Investigation on the Solar Absorption Property of the Nanoporous Alumina Sheet for Solar Application

In order to improve the absorption performance of the aluminum sheet for solar application, the nanoporous alumina sheets with the pore diameters of 30 nm and 400 nm were prepared by the anodic oxidation method. The absorption properties of the nanoporous alumina sheets under different solar radiation intensity were studied and compared with the conventional polished aluminum sheet. The results showed that the average absorptivity of the aluminum sheets decreased with the increase of the radiation intensity. When the radiation intensity was 100 W/m2, the nanoporous alumina sheet with the 30 nm pore diameter had the highest average solar absorptivity of 0.39, which was 18% higher than that of the nanoporous alumina sheet with 400 nm pore diameter, and 50% higher than that of the polished aluminum sheet. The maximum instantaneous absorption efficiency of the nanoporous alumina sheet with 30 nm pore diameter was found at 0.92 when the radiation intensity was 100 W/m2. The testing results indicated that the nanoporous alumina sheet with the 30 nm pore diameter performed the best compared with the other two aluminum sheets. By error propagation analysis, the relative error of the average amount of heat absorption and the average absorptivity were acceptable.


Introduction
Over the past few decades, the sharp increase in the energy demand has occurred due to global economic development and population growth, leading to rapid consumption of fossil fuels and serious environmental pollution consequences, e.g., air pollution, acid rain, depletion of the ozone layer and global climate change. The development of the renewable energy to replace the traditional energy is imminent. Renewable energy sources (including hydropower, wind, biomass, geothermal, tidal, wave and solar energy sources) can satisfy the energy demands with minor environmental impact compared with the traditional energy sources [1][2][3]. Of which, solar energy, due to it being abundant, cheap and pollution-free, offers a great alternative to conventional fossil fuel resources and is expected to play an increasingly significant role in the global energy future [4,5]. The solar radiation reaching the earth's surface is approximately 3.4 × 10 24 J in one year; more than 7500 times the world's total annual primary energy consumption of 4.5 × 10 20 J [6]. Therefore, directly and efficiently absorbing solar energy is a significant method to improve the efficiency of solar application systems, e.g., the solar thermal system and PV (photovoltaic) system. The purpose of this work is not to develop new materials, nor to optimize the absorption and emissivity. Porous alumina layers with inclusion of transition metals like Fe, Co, Ni, Cu, Au, Ag, Mo, Cr and W have been widely studied [22]. These surfaces have been proven to be highly efficient in converting solar energy into heat. However, there has been little research on a pure porous alumina layer, and most previous porous aluminum layer pore depths were about 1 µm or less [23,24]. This paper aims to study the absorption of solar energy by pure porous alumina layer with a pore depth of 100 µm, highly absorbing surfaces can be obtained by increasing the number of reflections of solar incident ray in the nanopores. Thereby simplifying the preparation process.

Working Principle of the Nanoporous Alumina Sheet
As shown in Figure 1, the working principle of the nanoporous alumina sheet would be summarized as follows. When the sunlight reaches to the nanopores on the surface of the aluminum sheet, part of them will be absorbed by the aluminum sheet, while the remaining part will be reflected inside the nanopores and eventually absorbed by the aluminum sheet. This process could reduce the reflection of the sunlight from the surface of the aluminum sheet to the environment, and therefore, enhance the solar absorption efficiency. In addition, the multiple-reflecting effects of the nanoporous alumina sheet with small aperture are more obvious. At the same pore depth, the smaller the aperture is, the more times of reflection in the nanopores, and the more sufficient the heat absorption of the aluminum sheet [25]. advantages of the prepared nanoporous material and indicate the potential application in the solar market.
The purpose of this work is not to develop new materials, nor to optimize the absorption and emissivity. Porous alumina layers with inclusion of transition metals like Fe, Co, Ni, Cu, Au, Ag, Mo, Cr and W have been widely studied [22]. These surfaces have been proven to be highly efficient in converting solar energy into heat. However, there has been little research on a pure porous alumina layer, and most previous porous aluminum layer pore depths were about 1 μm or less [23,24]. This paper aims to study the absorption of solar energy by pure porous alumina layer with a pore depth of 100 μm, highly absorbing surfaces can be obtained by increasing the number of reflections of solar incident ray in the nanopores. Thereby simplifying the preparation process.

