Optimum Insulation Thickness for Building Exterior Walls in 32 Regions of China to Save Energy and Reduce CO 2 Emissions

China accounts for approximately 30% of the CO2 emissions—one of the largest proportions from a single nation. Therefore, reducing the CO2 emissions in China will play a decisive role in global CO2 emissions reduction. This paper is a proposal of optimum insulation thickness (OIT) for the exterior walls of buildings in 32 regions of China to save energy and reduce CO2 emissions. The determination of the OIT for exterior walls its impact on the annual total energy cost and annual CO2 emissions per unit area of building exterior walls were calculated for 32 regions of China using the life-cycle cost analysis (LCCA) and degree-days (DD) method. The results indicate that the annual total energy cost decreases up to the OIT level, and increases beyond the OIT level. The annual CO2 emissions can be reduced by increasing the insulation thickness. It is predicted that the average total energy cost of 32 regions can potentially be decreased by about $5/m2-year (40%) and the average CO2 emissions of the 32 regions can potentially be reduced by about 27 kg/m2-year (63%) when the OIT is applied. It also shows it is more effective to apply the OIT for the exterior walls of buildings to save annual total energy cost and reduce annual CO2 emissions in the Severe Cold and Hot Summer & Cold Winter climatic zones rather than the other climatic zones of China.


Introduction
The energy demands of buildings are high due in part to the indoor thermal comfort requirements of buildings.A continuous and cheap supply of energy is desired for economic and social development [1].The use of nonrenewable energy can cause environmental problems, global warming and a reduced quality of life in humans.One of the most effective ways of reducing the energy use is to utilize fossil fuel sources efficiently [2,3].A proposed theoretical model indicated that increasing the albedo and thermal insulation of rooftops can effectively reduce the heat gain in buildings during the summer season [4].Thermal insulation in building exterior walls can decrease the heat loss or gain through the building envelopes in the winter, but at increasing cost [5].Design and construction with optimal insulation thickness (OIT) should be considered as a prerequisite and a top priority for energy savings in buildings [6,7].The definition of OIT has been detailed by many researchers worldwide [8][9][10].The degree-day (DD) method is commonly used to calculate the energy needs of buildings, and methods of calculating the OIT are proposed based on the DD method [11][12][13].
The thermal properties of the building envelope are determined by the combination of wall mass, thermal resistance, insulation thickness and location, exterior surface color, etc. [14].The thermal insulation of building exterior walls significantly reduces the heating and cooling needs of the zone [15].
The influence of the insulation configuration on thermal loads of buildings has been detailed by many researchers.A study on the performances of the heat and multilayer reflection insulators of buildings was implemented by Lee et al. [16], and indicated that the multilayer reflection insulator keeps the interior wall surface temperature high in winter and low in summer, improves the thermal comfort of the habitants and reduces the yearly heat loads.The impact of thermal insulation on building heat loads was implemented by Kossecka and Kosny [17], and a predication of yearly heating and cooling energy demand for a one-story residential building was carried out using DOE-2.1E.It was known that the insulating material configuration of the building external wall can significantly affect the yearly thermal property of the building under various climatic and weather conditions.A numerical model for calculating the yearly cooling and heating transmission loads was adopted by Ozel [18].The calculated cooling and heating transmission loads were imported to an economic model to decide the OIT for a south-facing wall in the climatic conditions of Elazı g, Turkey.The influence of windows on the thermal insulation of buildings was analyzed by Granzotto et al. [19].It showed that the single components of windows will not affect the thermal insulation, although the acoustic properties will be influenced by unique constituent of windows.Baldinelli et al. [20] implemented the study on the influence of windows on the energy and environmental performance via a holistic approach using a sample of wooden windows.It showed that enhancing the thermal characteristics of windows can properly control the solar gains and strongly contribute to the optimization of energy and environmental performance.Thalfeldt et al. [21] carried out the analysis on the optimal façade designs including window properties, thermal insulation of exterior walls, window-to-wall ratio and shading for Estonia in the cold climate.The analysis indicated that the cost optimal façade solution was obtained by the triple pane low-E glazing with a window-to-wall ratio of 25% and the insulation thickness of an exterior wall of 200 mm as a design principle.
According to the China Climate Change Info-Net (CCCIN), it is known that China's CO 2 emissions accounted for a relatively large proportion of the world's CO 2 emissions-about 30% in 2016 [22].According to China's thermal design code of civil buildings (GB 50176-93) [23] and Li and Yao's previous research [24], five main different climatic zones are defined in China as shown in Figure 1 In global efforts to prevent global warming and environmental problems, measures to reduce CO 2 emissions in China would have a much greater impact than in other developed countries.The OIT design for building exterior walls can play an important role in reducing the CO 2 emissions by directly reducing the heating and cooling loads of buildings.Zhu et al. [25] have calculated the OIT of exterior walls for five typical cities, Urumqi, Beijing, Shanghai, Guangzhou and Kunming that are in different climatic zones of China, with consideration of annual heating degree-days (HDD) and cooling degree-days (CDD).
In order to save energy cost of buildings and reduce CO 2 emissions, this paper aims to determine the OIT of building exterior walls for 32 regions of China.The OIT of building exterior walls for the selected 32 regions of China is proposed using DD method and life-cycle cost analysis (LCCA), without considering the influence of windows and external solar gains.A distribution map of OIT of building exterior walls for the 32 regions of China is created.In addition, the potential of annual total energy cost savings and annual CO 2 emission reduction per unit area of building exterior walls when applying the OIT on exterior walls are evaluated for the 32 regions of China in this study.
exterior walls when applying the OIT on exterior walls are evaluated for the 32 regions of China in this study.

