Experimental Performance of a Solar Air Collector with a Perforated Back Plate in New Zealand

This study investigates the thermal efficiency of a solar air heater (SAH), when it was mounted on a custom-made support frame, and was operated under different air mass flow rate. This SAH is composed of a transparent polycarbonate cover plate, a felt absorber layer, a perforated aluminium back plate and an aluminium frame. The ambient inlet air of this SAH is heated as it passes through the perforated back plate and over the felt absorber layer. The heated air is blown out through the outlet. Studies of SAHs with a similar design to this SAH were not found in the literature. The experiment was carried out at Massey University, Auckland campus, NZ (36.7◦ S, 174.7◦ E). The global horizontal solar irradiance, the ambient temperature and the wind speed were recorded using an on-site weather station. Temperature and velocity of the air at the outlet were measured using a hot wire anemometer. During the experiment, the air mass flow rate was between 0.022 ± 0.001 kg/s and 0.056 ± 0.005 kg/s. Results showed that when the SAH was operated at the airflow between 0.0054 kg/s and 0.0058 kg/s, the inlet air temperature and the wind speed (between 0 and 6.0 m/s) did not impact the temperature difference between the outlet air and the inlet air. The thermal efficiency of the SAH increased from 34 ± 5% at the airflow between 0.021 kg/s and 0.023 kg/s, to 47 ± 6% at the airflow ranging from 0.032 kg/s to 0.038 kg/s, to 71 ± 4% at the airflow of 0.056 ± 0.005 kg/s. The maximum thermal efficiency of 75% was obtained at the airflow of 0.057 kg/s. The effective efficiency of the SAH was 32 ± 5% at the airflow between 0.021 kg/s and 0.023 kg/s, 42 ± 6% at the airflow ranging from 0.032 kg/s to 0.038 kg/s, and 46 ± 11% at the airflow of 0.056 ± 0.005 kg/s.