Working Principle of the Nanoporous Alumina Sheet
As shown in Figure 1, the working principle of the nanoporous alumina sheet would be summarized as follows. When the sunlight reaches to the nanopores on the surface of the aluminum sheet, part of them will be absorbed by the aluminum sheet, while the remaining part will be reflected inside the nanopores and eventually absorbed by the aluminum sheet. This process could reduce the reflection of the sunlight from the surface of the aluminum sheet to the environment, and therefore, enhance the solar absorption efficiency. In addition, the multiple-reflecting effects of the nanoporous alumina sheet with small aperture are more obvious. At the same pore depth, the smaller the aperture is, the more times of reflection in the nanopores, and the more sufficient the heat absorption of the aluminum sheet [25].

Preparation of the Nanoporous Alumina Sheet
The preparation of the nanoporous alumina sheet could be summarized into two steps: (1) Pretreatment of the aluminum sheet to make it smooth, clean and flat; and (2) anodic oxidation process to form the nanopores on the surface of the aluminum sheet.

Pretreatment
The pretreatment process of the aluminum sheet was shown in Figure 2.

Ultrasonic clean
Oxide film removal Polishing

Preparation of the Nanoporous Alumina Sheet
The preparation of the nanoporous alumina sheet could be summarized into two steps: (1) Pretreatment of the aluminum sheet to make it smooth, clean and flat; and (2) anodic oxidation process to form the nanopores on the surface of the aluminum sheet.

Pretreatment
The pretreatment process of the aluminum sheet was shown in Figure 2. advantages of the prepared nanoporous material and indicate the potential application in the solar market. The purpose of this work is not to develop new materials, nor to optimize the absorption and emissivity. Porous alumina layers with inclusion of transition metals like Fe, Co, Ni, Cu, Au, Ag, Mo, Cr and W have been widely studied [22]. These surfaces have been proven to be highly efficient in converting solar energy into heat. However, there has been little research on a pure porous alumina layer, and most previous porous aluminum layer pore depths were about 1 μm or less [23,24]. This paper aims to study the absorption of solar energy by pure porous alumina layer with a pore depth of 100 μm, highly absorbing surfaces can be obtained by increasing the number of reflections of solar incident ray in the nanopores. Thereby simplifying the preparation process.

Working Principle of the Nanoporous Alumina Sheet
As shown in Figure 1, the working principle of the nanoporous alumina sheet would be summarized as follows. When the sunlight reaches to the nanopores on the surface of the aluminum sheet, part of them will be absorbed by the aluminum sheet, while the remaining part will be reflected inside the nanopores and eventually absorbed by the aluminum sheet. This process could reduce the reflection of the sunlight from the surface of the aluminum sheet to the environment, and therefore, enhance the solar absorption efficiency. In addition, the multiple-reflecting effects of the nanoporous alumina sheet with small aperture are more obvious. At the same pore depth, the smaller the aperture is, the more times of reflection in the nanopores, and the more sufficient the heat absorption of the aluminum sheet [25].

Preparation of the Nanoporous Alumina Sheet
The preparation of the nanoporous alumina sheet could be summarized into two steps: (1) Pretreatment of the aluminum sheet to make it smooth, clean and flat; and (2) anodic oxidation process to form the nanopores on the surface of the aluminum sheet.

Pretreatment
The pretreatment process of the aluminum sheet was shown in Figure 2.

