Efficiency Enhancement in Double ‐ Pass Perforated Glazed Solar Air Heaters with Porous Beds: Taguchi ‐ Artificial Neural Network Optimization and Cost–Benefit Analysis

: Analyzing the combination of involving parameters impacting the efficiency of solar air heaters is an attractive research areas. In this study, cost ‐ effective double ‐ pass perforated glazed solar air heaters (SAHs) packed with wire mesh layers (DPGSAHM), and iron wools (DPGSAHI) were fabricated, tested and experimentally enhanced under different operating conditions. Forty ‐ eight iron pieces of wool and fifteen steel wire mesh layers were located between the external plex ‐ iglass and internal glass, which is utilized as an absorber plate. The experimental outcomes show that the thermal efficiency enhances as the air mass flow rate increases for the range of 0.014–0.033 kg/s. The highest thermal efficiency gained by utilizing the hybrid optimized DPGSAHM and DPG ‐ SAHI was 94 and 97%, respectively. The exergy efficiency and temperature difference ( ∆ T) indicated an inverse relationship with mass flow rate. When the DPGSAHM and DPGSAHI were optimized by the hybrid procedure and employing the Taguchi ‐ artificial neural network, enhancements in the thermal efficiency by 1.25% and in exergy efficiency by 2.4% were delivered. The results show the average cost per kW (USD 0.028) of useful heat gained by the DPGSAHM and DPGSAHI to be relatively higher than some double ‐ pass SAHs reported in the literature. Enhancement


Introduction
Recently, concerted interests have been directed toward renewable energy conversion systems due to their potential in providing a sustainable future. Solar collectors (water/air) are widely applied in various thermal equipment for the optimal and efficient utilization of solar energy. The conventional solar air heaters (SAHs) consist of a solar radiation absorber plate and a parallel plate below through which the inlet air is heated and obtained hot air utilized for various applications, such as greenhouse heating, curing of concrete building components and seasoning of timber [1][2][3]. The conventional SAHs are cheap, simple in design and require little maintenance [4].
Despite the numerous areas of application, the conventional SAHs have less heat storage capability and thus exhibited relatively low thermal efficiency attributed to various controllable (collector materials, absorber plat and depth of bed) and uncontrollable factors (solar intensity, wind speed, humidity and ambient temperature) [5][6][7]. To this end, increasing efforts have been focused on the enhancement of thermal performance and the total general SAH efficiency. Application of extended/corrugated surfaces, the double-pass solar air heater (DPSAH) with packed bed, perforated glazed absorber and using porous material inside the collector are a few examples of these modifications to enhance the heat transfer coefficient inside the collector and to improve the SAH performance [5,6,8,9]. Alta et al. [2] investigated various models of SAHs. They showed that the thermal efficiency of SAH with obstacles attached to the absorber plate is higher than those without obstacles. The use of porous media (iron wools, wire mesh, gravels and limestone) tends to significantly increase the turbulence of air streams and the ratio of surface area to unit volume [10,11]. Paisarn [12] reported that the thermal efficiency of a double-passed SAH with porous media is higher (42-70%) than that without a porous medium (38-59%).
Therefore, the controllable factors (collector materials, absorber plate and depth of bed) play a significant role in the SAH performance. Practically, an accurate mechanism to predict the values of the uncontrollable factors is necessary for a comprehensive and precise estimation of the performance of the SAH with minimal experimental flaws and design. The thermodynamic and experimental analysis of SAH is complicated due to the numerous measurements and heat transfer processes. To solve these issues, many studies have focused on predicting both controllable and uncontrollable factors that contribute toward the thermal performance of SAHs, particularly using various analytical computer codes and optimization algorithms [13,14].
According to [15], the authors applied a techniquie of machine learning regression to estimate thermal efficiency and heat transfer of a helical corrugation with perforated circular disc SAH tubes. Alam and Souayeh [16] conducted a numerical investigation on thermo-hydraulic characteristics, which lead to increasing the heat transfer in SAH.