Regions of China
In this study, we chose 32 regions of China to propose the OIT for building exterior walls.The data is from the China Meteorological Data Service Center (CMDC) [26], which does not include meteorological data of Hong Kong, Macao and Taiwan regions.The geographic locations of selected 32 regions are detailed in Figure 2.

Determination of HDD and CDD
For determination of the HDD and CDD in this study, we obtained the mean daily outdoor dry-bulb temperature for 35 years (1981-2015) from 32 regions from the CMDC.The HDD is calculated at base dry-bulb temperature of 18.0 °C, and the CDD is calculated at base dry-bulb

Regions of China
In this study, we chose 32 regions of China to propose the OIT for building exterior walls.The data is from the China Meteorological Data Service Center (CMDC) [26], which does not include meteorological data of Hong Kong, Macao and Taiwan regions.The geographic locations of selected 32 regions are detailed in Figure 2. exterior walls when applying the OIT on exterior walls are evaluated for the 32 regions of China in this study.

Regions of China
In this study, we chose 32 regions of China to propose the OIT for building exterior walls.The data is from the China Meteorological Data Service Center (CMDC) [26], which does not include meteorological data of Hong Kong, Macao and Taiwan regions.The geographic locations of selected 32 regions are detailed in Figure 2.

Determination of HDD and CDD
For determination of the HDD and CDD in this study, we obtained the mean daily outdoor dry-bulb temperature for 35 years (1981-2015) from 32 regions from the CMDC.The HDD is calculated at base dry-bulb temperature of 18.0 °C, and the CDD is calculated at base dry-bulb

Determination of HDD and CDD
For determination of the HDD and CDD in this study, we obtained the mean daily outdoor dry-bulb temperature for 35 years (1981-2015) from 32 regions from the CMDC.The HDD is calculated at base dry-bulb temperature of 18.0 • C, and the CDD is calculated at base dry-bulb temperature of 28.0 • C. The HDD and CDD are determined using the following Equations ( 1) and (2), respectively, where HDD 18.0 is the heating degree-days at base dry-bulb temperature of 18.0