Ultrasonic clean
Oxide film removal Polishing The detailed processes could be summarized as follows. Firstly, the aluminum sheets with a purity of 99.99% purchased from Guantai Metal Materials Co., Ltd. (Xingtai, China) was flattened by using the flattening machine (HD-25, Guang'an Haoxin Machinery Equipment Co., Ltd., Langfang, China). Then the aluminum sheet placed in the ethanol/acetone solution was cleaned for 10 min in the ultrasonic cleaner (JP-040, Jiemeng Cleaning Equipment Co., Ltd., Shenzhen, China) to eliminate the oil. After that, the aluminum sheet was placed in the 1 mol/L sodium hydroxide solution (99.6% powder, Shanghai Bio-way Technology Co., Ltd., Shanghai, China) for five minutes to further remove the dirt and completely remove the natural oxide film on the surface to reveal the pure metal matrix, which was to ensure the uniformity of the surface. At last, the aluminum sheet would be polished in the 400 mL perchloric acid/ethanol solution (72%/75%, Shanghai Bio-way Technology Co., Ltd., Shanghai, China) mixed in the ratio of 1:9 by using the aluminum as the anode and graphite (S150100, Beijing Diantan, Beijing, China) as the cathode, and stirring using the magnetic rod (N52, Hongsheng Magnetic Industry, Shanghai, China) for two minutes.

Anodic Oxidation Process
The schematic of the anodic oxidation process of the aluminum sheet was shown in Figure 3, and this process was carried out in the low-constant temperature device (C4000, Xi'an Xiaxi Electronic Technology Co., Ltd., Xi'an, China) shown in Figure 4, which could provide a constant temperature of 0 • C for the oxidation process of the aluminum sheet, ensuring the uniform distribution of the nanopores on the surface of the aluminum sheet and reducing the current breakdown of the aluminum sheet due to excessive temperature, improving the success rate of preparation of the nanoporous alumina sheet. In this process, the aluminum sheet was taken as the anode, while the graphite was as the cathode. Both would be immersed in the oxalic acid solution (1%, Shanghai Bio-way Technology Co., Ltd., Shanghai, China), and connected to the DC (direct current) power to form the nanopores on the surface of the aluminum sheet, the current was applied in the Ampere. The distance between the aluminum sheet and graphite was at 5 cm, and the process was controlled at the temperature of 0 • C. The magnetic stirrer would be used to make sure the reaction evenly. The detailed processes could be summarized as follows. Firstly, the aluminum sheets with a purity of 99.99% purchased from Guantai Metal Materials Co., Ltd. (Xingtai, China) was flattened by using the flattening machine (HD-25, Guang'an Haoxin Machinery Equipment Co., Ltd., Langfang, China). Then the aluminum sheet placed in the ethanol/acetone solution was cleaned for 10 minutes in the ultrasonic cleaner (JP-040, Jiemeng Cleaning Equipment Co., Ltd., Shenzhen, China) to eliminate the oil. After that, the aluminum sheet was placed in the 1 mol/L sodium hydroxide solution (99.6% powder, Shanghai Bio-way Technology Co., Ltd., Shanghai, China) for five minutes to further remove the dirt and completely remove the natural oxide film on the surface to reveal the pure metal matrix, which was to ensure the uniformity of the surface. At last, the aluminum sheet would be polished in the 400 mL perchloric acid/ethanol solution (72%/75%, Shanghai Bio-way Technology Co., Ltd., Shanghai, China) mixed in the ratio of 1:9 by using the aluminum as the anode and graphite (S150100, Beijing Diantan, Beijing, China) as the cathode, and stirring using the magnetic rod (N52, Hongsheng Magnetic Industry, Shanghai, China) for two minutes.