Panda et al. [17] employed a finite difference method (FDM) and binary-coded genetic algorithm (GA) to optimize the controllable characteristics parameters (thermal conductivity of the absorber plate, incident solar heat flux and overall heat loss coefficient) in a flat-plate solar system to achieve a given temperature field. Using this combined optimization approach, the authors proposed varying locations and suitable materials for the absorber plate satisfying the prescribed temperature field in the collector. Similarly, Das et al. [18] applied an artificial bee colony (ABC) algorithm to optimize five influencing parameters affecting the heat loss factor of a double glazed solar collector in the domestic water heating system. After using the ABC algorithm, the authors reduced the size of the collector by 6-32% and introduced absorber plate emissivity as an important parameter to control the heat loss factor of the double-glazed collector.
Even though the use of some of these analytical computer codes or optimization algorithms (ABC, FDM etc.) has achieved reasonable results, they are slow. The software is relatively expensive, requires a high amount of computing power and often involves complex differential equations. To avoid complex solutions and time-consuming routines, artificial intelligence and Taguchi's analysis-based models have proven to be a cheaper and accurate alternative to tackling these problems.
Unlike the ABC, the Taguchi technique reduces variation in a process through the robust design of experiments. In addition, its data exploration and exploitation behavior are quick, making it helpful in manufacturing industries.
The Taguchi methodology involves using orthogonal arrays (OA) to classify the parameters influencing a process and the levels at which these parameters should be varied and are more efficient than ABCʹs multistep system exploration [19,20]. The Taguchi methodology tests pairs of combinations of data to investigate which factors most influence product efficiency with a minimum amount of experimentation, thus saving resources and time [20]. Kuo et al. [21] applied the Taguchi methodology and grey relational analysis to optimize the flat-plate collector process. In this study, the authors reported 0.7911 as the efficiency coefficient and 3.470 W/°C m 2 as the heat dispersion factor under optimal conditions. By using the Taguchi method, the experimental time and costs were greatly reduced.
In the last decade, the utilization of artificial intelligence methods in scientific and engineering experiments has been gradually increasing. The artificial neural network (ANN) model is relatively fast and, by using trained parameters (inputs, weights and biases), can solve complex problems and estimate target data of various systems, including the thermal systems in engineering applications with high accuracy [19,22]. Omojaro et al. [23] applied ANN to train and test measurable controlled and conditional factors of a single pass SAH. For the tested network, the authors reported an average thermal efficiency of 43.7% and mean square error of 0.0036, and the variation in the efficiency of the neural network was 2.032% when compared with physical experimental data. The obtained results indicate that ANN can be a useful tool for estimating both conditional and unconditional factors of SAHs with reasonable accuracy to design effective, economical and highperformance SAH.
Ghritlahre and Prasad [24] presented the different models of ANN technique to anticipate the thermal performance of unidirectional flow porous bed solar air heater.
Furthermore, Ghritlahre et al. [25] utilized the ANN technique to predict the thermal performance of two various types of SAHs. Additionally, their study illustrated that the air mass flow rate has a drastic effect on the efficiency of SAH among the sensitive input parameters.
The scholars obtained that the thermo-hydraulic performance of a solar air heater with circular perforated absorber plate could be predicted by utilization of ANN [26].
The objective of the present work was to use a Taguchi methodology for the design and selection of the right configuration of double-pass perforated glazed solar air heaters with porous materials (iron wool and wire mesh) as absorbers. The Taguchi method was used to maximize the efficiency of the as-fabricated SAHs by determining the optimum combination of various system parameters. Then, data from uncontrollable input variables were fed into the ANN to predict the efficiency of the optimized SAHs.
According to the literature review, several researchers have worked on SAHs with effective absorber designs to increase their thermal performance. Despite the vast research on solar air heaters, the bulk of these studies only consider a single parameter (such as the roughness or porosity of the absorber plate) while keeping the other factors constant. As a result, the combined influence of various parameters was not taken into account. The most novel aspect of this report is the comprehensive assessment of combined parameters impacting the efficiency of double-pass perforated glazing solar air heaters with different porous materials using two widely used modeling tools. This method is broadly acknowledged as a useful tool for determining the best performance of solar air heaters while remaining cost-effective and environmentally friendly.