Introduction
The thermal efficiency of a solar air heater (SAH) is defined as the ratio of the energy converted to the solar energy incident on the SAH collector panel [1]. The design and the operation conditions are the main factors that influence the efficiency of a SAH. The main components for the design include the cover, flow types and absorber layer. Operation conditions include the air mass flow rate and the weather conditions (solar radiation, ambient temperature and wind speed).
Several research projects have focused on modifying the configurations of the SAH to increase the heat transfer performances. These modifications include changing shapes and materials of the absorber layer [2][3][4][5][6][7], increasing the air channel turbulence [8][9][10][11], modifying the flow type [12][13][14] and the cover plate [15]. Table 1 shows the efficiencies of several types of SAH, when they were operated at different air mass flow rate. Among all the reported SAH in Table 1, efficiencies ranged from 35% to 86% when they were operated at the mass flow rate from 0.010 kg/s to 0.060 kg/s. Study 6 Type 3 SAH showed the maximum efficiency of 86% at the air mass flow rate of 0.042 kg/s.  (Table 1) to Study 4 (Table 1) showed artificially roughening the absorber layer can increase the efficiency of the SAH [9,[15][16][17][18]. Study 1 [15,16] showed that the double pass SAH with V corrugated shape absorber layer was from 11% to 14% and from 9% to 12% more efficient than the double pass SAH with flat and finned absorber layer respectively. Karim and Hawlader [17] (Table 1, Study 2) found a single pass SAH with finned absorber layer was 4% more efficient than the flat plate SAH. The single pass SAH with V corrugated shape absorber layer was 10% more efficient than the flat plate SAH. Chabane, Moummi and Benramache [9] (Table 1, Study 3) reported that the maximum efficiency of a single pass SAH with fins below the absorber layer was 5% and 8% more efficient than the one without fins, at the air mass flow rates of 0.012 kg/s and 0.016 kg/s respectively. Ozgen, Esen and Esen [18] (Table 1, Study 4) compared a parallel double flow SAH with zigzag arranged aluminium cans on the absorber layer, orderly arranged aluminium cans on the absorber layer, and the smooth absorber layer at the air mass flow rate of 0.030 kg/s and 0.050 kg/s. The maximum efficiency of 73% was found for the SAH with zigzag-arranged cans on absorber layer at the air mass flow rate of 0.050 kg/s. In short, artificially roughening the SAH absorber layer can increase the efficiency of the SAH.
Modifying the airflow type is another way to increase the heat transfer of the SAH [12][13][14]. Airflow types can be categorized as: (i) single flow (with only one flow channel over or under the absorber layer); (ii) double flows (double pass parallel flow or double pass counter flow); and (iii) air flow through a matrix absorber layer [13]. There are two ways to create the double flow. One is using the top glass cover and the bottom glass cover (double glazed SAH) forming the upper channel, with the lower glass cover and the absorber layer forming the lower channel. Another double flow SAH is designed by placing the absorber layer inside the air duct to form the double air passage around absorber layer. The maximum thermal efficiency was achieved by placing the absorber layer in the middle of the air channel, with the upper and lower channels of equal size [21]. Omojaro and Aldabbagh [19] ( Table 1, Study 5) showed a 4% increase of the thermal efficiency when the SAH was modified from single flow to double flow. Karim and Hawlader [17] (Table 1, Study 2) reported a 13%, 10% and 7% thermal efficiency increase for V corrugated shape, finned and flat plate absorber layer when changing the airflow type from single flow to double flow. Dhiman, Thakur and Chauhan [12] found that the thermal efficiency of a counter flow SAH was from 11% to 17% higher than the same SAH with parallel flow, when they were operated at the air mass flow rate from 0.012 kg/s to 0.038 kg/s. In conclusion, modifying the airflow type can increase the thermal efficiency of a SAH.
The thermal performance of six types of SAH was investigated [19,20,[22][23][24]. The first SAH had a steel wire mesh absorber layer [22], the second SAH had a steel wire mesh absorber layer and longitude fins attached [19]. The third one had a steel wire mesh absorber layer with transverse fins attached and 'S-shape' airflow (Table 1, Study 6) [20]. The forth one had a steel wire mesh absorber layer with transverse fins attached and '8-Shape' airflow [23]. The fifth one had a steel wire mesh absorber layer and a partially perforated cover [24]. The performance of these five SAHs was compared with a similar SAH without any modifications (the sixth type SAH).
The authors concluded that the SAH with the wire mesh absorber layer (matrix layer) was efficient, as air passing through the wire mesh absorber layer can maximize heat extraction [5]. The SAH with modified rough air channels performed better than the SAH with smooth air channel. The double-pass SAH was more efficient than the single pass SAH. For the double-pass SAH, the height of the upper channel negatively impacted on the thermal efficiency. The narrower the upper channel, the more efficient the SAH was. When the SAH was operated at air mass flow rate of 0.036 kg/s, thermal efficiencies were respectively 62%, 59% and 57% at the height of the upper channel of 30 mm, 50mm and 70 mm [19]. The maximum thermal efficiency (86%) was obtained from the third type SAH (the double-pass counter flow SAH with six transverse fins and 'S-shape' airflow channel) at the air mass flow rate of 0.042 kg/s [20].
Our study aims to investigate the thermal efficiency of a SAH when it was operated at different air mass flow rate. The experiment was conducted under Auckland, NZ weather conditions. The thermal efficiency of this studied SAH is compared to some other SAHs reported in the introduction. This studied SAH has the inlet air coming from a perforated back plate and then passing through and over the absorber layer before it is ducted. Results for investigating thermal efficiency of such type SAH have not been reported in the literature yet.
The paper is organized as following: materials and methods for investigating thermal efficiency of the SAH are presented in Section 2, including the structure of this studied SAH; experiment setup, test procedure and the thermal efficiency calculation. Section 3 presents the experimental results. Section 4 concludes the finding along with the future research. Figure 1 shows the exploded view of the studied SAH. the more efficient the SAH was. When the SAH was operated at air mass flow rate of 0.036 kg/s, thermal efficiencies were respectively 62%, 59% and 57% at the height of the upper channel of 30 mm, 50mm and 70 mm [19]. The maximum thermal efficiency (86%) was obtained from the third type SAH (the double-pass counter flow SAH with six transverse fins and 'S-shape' airflow channel) at the air mass flow rate of 0.042 kg/s [20].