Anodic Oxidation Process
The schematic of the anodic oxidation process of the aluminum sheet was shown in Figure 3, and this process was carried out in the low-constant temperature device (C4000, Xi'an Xiaxi Electronic Technology Co., Ltd., Xi'an, China) shown in Figure 4, which could provide a constant temperature of 0 °C for the oxidation process of the aluminum sheet, ensuring the uniform distribution of the nanopores on the surface of the aluminum sheet and reducing the current breakdown of the aluminum sheet due to excessive temperature, improving the success rate of preparation of the nanoporous alumina sheet. In this process, the aluminum sheet was taken as the anode, while the graphite was as the cathode. Both would be immersed in the oxalic acid solution (1%, Shanghai Bio-way Technology Co., Ltd., Shanghai, China), and connected to the DC (direct current) power to form the nanopores on the surface of the aluminum sheet, the current was applied in the Ampere. The distance between the aluminum sheet and graphite was at 5 cm, and the process was controlled at the temperature of 0 °C. The magnetic stirrer would be used to make sure the reaction evenly.

Scanning Electron Microscope
The scanning electron microscope (SEM, S-3400N, HITACHI, Japan) would be used to inspect whether the micro-pores distributed uniformly on the surface of the aluminum sheet, and Figure 5 showed the SEM image of the aluminum sheet. Figure 5a

Scanning Electron Microscope
The scanning electron microscope (SEM, S-3400N, HITACHI, Japan) would be used to inspect whether the micro-pores distributed uniformly on the surface of the aluminum sheet, and Figure 5 showed the SEM image of the aluminum sheet. Figure 5a was a polished aluminum sheet for comparison with porous alumina sheets, Figure 5b detected the average pore size of 30 nm when the image magnified 100,000 times, and Figure 5c for the average pore size of 400 nm when the image magnified 25,000 times. Both indicated that the nanoporous alumina sheet performed with the evenly distributed micro-porous structure and consistent aperture.

Scanning Electron Microscope
The scanning electron microscope (SEM, S-3400N, HITACHI, Japan) would be used to inspect whether the micro-pores distributed uniformly on the surface of the aluminum sheet, and Figure 5 showed the SEM image of the aluminum sheet. Figure 5a was a polished aluminum sheet for comparison with porous alumina sheets, Figure 5b detected the average pore size of 30 nm when the image magnified 100,000 times, and Figure 5c for the average pore size of 400 nm when the image magnified 25,000 times. Both indicated that the nanoporous alumina sheet performed with the evenly distributed micro-porous structure and consistent aperture.

Experimental Performance Investigation
In order to investigate the solar absorption performance of the nanoporous alumina sheet, the aluminum sheets with the pore diameters of 30 nm and 400 nm were prepared using the anodic oxidation method mentioned above and compared with the conventional polished aluminum sheet. It should be mentioned that due to the limits of the budget and experimental conditions, these two typical types of the nanoporous alumina sheet would only be made. Further tests will be conducted for the wide range of the pore diameters of the aluminum sheet.

Construction of the Testing Rig
As shown in Figures 6 and 7, the testing rig was constructed in the laboratory of the Guangdong University of Technology, China. The testing rig included the water container, insulation material, and aluminum sheets (i.e., polished aluminum sheet, nanoporous alumina sheet with the pore diameter of 30 nm, and nanoporous alumina sheet with the pore diameter of 400 nm). The water containers, each sized at 150 mm × 100 mm × 10 mm and filled in with 150 g water, were made of plexiglass. The thermal insulation material, i.e., extruded polystyrene board with the thermal conductivity ranged at 0.04-0.2 W/(m·K), surrounded the water container to prevent the heat losses to the surroundings. The three prepared aluminum sheets, each sized at 150 mm × 100 mm × 0.2 mm and weight at 8 g, were put above the water container to measure the solar absorption and heat transfer from the sunlight to the cold water in the water container through the aluminum sheets.
Nanopores with 400 nm diameter

Experimental Performance Investigation
In order to investigate the solar absorption performance of the nanoporous alumina sheet, the aluminum sheets with the pore diameters of 30 nm and 400 nm were prepared using the anodic oxidation method mentioned above and compared with the conventional polished aluminum sheet. It should be mentioned that due to the limits of the budget and experimental conditions, these two typical types of the nanoporous alumina sheet would only be made. Further tests will be conducted for the wide range of the pore diameters of the aluminum sheet.