Experimental Setup
In this study, the efficiency of two different configurations of double-pass perforated glazed SAH packed with iron wools (DPGSAHI) and mesh layers (DPGSAHM) (Figure 1) were experimentally investigated at Famagusta, North Cyprus (35.13° North latitude, 33.95° East longitude and 1 m elevation above the sea level). The experiments were accomplished on clear sunny days using each SAH configuration at varying air mass flow rates (0.014-0.033 kg/s). The double-pass perforated glazed SAHs (DPGSAH) is 90 cm×90 cm in dimension and consists of perforated plexiglass (PG) as a glazed cover, a normal glass inside the collector, radial fan and mesh layers, or iron wools were utilized as packed beds. The packing materials were painted black to enhance absorptivity, and the SAHs were insulated by 3 cm dark-coloured thick polystyrene to decrease the heat losses significantly.
The dimensions of PG are (88 × 88) cm 2, and the diameter of holes in PG is 3 mm with pitch (distance between holes) of 3 cm. A standard glass of 3 mm thick with dimensions of (85 × 60) cm 2 is inserted inside the DPGSAH at 10 cm from the PG as schematically shown in Figure 1. The DPGSAHM consists of 15 blackened steel wire mesh layers with 1.2 × 1.2 cm 2 in cross-section voids and 0.085 cm in diameter of wire situated parallel between the upper side of normal glass and back of the PG. The distance between each mesh layer is 0.5 cm. The DPGSAHI has 60 blackened iron pieces of wool located between the upper side of the normal glass and the backside of PG.
The packing materials were systematically arranged in layers to provide high porosity, ∅ 95.2-98.3% and thus decreased the pressure drop through the collector significantly as measured by the inclined manometer. The air flow was circulated by the 250 W PV-powered radial fan situated at the backside of the collector, and a 50-cm pipe was installed on the outlet of the radial fan to reduce turbulent flow. The tests were conducted under actual conditions.

Taguchi Methodology
Taguchi methodology is extensively utilized in engineering problems via the application of statistical and engineering concepts to achieve desired product efficiency. The Taguchi design method applies a mathematical tool called orthogonal arrays (OAs) and signals to noise (S/N) ratio to study experimental design techniques and factors variations with product efficiency [19,27,28]. Taguchi suggests a three-phase process flow: system design, parameter design and tolerance design [28]. The parameter design is the key thrust of Taguchiʹs approach; here, the variables are experimentally analyzed to determine how the process reacts to uncontrollable "noise" in the system [27].
In Taguchi's parameter design stage, an experimental design is employed to arrange the control and noise factors in the inner and outer orthogonal arrays, respectively. Thereafter, the S/N ratio for each experimental combination is computed and analyzed to determine the optimal control factor level. Three different computation equations for the S/N ratio have been suggested depending on the characteristics as follows: smaller-is-better, nominal-is-better and larger-is-better [19,27]. The quality characteristics discussed herein are efficiency (thermal and exergy) and outlet air temperature of the SAH. Higher efficiency is desired; hence, the larger-the-better characteristic is chosen and expressed as follows: which y is the response and n is the number of tests in a level combination. The levels of various control factors used in this experiment are presented in Table 1. The Taguchi analysis is performed with Quantum XL 2016 (SigmaZone, USA) software package, and the L8 orthogonal array has been chosen for the present empirical study. In traditional full factorial experiment design, the seven controllable factors each at two levels would require 6 2 = 36 runs to study the different factors. However, Taguchi's robust approach decreased it to 8 runs, offering a better advantage in terms of experimental time and cost. The optimized observed responses were determined by comparing the standard method and analysis of variance (ANOVA).

Artificial Neural Network
Artificial neural network (ANN) is inspired by the way biological nervous systems (brain) process information [29]. The ANN usually consists of an input layer, hidden layer and an output layer. The network is trained by adjusting weight connections between the neurons until maximum epochs are reached [22], and like people, ANNs learn by example.