Structure of the Studied Solar Air Heater
Our study aims to investigate the thermal efficiency of a SAH when it was operated at different air mass flow rate. The experiment was conducted under Auckland, NZ weather conditions. The thermal efficiency of this studied SAH is compared to some other SAHs reported in the introduction. This studied SAH has the inlet air coming from a perforated back plate and then passing through and over the absorber layer before it is ducted. Results for investigating thermal efficiency of such type SAH have not been reported in the literature yet.
The paper is organized as following: materials and methods for investigating thermal efficiency of the SAH are presented in Section 2, including the structure of this studied SAH; experiment setup, test procedure and the thermal efficiency calculation. Section 3 presents the experimental results. Section 4 concludes the finding along with the future research. Figure 1 shows the exploded view of the studied SAH.  Figure 1 shows that this SAH, from the front to the back, is composed of a transparent cover (polycarbonate), an absorber layer (black felt), a perforated back plate (aluminium) and an aluminium frame. The diameter of the outlet air duct is 125 mm. The diameter of the air inlet holes on the perforated back plate is 1.5 mm. These holes are evenly distributed in a grid, spaced at 15 mm apart (approximately 4300 holes/m 2 ). Figure 2 shows the schematic view of the studied SAH.  The length, width, and air channel depth of this SAH are 3000 mm, 1020 mm and 75 mm respectively. The collector gross area and the absorber layer effective area are both 3 m 2 . The SAH has a fan (power consumption: 5.1 Watt), a fan speed on/off controller (regulator) and an outlet duct. The fan is powered by an 18 Watt photovoltaic panel. The ambient air enters into the SAH through the perforated back plate. The heated air is pushed in the outlet duct by the fan. The velocity of the outlet air was controlled by the fan speed controller (regulator).

Experiment Setup and Test Procedure
During the experiment, the SAH was mounted on a custom-made galvanized metal frame. The length, width, and air channel depth of this SAH are 3000 mm, 1020 mm and 75 mm respectively. The collector gross area and the absorber layer effective area are both 3 m 2 . The SAH has a fan (power consumption: 5.1 Watt), a fan speed on/off controller (regulator) and an outlet duct. The fan is powered by an 18 Watt photovoltaic panel. The ambient air enters into the SAH through the Energies 2020, 13, 1415 5 of 16 perforated back plate. The heated air is pushed in the outlet duct by the fan. The velocity of the outlet air was controlled by the fan speed controller (regulator).

Experiment Setup and Test Procedure
During the experiment, the SAH was mounted on a custom-made galvanized metal frame. Figure 3 shows the setup of the experiment. The length, width, and air channel depth of this SAH are 3000 mm, 1020 mm and 75 mm respectively. The collector gross area and the absorber layer effective area are both 3 m 2 . The SAH has a fan (power consumption: 5.1 Watt), a fan speed on/off controller (regulator) and an outlet duct. The fan is powered by an 18 Watt photovoltaic panel. The ambient air enters into the SAH through the perforated back plate. The heated air is pushed in the outlet duct by the fan. The velocity of the outlet air was controlled by the fan speed controller (regulator).