Construction of the Testing Rig
As shown in Figures 6 and 7, the testing rig was constructed in the laboratory of the Guangdong University of Technology, China. The testing rig included the water container, insulation material, and aluminum sheets (i.e., polished aluminum sheet, nanoporous alumina sheet with the pore diameter of 30 nm, and nanoporous alumina sheet with the pore diameter of 400 nm). The water containers, each sized at 150 mm × 100 mm × 10 mm and filled in with 150 g water, were made of plexiglass. The thermal insulation material, i.e., extruded polystyrene board with the thermal conductivity ranged at 0.04-0.2 W/(m·K), surrounded the water container to prevent the heat losses to the surroundings. The three prepared aluminum sheets, each sized at 150 mm × 100 mm × 0.2 mm and weight at 8 g, were put above the water container to measure the solar absorption and heat transfer from the sunlight to the cold water in the water container through the aluminum sheets.
One xenon lamp was used to simulate the sunlight with the different radiations from 100 W/m 2 to 800 W/m 2 through regulating the input voltage of the lamp, and the simulated radiations were recorded by the pyranometer. The solar radiation intensity has been tested around the surface of the container, and their deviations were less than 5%. The testing would be operated in three hours, and the temperatures of the system components, e.g., aluminum sheet and water, were recorded every 20 min. The thermocouple wires transmitted the signal from the temperature measuring points to the temperature monitor. The characteristics of the devices used in the experiments were presented in Table 1. 7-water; 8-pyranometer; 9-thermocouples; 10-bracket; 11-temperature/humidity probes; 12-solar radiation observation station; 13-multichannel temperature monitor; 14-multichannel temperature/humidity detection system. 1-solar radiation simulator; 2-baffle plate; 3-floor; 4-heat insulating material; 5-aluminum sheets; 6-water container; 7-water; 8-pyranometer; 9-thermocouples; 10-bracket; 11-temperature/humidity probes; 12-solar radiation observation station; 13-multichannel temperature monitor; 14-multichannel temperature/humidity detection system. One xenon lamp was used to simulate the sunlight with the different radiations from 100 W/m 2 to 800 W/m 2 through regulating the input voltage of the lamp, and the simulated radiations were recorded by the pyranometer. The solar radiation intensity has been tested around the surface of the container, and their deviations were less than 5%. The testing would be operated in three hours, and the temperatures of the system components, e.g., aluminum sheet and water, were recorded every 20 minutes. The thermocouple wires transmitted the signal from the temperature measuring points to the temperature monitor.

Analysis and Discussion of the Testing Results
The three parameters determining the solar absorption property of the aluminum sheets, i.e., instantaneous absorptivity, average amount of heat absorption and average absorptivity, would be analyzed and discussed.

Instantaneous Absorptivity
The instantaneous absorptivity of the system could be calculated according to Equation (1) [26], and presented from Figures 8-10. Q t was the total amount of heat absorbed by the aluminum sheet and water every 20 min, which could be calculated by the change of water temperature and aluminum sheet temperature, due to their mass and specific heat capacity were known.

Analysis and Discussion of the Testing Results
The three parameters determining the solar absorption property of the aluminum sheets, i.e., instantaneous absorptivity, average amount of heat absorption and average absorptivity, would be analyzed and discussed.