In the present work, the SAH systems modelled by the ANN had four inputs and three outputs, as presented in Table 2. All network calculations were performed using Neuroph 2.94 software. 89 datasets were fed into the network, which from them, 65 data were used for training, 15 for testing and the remaining 9 were used as the validated data set. To enhance the training process and the network's generalization capabilities, whole input information was normalized to quantities between 0.12 and 0.98 using Equation (2). Here, represents the normalized value, is the actual value of input variables;,and and are the maximum and minimum values of input variables, respectively.
The quasi-Newton method was chosen as the training algorithm because of the lowest normalized squared error of 0.864759, which is lower than other training algorithms shown in Table 2. The plots in Figure 2 show the training and selection errors in each iteration using both Levenberg-Marquardt (LM) and quasi-Newton method (QNM) training algorithms. The blue line represents the training error, and the orange line represents the selection error. For the LM, the initial value of the training error was 1.61517, and the final value after 39 epochs was 0.959036. The initial value of the selection error is 1.90175, and the final value after 39 epochs was 1.11392. While for the QNM, the initial value of the training error was 1.47391, and the final value after 134 epochs was 0.864759.
The initial value of the selection error was 1.98173, and the final value after 134 epochs is 0.914968.  Different network architectures were tested to find the best (Table 2); then, a 3-layered ANN (3:6:3) by logsig activation function at the hidden layer and linear transfer function (purelin) at the output layer was expanded as shown in Figure 3. To characterize prediction efficiency of the optimized ANN architecture, the root mean square error (RMSE) and the coefficient of determinations (R 2 ) were used to compare the actual experimental and predicted values.

Experimental Uncertainty, Energy and Exergy Analysis
Generally, the precision of the experiments is ascertained by uncertainty analysis. In addition, the air temperature, rate of air mass flow and solar intensity were calculated with devices as described in our recent report [4], and the uncertainties are estimated according to [30]: Where R is a certain function and the input variables are x1 x2,.... xn, which total uncertainty is wr, and the uncertainty in the input variables are w1, w2. . .wn [9]. The uncertainties in thermal efficiency, outlet air temperature and exergy efficiency are 4.8%, ±2.6% and ±5.4%, respectively. The measurements demonstrated the fractional uncertainties for Tair, V, r, ΔT and I, to be 0.0016, 0.0013, 0.005, 0.025 and 5.7 × 10 −6 , respectively The efficiency of the SAH, η , was calculated, which is the proportion of obtained energy to incident solar radiance over the collector plate [4]: The exergy analysis is based on the two laws of thermodynamics explained in details elsewhere [31], and the following assumptions were considered during the exergy analyses [32]:  The procedure is conducted in a stable flow operation.  Air is assumed as an ideal gas with an unchanging specific heat.  Effects due to the kinetic and potential energy changes are neglected.
The exergetic efficiency is calculated as follows [31,32]: supplied Exergy Considering the amount of irreversibility in SAH and the negligible pressure drop, the final form of the exergy efficiency can be written as: Here, the Ts is the sun temperature and is assumed to be 5900 K.

Taguchi OA Analysis of Controllable Factors on Thermal Efficiency and Temperature Difference of SAHs
The L8 orthogonal design described by the Taguchi method was used for the optimization of the configuration of the SAH packed with iron wools (DPGSAHI) and mesh layers (DPGSAHM). The selected response of the parameters and the S/N ratios are shown in Table 3. As shown in Table 3, duplicates of eight runs were conducted, and relatively high S/N ratios were observed. A higher S/N ratio generally indicates a better specification, suggesting that more useful information (signal) than unwanted constraints (noise) occurred during the optimization process [19,28].