Experiment Setup and Test Procedure
During the experiment, the SAH was mounted on a custom-made galvanized metal frame. Figure 3 shows the setup of the experiment. The SAH panel was 52° off the horizontal surface (local latitude 37° plus 15°). The panel faced due north (at the azimuth angle of 0°). The global horizontal solar irradiance, the ambient temperature and the wind speed were recorded by an onsite weather station (HP2000 Wi-Fi Weather Station, Fine Offset Electronics Co., Ltd.), as shown in Figure 3. The velocity and the temperature of the outlet air were monitored by a hot wire anemometer (AM4214SD, Lutron Electronic Enterprise Co. Ltd.). Table 2 shows the characteristics of the monitoring devices. The SAH panel was 52 • off the horizontal surface (local latitude 37 • plus 15 • ). The panel faced due north (at the azimuth angle of 0 • ). The global horizontal solar irradiance, the ambient temperature and the wind speed were recorded by an onsite weather station (HP2000 Wi-Fi Weather Station, Fine Offset Electronics Co., Ltd., Shenzhen, China), as shown in Figure 3. The velocity and the temperature of the outlet air were monitored by a hot wire anemometer (AM4214SD, Lutron Electronic Enterprise Co. Ltd., Taipei City, Taiwan). Table 2 shows the characteristics of the monitoring devices.
The experiment was carried out for 9 days at Massey University's Auckland campus, NZ (36.7 • S, 174.7 • E). The test began at 9 am and ended at 4 pm (New Zealand Daylight Time). On each day, the air was circulated through the panel for at least 10 min prior to commencing the measurement. During the test, the fan regulator was set at 50% maximum speed of the ventilator from Day 1 to Day 4; at 75% maximum speed of the ventilator from Day 5 to Day 8, and 100% maximum speed of the ventilator on Day 9. The 50% and 75% maximum speed of the ventilator were set to investigate the efficiency and the outlet air temperature rise (between the outlet air and inlet air) of this SAH, when it was operated at different air mass flow rate.

Thermal Efficiency Calculation
The thermal efficiency of the SAH was estimated based on Equation (1).
where, Air velocity (m/s) During the calculation, it was assumed that the monitored air velocity was the mean air velocity. The ambient air temperature was the inlet air temperature. Equation (1) shows that efficiency of the SAH depends on air mass flow rate and the parameter that temperature difference between outlet air and inlet air divide the solar radiation on the tilted solar collector surface, as air specific heat capacity and solar collector effective area were constant. The air density and the air specific heat capacity were set according to the air temperature, as shown in Table 3 [25]. The solar radiation incident on the absorber layer was calculated using the computer program solaR [26]. The Spencer model [27] was chose to calculate the declination angle and the extra-terrestrial radiation incident on the plane. The Boland-Ridley-Lauret model was used to calculate the horizontal diffuse solar radiation based on the measured global horizontal solar radiation [28,29]. The Boland-Ridley-Lauret model performed well in both North and South Hemispheres [28]. The Hay and McKay model was used to estimate the diffuse radiation on the inclined absorber plate [30]. All equations for calculating the solar radiation incident are attached in Appendix A.

Effective Efficiency Calculation
To evaluate the economic performance, the effective efficiency of the solar air heater is estimated according to the Equation (2) [31].
where, The conversion factor (C) is the energy conversion efficiency from the primary energy to the mechanical energy, and a typical value of 0.18 is suggested to be considered [31,32].
The required mechanical power (P m ) can be estimated according to the Equation (3).
where, In this study, the pressure drops due to others have been discarded, while the pressure drops due to the air moves through the absorber layer and inside the air channel are estimated according to the Equation (4) [33].
where, The fraction factor can be estimated according to the Equation (5) and Equation (6) [16].
The hydraulic diameter of the air channel can be estimated according to the Equation (7). where, Width of the air channel (m) b Depth of the air channel (m) The hydraulic diameter of the absorber layer needs to multiply the porosity of the absorber layer. The porosity can be estimated according to the Equation (8).
where, Reynolds number can be estimated according to Equation (9).
where, R e Reynolds number µ Dynamic viscosity (kg/(m*s)) The dynamic viscosity of the air was set according to the air temperature, as shown in Table 3.