Instantaneous Absorptivity
The instantaneous absorptivity of the system could be calculated according to Equation (1) [26], and presented from Figures 8-10. Q´t was the total amount of heat absorbed by the aluminum sheet and water every 20 minutes, which could be calculated by the change of water temperature and aluminum sheet temperature, due to their mass and specific heat capacity were known.

t AI
(1)  From above Figures 8-10, it could be seen that the variation of the instantaneous absorptivity of the three testing rigs presented similarly that it decreased and then reached stable due to part of the absorbed energy by the aluminum sheet dissipated to the environment. The instantaneous absorptivity of the nanoporous alumina sheet with 30 nm pore diameter decreased significantly than that of the other two testing rigs for the first hour of the testing, since the pore size of this type of the aluminum sheet was much smaller than the other two sheets, leading to much increased heat losses to the ambient and decreased solar absorptivity eventually. The instantaneous absorptivity was also found to be decreased with the increasing of the radiation intensity. When the simulated solar radiation was at 100 W/m 2 , the maximum instantaneous absorptivity of the three testing rigs reached 0.92, 0.82 and 0.49 respectively. From above Figures 8-10, it could be seen that the variation of the instantaneous absorptivity of the three testing rigs presented similarly that it decreased and then reached stable due to part of the absorbed energy by the aluminum sheet dissipated to the environment. The instantaneous absorptivity of the nanoporous alumina sheet with 30 nm pore diameter decreased significantly than that of the other two testing rigs for the first hour of the testing, since the pore size of this type of the aluminum sheet was much smaller than the other two sheets, leading to much increased heat losses to the ambient and decreased solar absorptivity eventually. The instantaneous absorptivity was also found to be decreased with the increasing of the radiation intensity. When the simulated solar radiation was at 100 W/m 2 , the maximum instantaneous absorptivity of the three testing rigs reached 0.92, 0.82 and 0.49 respectively. From above Figures 8-10, it could be seen that the variation of the instantaneous absorptivity of the three testing rigs presented similarly that it decreased and then reached stable due to part of the absorbed energy by the aluminum sheet dissipated to the environment. The instantaneous absorptivity of the nanoporous alumina sheet with 30 nm pore diameter decreased significantly than that of the other two testing rigs for the first hour of the testing, since the pore size of this type of the aluminum sheet was much smaller than the other two sheets, leading to much increased heat losses to the ambient and decreased solar absorptivity eventually. The instantaneous absorptivity was also found to be decreased with the increasing of the radiation intensity. When the simulated solar radiation was at 100 W/m 2 , the maximum instantaneous absorptivity of the three testing rigs reached 0.92, 0.82 and 0.49 respectively.

Average Amount of Heat Absorption
The thermal energy absorbed by the testing rig was composed of the amount of the heat absorbed by the aluminum sheet and cold water inside the water container, which were expressed from Equation (2) to Equation (4) [27], and the results were shown from Figures 11-13 for the testing rigs operated under different simulated radiations. It should be mentioned that due to the well thermal insulation of the extruded polystyrene board, the heat losses from the water container to the environment were ignored. The thermal energy absorbed by the testing rig was composed of the amount of the heat absorbed by the aluminum sheet and cold water inside the water container, which were expressed from Equation (2) to Equation (4) [27], and the results were shown from Figures 11-13 for the testing rigs operated under different simulated radiations. It should be mentioned that due to the well thermal insulation of the extruded polystyrene board, the heat losses from the water container to the environment were ignored.    From the above Figures 11-13, it could be seen that the thermal energy absorbed by the testing rigs increased from the beginning of the test and then tended to be constant. During the start-up stage, the temperature of the aluminum sheet was relatively low, and therefore, the amount of heat absorbed by the aluminum sheet was greater than the radiant heat losses, leading to the increased solar absorption heat of the aluminum sheet. After that, the temperature of the aluminum sheet From the above Figures 11-13, it could be seen that the thermal energy absorbed by the testing rigs increased from the beginning of the test and then tended to be constant. During the start-up stage, the temperature of the aluminum sheet was relatively low, and therefore, the amount of heat absorbed by the aluminum sheet was greater than the radiant heat losses, leading to the increased solar absorption heat of the aluminum sheet. After that, the temperature of the aluminum sheet gradually increased, and the temperature difference between the aluminum sheet and ambient directly increased the radiant heat losses.
It could also be found that for the testing rigs operated under different working conditions, the amount of absorbed heat increased with the increase of the simulated solar radiation. When the simulated solar radiation was at 800 W/m 2 , the heat absorption of the three testing rigs, i.e., the nanoporous alumina sheets with 30 nm and 400 nm pore diameters, and polished aluminum sheet, reached the maximum at 17,003 J, 13,974 J and 12,887 J respectively. This meant that the nanoporous alumina sheet performed better than the conventional polished aluminum sheet on the solar absorption characteristics, and the nanopore size of the aluminum sheet influenced its performance that the aluminum sheet with 30 nm nanopore diameter worked better than the sheet with 400 nm nanopore diameter.