Total Energy Cost Analysis
The LCCA method is used to assess the annual total energy cost per unit area of building exterior walls over the lifetime of building exterior wall materials.
Heat loss or gain from unit exterior wall surface, can be calculated using the following Equations ( 3) and ( 4), where q is the heat loss or gain from the unit exterior wall surface, [W/m 2 ]; U is the coefficient of heat transmission of exterior walls, [W/m 2 K]; ∆T is the temperature difference between indoor and outdoor sides, The R ins can be derived through the following Equation ( 5), where x is the insulation thickness, [m]; and k is the thermal conductivity of insulation material, [W/mK].
The annual fuel consumption per unit area of building exterior walls in heating and cooling periods can be derived using the following Equations ( 6) and (7), respectively, where m H and m C are the annual fuel consumption per unit area of building exterior walls in heating and cooling periods, respectively, [kg/m The annual total cost per unit area of building exterior walls, can be derived by the following Equations ( 8)-( 10) via the LCCA, where C T is the annual total cost per unit area of building exterior walls, [$/m

Determination of Optimum Insulation Thickness
The minimum C T is taken as the point when the derivative of the cost as a function of insulation thickness (8) reaches zero, in the following Equations ( 11) and ( 12) [27], and The OIT can be also derived using the following Equation ( 13) [28],

Energy Cost Saving Analysis
The potential annual energy cost saving per unit area of building exterior walls can be derived by subtracting the annual total energy cost per unit area of building exterior walls for noninsulated walls and the annual total cost per unit area of building exterior walls for insulated walls.The relationship is shown as the following Equation ( 14), where E cs is the annual energy cost saving per unit area of building exterior walls, [$/m 2 -yr]; (C T )nins is the annual total cost per unit area of building exterior walls for non-insulated walls, [$/m 2 -yr]; and (C T )ins is the annual total cost per unit area of building exterior walls for insulated walls, [$/m 2 -yr].

CO 2 Emission Calculation
The annual CO 2 emissions per unit area of building exterior walls can be derived through the following Equations ( 15)-( 18) [29], where m is the mol number, [kmol/m

Results and Discussion
Despite the exterior wall structures in the different climatic zones of China being different, in order to unify calculation and better understand the change of OIT in the different climatic zones, this paper assumes two kinds of exterior wall structures, one as applicable to the 16 regions belonging to the Severe Cold and Cold climatic zones (Figure 3a) and the other for the 16 regions belonging to the Hot Summer & Cold Winter, Temperate and Hot Summer & Warm Winter climatic zones (Figure 3b).The parameters of calculation are given in Table 1.
(3.0 for cooling period and 2.5 for heating period), [-]; and

Results and Discussion
Despite the exterior wall structures in the different climatic zones of China being different, in order to unify calculation and better understand the change of OIT in the different climatic zones, this paper assumes two kinds of exterior wall structures, one as applicable to the 16 regions belonging to the Severe Cold and Cold climatic zones (Figure 3a) and the other for the 16 regions belonging to the Hot Summer & Cold Winter, Temperate and Hot Summer & Warm Winter climatic zones (Figure 3b).The parameters of calculation are given in Table 1.

Present worth factor (PWF)
Interest rate (i) [35] [-] 4.35% Inflation rate (g) [36] [-] 2.3% N [yr] 10 For this calculation, traditional fuel in China, such as coal and gas are selected as the boiler fuel source for heating, and electricity is selected as the power source of air conditioners for cooling.The coal as fuel source is used for the Severe Cold and Cold climatic zones and the natural gas as fuel is used for the Hot Summer & Cold Winter, Temperate and Hot Summer & Warm Winter climatic zones of China.The fuel cost in this calculation is considered as a slightly higher price than mean price in the last ten years, thus it is likely to lead to a relatively higher total energy cost and a relatively higher OIT.There are many insulation materials used for building exterior walls in China, i.e., polymer mortar, fiberglass mesh, expanded polyurethane (EPS), rock wool, foam board, extruded polystyrene (XPS), etc.Similar to the research of Andreola et al. [37], there are also some insulation materials made of nonflammable and recyclable waste materials.In order to simplify the calculation, this study selects the EPS as insulation material of exterior walls.

HDD and CDD for 32 Regions
The HDD 18.0 and CDD 28.0 are derived from the above Equations ( 1) and ( 2).The annual HDD 18.0 and CDD 28.0 for 32 regions of China are calculated and shown in Table 2.The distribution maps of annual HDD 18.0 and CDD 28.0 for 32 regions of China are created and shown in Figure 4a,b, respectively.relatively higher OIT.There are many insulation materials used for building exterior walls in China, i.e., polymer mortar, fiberglass mesh, expanded polyurethane (EPS), rock wool, foam board, extruded polystyrene (XPS), etc.Similar to the research of Andreola et al. [37], there are also some insulation materials made of nonflammable and recyclable waste materials.In order to simplify the calculation, this study selects the EPS as insulation material of exterior walls.