The Uncertainty Calculation
In this study, the errors from both the monitoring devices and the measurements have been analyzed [19]. The independent measurements include the inlet air temperature, the outlet air temperature, the outlet air velocity and the solar air radiation. The equipment used and the uncertainty of these equipment has shown in Equation (10). Considering the density of the air, the specific heat of the air as constant. The fractional uncertainty of the solar air heater thermal efficiency is estimated according to Equation (10).
where, ω x Uncertainty of the variable x The uncertainty of the variable x can be estimated according to Equation (11).
where, ω x Uncertainty of the variable x σ x Standard deviation of the variable x ∆ instrument Uncertainty of the instrument Results show that the mean values for all the days together for ∆T, T i , T o , . m, I T , and the thermal efficiency are 17.6 • C, 19.1 • C, 36.7 • C, 0.032 kg/s, 428 W/m 2 , and 44% respectively. The fractional uncertainty of the efficiency is found to be 0.0061. The theoretical prediction of this SAH was analyzed by McGowan [34]. This study focuses on the experimental results. All calculations were conducted using the statistical computing and graphics platform programming language R version 3.4.3 [35].

Ambient Weather Conditions during Experiment
During the test, the weather data was monitored at 1-min interval. It found that the solar radiation ranged from 104 W/m 2 (minimum) to 1298 W/m 2 (maximum), with the mean (± standard deviation, SD) level of 544 (± 270) W/m 2 . The ambient temperature ranged from 15.7 • C (minimum) to 22.8 • C (maximum), with the mean (± SD) of 19.1 ± 1.7 • C. The wind speed ranged from 0 m/s to 9.6 m/s, with the mean (± SD) level of 2.0 ± 1.3 m/s. For 99.3% of the time, the wind speed was between 0 m/s and 6.0 m/s, 0.7% of the monitored wind speed was above 6.0 m/s. The hourly solar radiation ranged from 157 W/m 2 (minimum) to 908 W/m 2 (maximum). The hourly ambient temperature was from 16.1 °C to 22.5 °C. The hourly wind speed was between 0.8 m/s to 3.4 m/s. The mean (± SD) values of the global horizontal solar radiation, ambient temperature and wind speed on each test day are shown in Table 4. The highest and the lowest mean global horizontal solar radiation during the test days was 703.3 ± 286.6 W/m 2 (Day 1) and 374.8 ± 161.6 W/m 2 (Day 2) respectively. The mean ambient temperature ranged from 17.3 ± 0.8 °C (Day 4) to 21.3 ± 1.0 °C (Day 6). The highest and lowest mean wind speed was 3.0 ± 1.5 m/s (Day 6), and 1.3 ± 1.0 m/s (Day 2) respectively.

Outlet Air Temperature of the Studied SAH
The air mass flow rate affects the outlet air temperature. A higher air mass flow rate makes the less time for air circulating inside the air channel and absorbing the heat. Consequently, it results in a lower outlet air temperature [36]. During the test, the air mass flow rate was between 0.022 ± 0.001 The hourly solar radiation ranged from 157 W/m 2 (minimum) to 908 W/m 2 (maximum). The hourly ambient temperature was from 16.1 • C to 22.5 • C. The hourly wind speed was between 0.8 m/s to 3.4 m/s. The mean (± SD) values of the global horizontal solar radiation, ambient temperature and wind speed on each test day are shown in Table 4. The highest and the lowest mean global horizontal solar radiation during the test days was 703.3 ± 286.6 W/m 2 (Day 1) and 374.8 ± 161.6 W/m 2 (Day 2) respectively. The mean ambient temperature ranged from 17.3 ± 0.8 • C (Day 4) to 21.3 ± 1.0 • C (Day 6). The highest and lowest mean wind speed was 3.0 ± 1.5 m/s (Day 6), and 1.3 ± 1.0 m/s (Day 2) respectively.