Average Absorptivity
The average absorptivity was defined as the ratio of the total absorbed radiation by the testing rigs to the total radiation emitted from the solar simulator as in Equation (5), and the testing results were calculated and presented in Table 2 and Figures 14-21. Q t could be calculated by Equation (2). ∆t was the radiation time. α = Q t 60 × AI∆t (5) From the above figures and table, the surface absorptivity was found to be decreased with the increase of the radiation intensity, and the average absorptivity of the nanoporous alumina sheet with 30 nm pore diameter reached the maximum at 0.39 when the simulated radiation was at 100 W/m 2 , which was 18% higher than that of the nanoporous alumina sheet with 400 nm pore diameter (0.33) and 50% higher than that of the polished aluminum sheet (0.26). When the simulated radiation was at 800 W/m 2 , the minimum average absorptivity of the three testing rigs was at 0.14, 0.10 and 0.08 respectively. The average absorptivity of the three aluminum sheets was also found to be decreased exponentially with time, and the nanoporous alumina sheets decreased significantly compared with the polished one due to the higher surface temperature of the nanoporous alumina sheets, leading to more radiant heat losses to the surroundings, as shown in the above Figures 14-21, the trend of the polished aluminum sheet was relatively flat and tended to be linear.        From the above figures and table, the surface absorptivity was found to be decreased with the increase of the radiation intensity, and the average absorptivity of the nanoporous alumina sheet with 30 nm pore diameter reached the maximum at 0.39 when the simulated radiation was at 100 W/m 2 , which was 18% higher than that of the nanoporous alumina sheet with 400 nm pore diameter (0.33) and 50% higher than that of the polished aluminum sheet (0.26). When the simulated radiation was at 800 W/m 2 , the minimum average absorptivity of the three testing rigs was at 0.14, 0.10 and 0.08 respectively. The average absorptivity of the three aluminum sheets was also found to be

Correlation of the Absorptivity with the Radiation Intensity
Based on the above test results, the correlation of the absorptivity of the aluminum sheet with the radiation intensity was established in the exponential function.
Assuming the boundary conditions, when: When: Equation (6) can be rewritten as: Then, the calculation results of the absorptivity of the three types of aluminum sheets were shown in Table 3, and the correlation of the absorptivity with the radiation intensity was presented in Figure 22. The exponential relation between the absorptivity and the radiation intensity was found for the three testing rigs that the increase of the radiation intensity had lead to the decrease of the absorptivity. The comparison between the testing results and the calculation results indicated that the exponential function could predict the absorptivity of the aluminum sheet under different irradiation within the acceptable error range.  Figure 22. Correlation of the absorptivity with radiation intensity for the three testing rigs.

Error Propagation Analysis
Affected by the accuracy class of the testing devices, the uncertainty range of the major measure quantities containing temperature and solar radiation would be considered. From Table 1, the uncertainty range of the temperature and solar radiation could be calculated [28].
Taking the polished aluminum sheet at the radiation intensity was 100 W/m 2 for example (due that the maximum error would appear at this condition), the relative error of the heat absorbed and absorptivity could be calculated [29].
The relative error of all the testing condition about heat absorbed would be less than 10.6%. The relative error of all the testing condition about absorptivity would be less than 14.6%. The relative error of the absorptivity for the other two sheets and at the other testing radiation intensity could be calculated by using the same method, the results were show in Figure 23.