Notably, the lowest S/N ratio (18.81 dB) was observed in run four and in relatively low thermal efficiency (60.8%), indicating that the combination of the parameters in run four is hindered, hence not obviously maximizing the thermal efficiency of the DPGSAHI. A low standard deviation of ~2.8 and a very high CI of 96.5% were obtained, suggesting that each trial of thermal efficiency tend to be close to the mean value at a significance level of 0.035. Based on the ranking of the S/N ratio, the diameter of holes of plexiglass (D) has the largest effect on the SAH thermal efficiency, and the thickness of packing material (C) has the smallest effect on the overall thermal efficiency of the as-fabricated SAHs. The graphical representation of the interaction effects of the parameters (Table 1) for the thermal efficiency and temperature difference at a constant mass flow rate of 0.024 kg/s and average solar intensity of 810.2 W/m 2 is shown in Figure 4. As noted in Figure  4a, parameter F significantly affects the thermal efficiencies of the as-fabricated SAHs. In all cases, the DPGSAHI exhibited a higher thermal efficiency as compared with the DPG-SAHM. Notably, increasing the thickness of the packing material and the gap between the internal and plexi glasses does not affect the thermal efficiency of the SAHs. On the other hand, the DPGSAHI and DPGSAHM thermal efficiency decreased from 91.5% and 83.2% to 72% and 62%, respectively, when the thickness of the insulation material increased from 2 cm to 4 cm.
At a mean value of wind speed of 4.57 m/s, the temperature difference of the SAHs was obviously influenced by variation in the value of the parameters (Figure 4b). Increasing the values of parameters B, C and F significantly decreased the outlet temperature. As the thickness of the packing material and the gap between the internal and plexi glasses increased, the temperature difference decreased accordingly. The reason for this can be described as follows; as the thickness of the packing material increases, the rate of heat transfer to the flowing air decreases resulting in a decrease in convective heat transfer coefficient between the bed and the glasses and higher thermal losses [31]. Variation due to each parameter influences the thermal efficiency and temperature difference. Hence, analysis of variance (ANOVA) was applied to analyze the results of the orthogonal array experiment and determine the variations due to each parameter (Table  4). In Table 5, the P and F values are important indicators in identifying the effect of each investigated parameter. Here, one numerator degree of freedom was observed for each parameter, and seven denominator degrees of freedom were observed for the total parameter. By looking at the F-distribution table with α = 5%, the SAH input parameter was considered to influence the response (thermal efficiency and temperature difference) if its F-value was higher than F0.05 (1,7) = 5.59. Moreover, if the P-value is less than α = 0.05, the influence of that parameter on the response is significant [33]. It is evident that parameters A, D, E and F have F-values higher than 5.59 and Pvalues ˂0.05, confirming that these parameters have a significant statistical influence on the thermal efficiency and temperature difference of the DPGSAHI and DPGSAHM, at a 95% confidence level [34]. On the other hand, parameters B and C both have P-values ≥ 0.05 and F-values less than 5.59. This indicates that these parameters do not significantly influence the thermal efficiency and temperature difference of the as-fabricated SAHs. According to the ANOVA results and S/N ratio rank, the most significant parameter was found to be the diameter of holes of plexiglass (D) since a higher F-value signifies a more significant effect on the response [22]. The confirmation analysis indicated that the model has a larger Pred R 2 (97.6%) compared with the R 2 (95.6%). Hence the applied model is sufficiently suitable, and thus, the level of selected parameters can produce the best results with good predictability.

Effect of Uncontrollable Factors on the Performance of the As-Fabricated DPGSAHI and DPGSAHM
Here, the effect of uncontrollable factors (solar intensity, inlet and ambient temperatures) was examined on the conventional and Taguchi optimized DPGSAHI and DPG-SAHM. First, the wire mesh and iron wool were located in layers with the distance between them to decrease the pressure drop inside the SAHs. The official resources stated that the average hourly wind speed of Famagusta city was 4.57 m/s. The tests and readings started at 9:00 and continued until 16:00 on each day of the experiment. Figure 5 shows the change of solar flux intensity hour by hour against the local time per day in the current investigation. For reproducibility, duplicate studies were conducted, average results reported, and standard errors (less than 2%) were shown as error bars in the figures.