Outlet Air Temperature of the Studied SAH
The air mass flow rate affects the outlet air temperature. A higher air mass flow rate makes the less time for air circulating inside the air channel and absorbing the heat. Consequently, it results in a lower outlet air temperature [36]. During the test, the air mass flow rate was between 0.022 ± 0.001 kg/s and 0.056 ± 0.005 kg/s. Table 5 shows mean (± SD) values of the outlet air velocity (m/s), air mass flow rate (kg/s), solar radiation on the SAH collector surface (W/m 2 ), the outlet air temperature ( • C), and the temperature difference between the outlet air and the inlet air (∆T, T outlet -T inlet ) on each test day. Table 5. The mean and standard deviation (SD) of the velocity, air mass flow rate, solar radiation on the collector surface, outlet air temperature, and the temperature difference between the outlet air and the inlet air of the SAH on each test day. The outlet air temperature ranged from 19.9 • C to 59.8 • C, with the mean level of 36.7 • C (SD: 8.5 • C). Table 5 shows the mean (± SD) values of the outlet air temperature ranged from 29.7 ± 6.3 • C (Day 9) to 45.2 ± 9.3 • C (Day 1). The mean level of the solar radiation on Day 1 was higher than on the other days that had the same setting of the fan speed controller (Day 2 to Day 4, 50% maximum speed of the ventilator). This resulted in the mean outlet air temperature on Day 1 higher than on Day 2 to Day 4. Consequently, the air density and the mass flow rate on Day 1 were lower than on Day 2, Day 3 and Day 4 regardless of the similar air velocity. The mean air mass flow rate on Day 5 to Day 8 was between 0.032 kg/s and 0.038 kg/s, at 75% maximum speed of the ventilator. The mean (± SD) value of mass flow rate on Day 9 was 0.056 ± 0.005 kg/s. The fieldwork performance of this SAH when it was roof-mounted on the NZ primary schools in winter has been reported [37,38].