Error Propagation Analysis
Affected by the accuracy class of the testing devices, the uncertainty range of the major measure quantities containing temperature and solar radiation would be considered. From Table 1, the uncertainty range of the temperature and solar radiation could be calculated [28].
Taking the polished aluminum sheet at the radiation intensity was 100 W/m 2 for example (due that the maximum error would appear at this condition), the relative error of the heat absorbed and absorptivity could be calculated [29].
The relative error of all the testing condition about heat absorbed would be less than 10.6%. The relative error of all the testing condition about absorptivity would be less than 14.6%. The relative error of the absorptivity for the other two sheets and at the other testing radiation intensity could be calculated by using the same method, the results were show in Figure 23.
Therefore, the error with this experimental could be acceptable from Figure 23. Therefore, the error with this experimental could be acceptable from Figure 23.

Conclusions
In this paper, the nanoporous alumina sheets with the pore diameters of 30 nm and 400 nm were prepared by anodic oxidation method, and the SEM indicated that the nanopores evenly distributed on the surface of the aluminum sheets, which will be helpful in enhancing the stability of the aluminum surface and improving the solar absorption capability. In order to investigate the property of the nanoporous alumina sheet, the prepared aluminum sheets were compared with the conventional polished aluminum sheet and analyzed in the aspects of the instantaneous absorptivity, average absorbed heat and average absorptivity. The exponential correlation between the average absorptivity and the radiation intensity for the three testing rigs was also established.
The results showed that the maximum instantaneous absorption efficiency of the nanoporous alumina sheet with 30 nm pore diameter was found at 0.92 when the radiation intensity was at 100 W/m 2 . The absorbed heat by the testing rigs increased with the increase of the radiation, while the average absorptivity decreased with the increase of the radiation. When the radiation intensity was 100 W/m 2 , the nanoporous alumina sheet with the 30 nm pore diameter had the highest average solar absorptivity of 0.39, which was 18% higher than that of the nanoporous alumina sheet with 400 nm pore diameter, and 50% higher than that of the polished aluminum sheet. The results indicated that the nanoporous alumina sheet performed better than the conventional polished aluminum sheet in the solar absorption property, and the pore size significantly influenced the solar absorptivity of the aluminum sheet. By error propagation analysis, the relative error of the average amount of heat absorption and the average absorptivity were acceptable.

Conclusions
In this paper, the nanoporous alumina sheets with the pore diameters of 30 nm and 400 nm were prepared by anodic oxidation method, and the SEM indicated that the nanopores evenly distributed on the surface of the aluminum sheets, which will be helpful in enhancing the stability of the aluminum surface and improving the solar absorption capability. In order to investigate the property of the nanoporous alumina sheet, the prepared aluminum sheets were compared with the conventional polished aluminum sheet and analyzed in the aspects of the instantaneous absorptivity, average absorbed heat and average absorptivity. The exponential correlation between the average absorptivity and the radiation intensity for the three testing rigs was also established.
The results showed that the maximum instantaneous absorption efficiency of the nanoporous alumina sheet with 30 nm pore diameter was found at 0.92 when the radiation intensity was at 100 W/m 2 . The absorbed heat by the testing rigs increased with the increase of the radiation, while the average absorptivity decreased with the increase of the radiation. When the radiation intensity was 100 W/m 2 , the nanoporous alumina sheet with the 30 nm pore diameter had the highest average solar absorptivity of 0.39, which was 18% higher than that of the nanoporous alumina sheet with 400 nm pore diameter, and 50% higher than that of the polished aluminum sheet. The results indicated that the nanoporous alumina sheet performed better than the conventional polished aluminum sheet in the solar absorption property, and the pore size significantly influenced the solar absorptivity of the aluminum sheet. By error propagation analysis, the relative error of the average amount of heat absorption and the average absorptivity were acceptable.

Conflicts of Interest:
The authors declare no conflict of interest.