HDD and CDD for 32 Regions
The HDD18.0 and CDD28.0 are derived from the above Equations ( 1) and ( 2).The annual HDD18.0 and CDD28.0 for 32 regions of China are calculated and shown in Table 2.The distribution maps of annual HDD18.0 and CDD28.0 for 32 regions of China are created and shown in Figure 4a,b, respectively.Compared to annual HDD 18.0 , the annual CDD 28.0 is relatively small for the 32 regions of China.

Optimum Insulation Thickness
The OIT is derived from the above Equation ( 13).The OIT for the 32 regions are calculated and detailed in Table 2.The distribution map of OIT for the whole China territory is created and shown in Figure 5.
We can see that the OIT for building exterior walls in Severe Cold climatic zone is the thickest, followed by that in Compared to annual HDD18.0, the annual CDD28.0 is relatively small for the 32 regions of China.

Optimum Insulation Thickness
The OIT is derived from the above Equation ( 13).The OIT for the 32 regions are calculated and detailed in Table 2.The distribution map of OIT for the whole China territory is created and shown in Figure 5.
We can see that the OIT for building exterior walls in Severe Cold climatic zone is the thickest, followed by that in Hot Summer & Cold Winter, Temperate and Cold climatic zones, and the OIT in Hot Summer & Warm Winter climatic zone is the thinnest.

•
The base temperature of 28 • C is adopted for determining the annual CDD in this paper, however a relatively lower base temperature of 26 • C is adopted in Zhu et al.'s research.

Annual Total Cost
The annual total cost C T is derived from the above Equation (8).The curves of annual total cost, insulation cost and fuel cost per unit area of building exterior walls versus the insulation thickness for example regions of Tibet (Severe Cold), Shanghai (Hot Summer & Cold Winter), Yunnan (Temperate) and Guangdong (Hot Summer & Warm Winter) are calculated and shown in Figure 6.The C T is affected by insulation thickness and fuel consumption of buildings, etc.The heat losses decrease with an increase of insulation thickness.If the insulation thickness increases, the thermal load which directly related to fuel cost would decrease.However, increasing the insulation thickness will increase the insulation cost, thus the C T which is the sum of fuel and insulation costs decreases up to a certain value of the insulation thickness, OIT.Beyond this OIT value, the C T increases.
The graphs in Figure 6 show that the initial C T for noninsulated walls, (C T )nins, which is equal to the fuel cost is the largest-about $25/m 2 -yr for Tibet, which belongs to the Severe Cold climatic zone, followed by Shanghai ($13/m 2 -yr), which belongs to the Hot Summer & Cold Winter climatic zone and Yunnan (about $/10m 2 -yr), which belongs to the Temperate climatic zone.The smallest is about $4/m 2 -yr for Guangdong, which belongs to the Hot Summer & Warm Winter climatic zone.The C T decreases by about 52% for Tibet, about 41% for Shanghai, about 34% for Yunnan, and about 11% for Guangdong by increasing the insulation thickness up to the OIT value.

Annual Total Cost
The annual total cost CT is derived from the above Equation (8).The curves of annual total cost, insulation cost and fuel cost per unit area of building exterior walls versus the insulation thickness for example regions of Tibet (Severe Cold), Shanghai (Hot Summer & Cold Winter), Yunnan (Temperate) and Guangdong (Hot Summer & Warm Winter) are calculated and shown in Figure 6.
The CT is affected by insulation thickness and fuel consumption of buildings, etc.The heat losses decrease with an increase of insulation thickness.If the insulation thickness increases, the thermal load which directly related to fuel cost would decrease.However, increasing the insulation thickness will increase the insulation cost, thus the CT which is the sum of fuel and insulation costs decreases up to a certain value of the insulation thickness, OIT.Beyond this OIT value, the CT increases.
The graphs in Figure 6 show that the initial CT for noninsulated walls, (CT)nins, which is equal to the fuel cost is the largest-about $25/m 2 -yr for Tibet, which belongs to the Severe Cold climatic zone, followed by Shanghai ($13/m 2 -yr), which belongs to the Hot Summer & Cold Winter climatic zone and Yunnan (about $/10m 2 -yr), which belongs to the Temperate climatic zone.The smallest is about $4/m 2 -yr for Guangdong, which belongs to the Hot Summer & Warm Winter climatic zone.The CT decreases by about 52% for Tibet, about 41% for Shanghai, about 34% for Yunnan, and about 11% for Guangdong by increasing the insulation thickness up to the OIT value.