As expected, the solar radiation enhanced steadily from morning to a maximum value at noon and reduced afterwards until sunset. The measured solar intensities were relatively stable throughout the studies, and for all days of the experiments, the average value of solar intensity is 792.5 W/m 2 while the maximum value is 990.5 W/m 2 . The variation of both inlet (ambient) and outlet temperature during the days of the experiments were examined at different mass flow rates. The ambient temperature was increasing slightly from morning until evening, and the mean value at a mass flow rate of 0.033 kg/s was 26.8 °C, while the maximum value was 28.2 °C. The influence of mass flow rate on the DPGSAHI and DPGSAHM enhancement is demonstrated by the diurnal temperature difference (∆T = Tout-Tin) shown in Figure 6. As expected, ∆T increased with decreasing rate of air mass flow. The maximum amount of ∆T was observed between 10:30 h and 13:00 h of the apparent time, depending on the outdoor ambient conditions. It was also found that the DPGSAHI exhibited a higher magnitude of the ∆T in all mass flow rates investigated. This could be as a result of increased heat transfer area and higher porosity (98.3%) of the 48 iron pieces of wool in the DPG-SAHI. The highest instantaneous and average peak values of ∆T obtained for the DPG-SAHI were 21.2 °C and 16.4 °C , respectively, at a mass flow rate of 0.033 kg/s. For the least flow rate of m = 0.014 kg/s, the maximum value of ∆T was 29.1 °C and the average value of ∆T was 24.3 • C (Figure 6a).
In addition, the highest instantaneous peak and average ∆T achieved from the DPG-SAHM were 18.9 °C and 14.9 °C , correspondingly by a rate of mass flow of 0.033 kg/s. Whilst the peak and average value of ∆T at the rate of mass flow of 0.014 kg/s were 28.7 °C and 23.7 °C , correspondingly ( Figure 6b). As mentioned earlier, the configuration of the as-fabricated SAHs was optimized via Taguchi orthogonal arrays to obtain enhanced outlet air temperature and data obtained were fed into ANN architecture. It is interesting to note that the optimized parameters via Taguchi and ANN drastically enhanced the ∆T values of the DPGSAHI and DPGSAHM. The optimal conditions (Taguchi = B: 7cm, C: 0.07 cm, D: 1mm, E: 0.5 cm and F: 2cm) enhanced the ∆T of DPGSAHM by 40% from 18.9 °C to 26.5 °C at a mass flow rate 0.033 kg/s (Figure 6c). Moreover, combining the optimized ANN conditions (I: 880 W/m 2 , Tair: 26.5 °C and m=0.0033 kg/s) with the Taguchi optimal values generated a hybrid optimization (ANN-Taguchi), which significantly enhanced the ∆T by 75% (from 18.9 to 33 °C ). The enhancement acquired in ∆T is due to the increase in the area of heat transfer and reduction of heat loss. Reducing the thickness of the absorber material and distance between plexiglass and internal glass increased the air flow passages and reduced heat loss by convection, respectively. Specifically, as the air enters through the upper holes of the perforated plexiglass, it absorbs heat from the mesh layers as it propagates inside the collector, and due to the short distance between the plexiglass and the internal glass cover, the preheated air rapidly cools the internal cover, as a result, reduces the heat loss through the cover leading to increased ∆T [35]. A similar trend was observed for DPGSAHI where the hybrid optimization increased the ∆T of DPGSAHI by 27% from 28.9 to 37 °C ( Figure  6d).
Comparatively, the maximum temperature difference ∆T recorded by the optimized DPGSAHI is relatively higher than those reported in the literature, considering the mass flow rates and solar intensity radiation. At the same solar radiation (880 W/m 2 ) and lower mass flow rate (0.02 kg/s), Esen [36] recorded a maximum temperature of 23 °C from a double-flow flat plate SAH with obstacles. Ramadan et al. [10] reported that the maximum ∆T of double-pass SAH at the solar intensity of 850 W/m 2 was 35 °C by the m = 0.0105 kg/s. Furthermore, El-khawajah et al. [11] obtained 25.5 °C as the peak value of ∆T of two-fins SAH containing wire mesh as an absorber plate with a mass flow rate of m = 0.042 kg/s.