Percent of Maximum
Levels of ∆T (T outlet -T inlet ) obtained during the experiment was from 3.2 • C (minimum) to 41.0 • C (maximum). The mean (±SD) values of ∆T (T outlet -T inlet ) ranged from 11.5 ± 5.9 • C (Day 9) to 25.5 ± 8.3 • C (Day 1). The maximum ∆T (T outlet -T inlet ) was 41.0 • C. This was obtained on Day 4 noon when the wind speed was 2.2 m/s, the inlet air temperature was 17.5 • C, and the solar radiation was 901 W/m 2 . Multiple linear regressions were built to investigate the attribute of the ∆T (T outlet -T inlet ), when it was operated at different air mass flow rate. The model input variables include the solar radiation, air mass flow rate, inlet air temperature and the wind speed.
As expected, a positive relationship between ∆T (T outlet -T inlet ) and the solar radiation, a negative relationship between ∆T (T outlet -T inlet ) and the air mass flow rate were observed in this study. When the SAH was operated at air mass flow rate between 0.021 and 0.023 kg/s, ∆T (T outlet -T inlet ) was impacted by the solar radiation and mass flow rate. When the SAH was operated at flow rate between 0.032 and 0.038 kg/s, the solar radiation, the mass flow rate, the wind speed and the inlet air temperature all affected the ∆T (T outlet -T inlet ). When this SAH was operated at flow rate between 0.054 and 0.058 kg/s, only the solar radiation levels affected the ∆T (T outlet -T inlet ) levels. This result was supported by Omojaro and Aldabbagh [19] and Aldabbagh, Egelioglu and Ilkan [22], where there were a negative relationship between ∆T (T outlet -T inlet ) and the air mass flow rate, and a positive relationship between ∆T (T outlet -T inlet ) and the solar radiation.  Figure 5 shows the efficiency versus values of the efficiency function parameter (T (Toutlet-Tinlet)/IT) at different air mass flow rate. The regression models for efficiencies of the SAH under different mass flow rate have been added.  Figure 5 shows that during the experiment, the T (Toutlet-Tinlet)/IT was between 0.027 and 0.058 Km 2 /W. From the regression model, it can be estimated that, when the value of (Toutlet-Tinlet)/IT is ca. 0.04 Km 2 /W, the efficiency of the SAH was ca. 29%, 50% and 75% at an air mass flow rate of ca. 0.022 kg/s, 0.037 kg/s and 0.056 kg/s respectively. This difference of the efficiency is getting bigger when the value of T (Toutlet-Tinlet)/IT is increasing. This means the higher the air mass flow rate is, the more heat was transferred into the air. Figure 6 shows the efficiency versus values of the efficiency function parameter (T (Toutlet-Tinlet)/IT) at different air mass flow rate. The solid line is the thermal efficiency, and the dashed line is the effective efficiency.  Figure 5 shows that during the experiment, the ∆T (T outlet -T inlet )/I T was between 0.027 and 0.058 Km 2 /W. From the regression model, it can be estimated that, when the value of (T outlet -T inlet )/I T is ca. 0.04 Km 2 /W, the efficiency of the SAH was ca. 29%, 50% and 75% at an air mass flow rate of ca. 0.022 kg/s, 0.037 kg/s and 0.056 kg/s respectively. This difference of the efficiency is getting bigger when the value of ∆T (T outlet -T inlet )/I T is increasing. This means the higher the air mass flow rate is, the more heat was transferred into the air. Figure 6 shows the efficiency versus values of the efficiency function parameter (∆T (T outlet -T inlet )/I T ) at different air mass flow rate. The solid line is the thermal efficiency, and the dashed line is the effective efficiency. Figure 6 shows that although the thermal efficiency increased with the increasing of the air mass flow rate, when considering the mechanic power consumed by the fan, the mean effective efficiency only had a 4% increase when the operated air mass flow rate increased from the range between 0.032 kg/s and 0.038 kg/s to 0.057 kg/s. The effective efficiency of the SAH was 32 ± 5% at the airflow between 0.021 kg/s and 0.023 kg/s, to 42 ± 6% at the airflow ranging from 0.032 kg/s to 0.038 kg/s, and 46 ± 11% at the airflow of 0.056 ± 0.005 kg/s. Energies 2020, 13, x FOR PEER REVIEW 13 of 17 Figure 6. Thermal efficiency and effective efficiency of the solar air heater versus the value of the efficiency function at different air mass flow rate. The efficiency function is the temperature difference between outlet air (Toutlet), and inlet air (Tinlet) divide the solar radiation on the collector panel (IT). Figure 6 shows that although the thermal efficiency increased with the increasing of the air mass flow rate, when considering the mechanic power consumed by the fan, the mean effective efficiency only had a 4% increase when the operated air mass flow rate increased from the range between 0.032 kg/s and 0.038 kg/s to 0.057 kg/s. The effective efficiency of the SAH was 32 ± 5% at the airflow between 0.021 kg/s and 0.023 kg/s, to 42 ± 6% at the airflow ranging from 0.032 kg/s to 0.038 kg/s, and 46± 11% at the airflow of 0.056 ± 0.005 kg/s.