Potential Annual Energy Cost Savings
The potential annual energy cost savings per unit area of building exterior walls, E cs , is derived from the above Equation ( 14).The curves of E cs versus the insulation thickness for Tibet, Shanghai, Yunnan and Guangdong are shown in Figure 7.The curve shows that the E cs increases up to the OIT level.Beyond the level of OIT, the E cs decreases.
Figure 7 shows that Tibet has the largest E cs of about $13/m 2 -yr, when the insulation thickness increases up to the OIT value of 135 mm, followed by Shanghai (the largest E cs is about $5/m 2 -yr when the insulation thickness increases up to the OIT value of 78 mm) and Yunnan (the largest E cs is about $3/m 2 -yr when the insulation thickness increases up to the OIT value of 63 mm).Guangdong has the smallest E cs of about $0.40/m 2 -yr when the insulation thickness increases up to the OIT value of 22 mm.
If the OIT is applied for building exterior walls, the E cs for 32 regions of China are estimated and detailed in Table 2.
It shows that when the OIT for exterior walls is used, the average E cs of the 32 regions of China can potentially be decreased by up to about $5/m 2 -yr (40%), depending on initial conditions.

Potential Annual Energy Cost Savings
The potential annual energy cost savings per unit area of building exterior walls, Ecs, is derived from the above Equation ( 14).The curves of Ecs versus the insulation thickness for Tibet, Shanghai, Yunnan and Guangdong are shown in Figure 7.The curve shows that the Ecs increases up to the OIT level.Beyond the level of OIT, the Ecs decreases.If the OIT is applied for building exterior walls, the Ecs for 32 regions of China are estimated and detailed in Table 2.
It shows that when the OIT for exterior walls is used, the average Ecs of the 32 regions of China can potentially be decreased by up to about $5/m 2 -yr (40%), depending on initial conditions.

Potential Annual CO2 Emissions
The potential annual CO2 emission per unit area of building exterior walls, mco2, is derived from the above Equations ( 15)- (18).The curves of mco2 versus the insulation thickness for example regions of Tibet, Shanghai, Yunnan and Guangdong are shown in Figure 8.
Figure 8 shows that Tibet has the largest reduction of mco2 of about 53 kg/m 2 -yr when the insulation thickness increases up to the OIT value of 135 mm, followed by Shanghai (CO2 emission reduction is about 35 kg/m 2 -yr when the insulation thickness increases up to the OIT value of 78 mm) and Yunnan (CO2 emission reduction is about 24 kg/m 2 -yr when the insulation thickness increases up to the OIT value of 63 mm).Guangdong has the smallest reduction of mco2 of about 5 kg/m 2 -yr when the insulation thickness increases up to the OIT value of 22 mm.
If the OIT for building exterior walls is applied, the reduction of mco2 for 32 regions of China are predicted and detailed in Table 2.

