case 35			SR	Kunming	3109.7	17.7	3127.4

As shown in Figure 6, the AHEC of Harbin and Beijing are 19671.3 kWh and 2196.6 kWh, which are significantly higher than that of other cities. This is because: (1) heating loads of Harbin and Beijing are higher than in buildings in other cities due to the lower outdoor temperatures of severe cold climate zone and cold climate zone in winter; and (2) more serious heating penalty due to the cooling effect of MCR to the building in winter. This causes an increase of 9.3% and 27.5% of AHEC by comparing with the office building with SR located at Harbin and Beijing, respectively. Although the application of MCR can lead to an increase of AHEC, the ACEC is significantly decreased. Compared to the building with SR, the ACEC is decreased by 19% and 17% for the office building located at Harbin and Beijing, respectively. Thus, the roof must be covered in winter for the office building with MCR to avoid the serious heating penalty caused by the cooling effect of MCR.

For the office building located in other three cities, the application of MCR shows greatly electricity saving potentials. As shown in Table 6 and Figure 6, the saving of ATEC is 612.8 kWh in Shanghai, 1011.0 kWh in Guangzhou and 759.1 kWh in Kunming, results in the ATEC reduction of 13.2%, 15.7%, and 24.2% by comparing with the office building with SR even though the MCR is uncovered in winter. Furthermore, the cooling benefit can be further improved if the MCR is covered in winter, and then the reductions of ATEC would be higher than 16.1% in Shanghai and 24.9% in Kunming. However, it has little impact on the ATEC whether MCR is covered or not since no heating demand is required in winter for the building located at Guangzhou (hot-summer and warm-winter climate zone).

From above, the ATEC can be greatly reduced by the application of MCR on the office building. Especially for the building located in the hot-summer and cold-winter climate zone, hot-summer and warm-winter climate zone and moderate climate zone, the ATEC can be decreased by 13.2%, 15.7% and 24.2%, respectively, by comparing against the building with SR. Furthermore, the only additional work is to adhere the MCR to the original roof of the office building. However, the MCR must be covered for the office building located at severe cold climate zone and cold climate zone to reduce the serious heating penalty caused by MCR in winter for achieving the annual electricity saving.

Conclusions

The effect of roof and ceiling configuration on the energy performance of MCR for a low-rise office building was analysed based on the proposed optimization model in this study. To indicate the coupling influence of RTR and CTR, a dimensionless thermal resistance of θ_RTR has been proposed. An optimal roof pitch was derived for minimizing ATEC, and a method to determine the optimal roof pitch for the office building with MCR has also been proposed. The energy-saving potential of the office building with MCR for different climate zones has been discussed in detail. This study can provide further understanding for the application of cool roof based on the novel diurnal radiative cooling materials, particularly for configuration of the roof system, including roof and ceiling insulation and roof pitch. The analysis of energy-saving potential for the building with MCR located at different climate zones in China is helpful for the research and application of the similar innovative cool material in other countries. The main conclusions are as follows:

The configuration of roof and ceiling insulation should be considered carefully due to the coupled and complicated impact on the ATEC of the office building with MCR. Higher cooling benefits can be achieved, while the CTR is between R11 and R15 combined with a smaller RTR for the office building with MCR located at hot-summer and cold-winter climate zone in China.

Roof pitch has a significant effect on the ATEC of the office building with MCR. More than 13% of the ATEC saving can be achieved by considering the variation of roof pitch for an office building with MCR located at hot-summer and cold-winter climate zone in China.

Compared to the building with SR, the ACEC is decreased by 19% and 17% for the office building with MCR located at severe cold climate zone and cold climate zone, and more than 13.2%, 15.7%, and 24.2% of ATEC can be saved for the office building with MCR located at hot-summer and cold-winter climate zone, hot-summer and warm-winter climate zone, and moderate climate zone, respectively.

Footnotes

Authors’ contribution

S. Tang performed the simulations, conducted the analyses and validation, wrote the first draft of the manuscript; K. Zhang designed the study, developed methodology and conducted the validation. All authors read, modified, commented and approved the manuscript.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by grants from the National Natural Science Foundation of China (No. 51878342), Jiangsu Provincial Department of Housing and Urban Rural Construction (No. 2018ZD067) and Postgraduate Research & Practice Innovation Program of Jiangsu Province (SJCX20_0329).

ORCID iD

Kai Zhang

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