Discussions
The efficiency of the studied SAH was 71 ± 4% [min: 64%, max: 75%], at an air mass flow rate of 0.056 ± 0.004 kg/s. The maximum thermal efficiency of 75% was found at the mass flow rate of 0.057 kg/s. Karim and Hawlader [17] reported a double pass V-corrugated SAH with maximum efficiency of 82% at an air mass flow rate of 0.056 kg/s. The maximum efficiency of 80% was found from a SAH with porous material between the absorber layer and bottom plate, when it was operated at air mass flow rate of 0.070 kg/s [2]. Ozgen, Esen and Esen [18] found the maximum thermal efficiency of a double parallel flow SAH with aluminium absorber plate with zag-zig arranged aluminium cans on both side was 73% at an air mass flow rate of 0.055 kg/s. El-Sebaii, Aboul-Enein, Ramadan, Shalaby and Moharram [16] found the thermal efficiency of a double parallel pass V-corrugated SAH was 67% at an air mass flow rate of 0.060 kg/s; the thermal efficiency of a double parallel flat SAH was 59% at an air mass flow rate of 0.060 kg/s. At an air mass flow rate between 0.032 kg/s and 0.038 kg/s, the efficiency of the SAH found in this study was 47 ± 6% [min: 35%, max: 57%]. Prasad, et al. [39] found a single pass SAH with packed bed formed by wire mesh had the maximum efficiency of 59% at the mass flow rate of 0.035 kg/s. Omojaro and Aldabbagh [19] found the efficiency of a SAH with steel wire mesh was 60% (single pass SAH) and 64% (double pass SAH) when it was operated at mass flow rate of 0.038 kg/s. El-Sebaii, Aboul-Enein, Ramadan, Shalaby and Moharram [15] found a double parallel SAH had the thermal efficiency of 56% (flat absorber plate) and 65% (V-corrugated absorber plate) when they were operated at mass flow rate of 0.040 kg/s.

Discussions
The efficiency of the studied SAH was 71 ± 4% [min: 64%, max: 75%], at an air mass flow rate of 0.056 ± 0.004 kg/s. The maximum thermal efficiency of 75% was found at the mass flow rate of 0.057 kg/s. Karim and Hawlader [17] reported a double pass V-corrugated SAH with maximum efficiency of 82% at an air mass flow rate of 0.056 kg/s. The maximum efficiency of 80% was found from a SAH with porous material between the absorber layer and bottom plate, when it was operated at air mass flow rate of 0.070 kg/s [2]. Ozgen, Esen and Esen [18] found the maximum thermal efficiency of a double parallel flow SAH with aluminium absorber plate with zag-zig arranged aluminium cans on both side was 73% at an air mass flow rate of 0.055 kg/s. El-Sebaii, Aboul-Enein, Ramadan, Shalaby and Moharram [16] found the thermal efficiency of a double parallel pass V-corrugated SAH was 67% at an air mass flow rate of 0.060 kg/s; the thermal efficiency of a double parallel flat SAH was 59% at an air mass flow rate of 0.060 kg/s. At an air mass flow rate between 0.032 kg/s and 0.038 kg/s, the efficiency of the SAH found in this study was 47 ± 6% [min: 35%, max: 57%]. Prasad, et al. [39] found a single pass SAH with packed bed formed by wire mesh had the maximum efficiency of 59% at the mass flow rate of 0.035 kg/s. Omojaro and Aldabbagh [19] found the efficiency of a SAH with steel wire mesh was 60% (single pass SAH) and 64% (double pass SAH) when it was operated at mass flow rate of 0.038 kg/s. El-Sebaii, Aboul-Enein, Ramadan, Shalaby and Moharram [15] found a double parallel SAH had the thermal efficiency of 56% (flat absorber plate) and 65% (V-corrugated absorber plate) when they were operated at mass flow rate of 0.040 kg/s. At an air mass flow rate between 0.021 and 0.023 kg/s, the thermal efficiency of this studied SAH was 34 ± 5% [min: 24%, max: 44%]. Chabane, Moummi and Benramache [9] reported the thermal efficiency of a SAH both with the longitudinal fins installed under the absorber layer and without the fins installed. It reported that the thermal efficiency of this SAH without fins was 35% and 44% at the air mass flow rate of 0.012 kg/s and 0.016 kg/s respectively. This thermal efficiency was increased to 40% and 52% for the SAH with the fins [9].