Potential Annual CO 2 Emissions
The potential annual CO 2 emission per unit area of building exterior walls, m co2 , is derived from the above Equations ( 15)- (18).The curves of m co2 versus the insulation thickness for example regions of Tibet, Shanghai, Yunnan and Guangdong are shown in Figure 8.It is seen that the mco2 decreases by increasing the insulation thickness of exterior walls.When the OIT for exterior walls is used, the average mco2 of 32 regions of China can potentially be reduced by about 27 kg/m 2 -yr (63%).
In addition, we can see that when the region is much colder (such as Tibet), the reduction rate of mco2 as the insulation thickness increases is much larger.Thus, in order to greatly reduce mco2 in China, it is considered that it is more effective to implement the thermal insulation technology on the exterior walls of buildings in Severe Cold and Hot Summer & Cold Winter climatic zones rather than the other climatic zones of China.Figure 8 shows that Tibet has the largest reduction of m co2 of about 53 kg/m 2 -yr when the insulation thickness increases up to the OIT value of 135 mm, followed by Shanghai (CO 2 emission reduction is about 35 kg/m 2 -yr when the insulation thickness increases up to the OIT value of 78 mm) and Yunnan (CO 2 emission reduction is about 24 kg/m 2 -yr when the insulation thickness increases up to the OIT value of 63 mm).Guangdong has the smallest reduction of m co2 of about 5 kg/m 2 -yr when the insulation thickness increases up to the OIT value of 22 mm.

Conclusions and Future Work
If the OIT for building exterior walls is applied, the reduction of m co2 for 32 regions of China are predicted and detailed in Table 2.
It is seen that the m co2 decreases by increasing the insulation thickness of exterior walls.When the OIT for exterior walls is used, the average m co2 of 32 regions of China can potentially be reduced by about 27 kg/m 2 -yr (63%).
In addition, we can see that when the region is much colder (such as Tibet), the reduction rate of m co2 as the insulation thickness increases is much larger.Thus, in order to greatly reduce m co2 in China, it is considered that it is more effective to implement the thermal insulation technology on the exterior walls of buildings in Severe Cold and Hot Summer & Cold Winter climatic zones rather than the other climatic zones of China.

Conclusions and Future Work
For the purpose of contributing to the thermal insulation design of building exterior walls for energy cost savings and CO 2 emission reduction in China, this study proposed the OIT of exterior walls for 32 regions of China using more recent data via the DD method and LCCA over a hypothetical lifetime of 10 years, without considering the influence of windows and external solar gains.In addition, the impact of the OIT on the annual total energy cost and annual CO 2 emissions per unit area of building exterior walls were also implemented in this study.
The findings indicate the thermal insulation of exterior walls is more effective in Severe Cold and Hot Summer & Cold Winter climatic zones of China for both total energy cost saving and CO 2 emissions reduction per unit area of the building exterior walls, however it is the opposite in Hot Summer & Warm Winter climatic zones of China.It is predicted that the average annual total energy cost per unit area of building exterior walls can potentially be decreased by about $5/m 2 -yr (40%) and the average annual CO 2 emissions per unit area of building exterior walls can potentially be reduced by about 27 kg/m 2 -yr (63%) for the 32 regions of China if the OIT is adopted.
For the future research, it will focus on the impact of the other parameters, i.e., windows of exterior walls, solar gains of exterior walls, different energy sources and a greater variety of wall construction and materials, etc. on the OIT design, total energy cost and CO 2 emissions in different climatic zones of China.Furthermore, the cost of installing thermal insulation and labor will be considered when calculating the OIT of exterior walls.Finally, the potential for the possibility of introducing solar energy as a renewable energy to substitute for coal and natural gas in different climatic zones of China will be considered in future as it will largely affect the OIT design, total energy cost and CO 2 emissions.

Figure 1 .
Figure 1.Five different climatic zones in China.

Figure 2 .
Figure 2. Geographic locations of selected 32 regions of China.

Figure 1 .
Figure 1.Five different climatic zones in China.

Figure 1 .
Figure 1.Five different climatic zones in China.

Figure 2 .
Figure 2. Geographic locations of selected 32 regions of China.

Figure 2 .
Figure 2. Geographic locations of selected 32 regions of China.

Figure 3 .
Figure 3. Cross-sectional view of two kinds of exterior wall structures; (a) for Severe Cold and Cold climatic zones and (b) for Hot Summer & Cold Winter, Temperate and Hot Summer & Warm Winter climatic zones.

Figure 3 .
Figure 3. Cross-sectional view of two kinds of exterior wall structures; (a) for Severe Cold and Cold climatic zones and (b) for Hot Summer & Cold Winter, Temperate and Hot Summer & Warm Winter climatic zones.

Figure 4 .
Figure 4. Distribution maps of annual HDD 18.0 (a) and CDD 28.0 (b) for 32 regions of China.

Figure 5 .
Figure 5. Distribution map of OIT for the whole China territory.Figure 5. Distribution map of OIT for the whole China territory.

Figure 5 .
Figure 5. Distribution map of OIT for the whole China territory.Figure 5. Distribution map of OIT for the whole China territory.

Figure 6 .
Figure 6.Annual cost (total cost, insulation cost, fuel cost) versus insulation thickness for Tibet, Shanghai, Yunnan and Guangdong.

Figure 6 .
Figure 6.Annual cost (total cost, insulation cost, fuel cost) versus insulation thickness for Tibet, Shanghai, Yunnan and Guangdong.

Figure 7 .
Figure 7. Annual energy cost saving versus insulation thickness for Tibet, Shanghai, Yunnan and Guangdong.

Figure 7
Figure 7 shows that Tibet has the largest Ecs of about $13/m 2 -yr, when the insulation thickness increases up to the OIT value of 135 mm, followed by Shanghai (the largest Ecs is about $5/m 2 -yr when the insulation thickness increases up to the OIT value of 78 mm) and Yunnan (the largest Ecs is about $3/m 2 -yr when the insulation thickness increases up to the OIT value of 63 mm).Guangdong has the smallest Ecs of about $0.40/m 2 -yr when the insulation thickness increases up to the OIT value of 22 mm.If the OIT is applied for building exterior walls, the Ecs for 32 regions of China are estimated and detailed in Table2.It shows that when the OIT for exterior walls is used, the average Ecs of the 32 regions of China can potentially be decreased by up to about $5/m 2 -yr (40%), depending on initial conditions.

Figure 7 .
Figure 7. Annual energy cost saving versus insulation thickness for Tibet, Shanghai, Yunnan and Guangdong.

Figure 8 .
Figure 8. Annual CO 2 emissions versus insulation thickness for Tibet, Shanghai, Yunnan and Guangdong.
• C, [ • C-day]; CDD 28.0 is the cooling degree-days at base dry-bulb temperature of 28.0 • C, [ • C-day]; θ ih is the design indoor dry-bulb temperature of 18.0 • C for heating period; θ ic is the design indoor dry-bulb temperature of 28.0 • C for cooling period; θ om(n) is the mean daily outdoor dry-bulb temperature of the nth day, [ • C]; and n is the days of heating or cooling periods, [day].
2-yr]; M is the molar mass of fuel, 94.9 [kg/kmol] for coal and 17.5 [kg/kmol] for natural gas; m co 2 is the annual CO 2 emissions per unit area of building exterior walls, [kg/m 2 -yr]; a is the coefficient of CO 2 emissions (here it is assumed as 0.45 kg CO 2 /kWh); E is the electricity consumption, [kWh/m 2 -yr]; COP is the coefficient of performance of air-conditioner (3.0 for cooling period and 2.5 for heating period),[-]; and M co 2 is the molar mass of CO 2 , 44 [kg/kmol].

Table 1 .
Parameter value used in the calculations.

Table 1 .
Parameter value used in the calculations.
H and C C ) Natural gas[31]

Table 2 .
Calculation results for 32 regions of China.

Table 2 .
Calculation results for 32 regions of China.

(Optimum R ins [m 2 K/W]) E cs [$/m 2 -yr] m co2 Reduction [kg/m 2 -yr]
Note: the upper 16 regions belong to Severe Cold and Cold climatic zones and the lower 16 regions belong to Hot Summer & Cold Winter, Temperate and Hot Summer & Warm Winter climatic zones; the value in the parenthesis of OIT column is the value of optimum thermal resistance of insulation.
Hot Summer & Cold Winter, Temperate and Cold climatic zones, and the OIT in Hot Summer & Warm Winter climatic zone is the thinnest.: the upper 16 regions belong to Severe Cold and Cold climatic zones and the lower 16 regions belong to Hot Summer & Cold Winter, Temperate and Hot Summer & Warm Winter climatic zones; the value in the parenthesis of OIT column is the value of optimum thermal resistance of insulation. Note