The thermal efficiencies against hours of the day at various mass flow rates are illustrated in Figure 7. The thermal efficiencies enhance with an increment in the mass flow rate depending on the ambient conditions of the day. These observations are similar to our previous report [4] and those of Mahmood et al. [7] and Kabeel et al. [37]. The maximum efficiency obtained from the DPGSAHM and DPGSAHI were 81.4%, and 91.3% at 13:00, respectively, with an air mass flow rate of 0.033 kg/s. Depending on the inlet air temperatures and solar intensity, the thermal efficiency enhanced from morning to evening continuously. As the behaviour of input air temperature, in most cases, the thermal efficiency was observed to be enhanced by the standard local time of the day from daybreak to sunset, this attributed to the heat accumulated inside the porous media (wire mesh and iron wool) energy in the matrix bed. However, an inconsiderable reduction in the thermal efficiency was observed in the afternoon for high mass flow rates. Particularly, the DPGSAHI at a mass flow rate of 0.033 kg/s decreased from 91.3% to ~90% at 15:00. After 12:00, the solar intensity tends to diminish; meanwhile, the air mass flow rate carries the same amount of energy continuously, which is the energy absorbed from the porous media and the energy received from the sun [7]. In all cases investigated in the current study (Figure 7a-b), the thermal efficiency in the iron wool-based double-pass SAH (DPG-SAHI) was higher than that of a wire mesh layer-based double-pass SAH (DPGSAHM). The comparison of the average efficiencies of obtained data for double-pass SAHs with the present research indicates there is an enhancement in the proposed SAHs ( Figure  8). Notably, the average thermal efficiencies of DPGSAHI, DPGSAHM and hybrid optimized DPGSAHI (~82-97%) at relatively lower mass flow rates (0.014-0.033 kg/s) were found to be comparatively higher than the double-pass with porous media (steel wool) reported by Sopian et al. [3] and steel wire mesh based double-pass SAH reported by Omojaro and Aldabbagh [5]. Generally, under optimized conditions, increasing the number of iron wool (from 32 to 48) and wire mesh layers (10 to 15) increases the contact surface area in the SAH and significantly enhances the efficiency of the as-fabricated SAHs. Moreover, the low spacing between the plexiglass and the internal glass cover increases the average air flow velocity and subsequently increases the heat transfer coefficient. The irreversibility and exergy efficiency versus mass flow rate for DPGSAHI, DPG-SAHM and hybrid optimized SAHs are shown in Figure 9. Obviously, the exergy efficiencies show a minimum in non-optimized DPGSAHI and DPGSAHM (Figure 9a-b), 1.21% for DPGSAHI experimental and 1.45% for DPGSAHM at 0.033 kg/s whereas, ~3% and 2.4% exergy efficiencies were obtained for the hybrid optimized DPGSAHM and DPG-SAHI, respectively. Notably, the exergy efficiency became greater at a ṁ (7.1% for DPG-SAHI at 0.014 kg/s) and mitigated with increments in rate mass flow, compatible by the study of Velmurugan and Kalaivanan [32] and Chouksey and Sharma [31].
As indicated in Figure 6, the ∆T between the absorber plates and the current of air was greater at a lower mass flow rate of 0.014 kg/s. Therefore, the heat transfer to the flowing air was at the highest value, subsequently resulting in maximum exergy conversion and exergy efficiency (9-8.5% for hybrid optimized at 0.014 kg/s). At ṁ = 0.014 kg/s, the irreversibility was 510 W for DPGSAHI and 535 W for DPGSAHM demonstrating a greater loss in the DPGSAHM system. In both cases, the entropy generation rate was observed to increase exponentially with an increase in mass flow rate. Hence the irreversibility was less at a lower level of mass flow rate, possibly due to the highest value of existing energy transfer [38].

Cost Analysis for the Heat Gained
Here, the total cost of the hybrid optimized DPGSAHI and DPGSAHM at a fixed mass flow rate and the quantity of useful heat gained was estimated. The fixed cost (Fc), variable cost (Vc) and straight-line depreciation (SL) were considered. ṁ = 0.033 kg/s. Table 6 shows the fixed cost and the following points were considered during the cost-benefit analysis: a) One year of operation was assumed to equal 350 days. b) Ten years' straight-line depreciation method was considered at 2%. c) Miscellaneous charges, including labour and maintenance costs were excluded. d) The number of working hours is 8 h/day. e) The expected life time (ny) is assumed 15 years.
The average heat produced per year (Qav) was calculated as follows: .
. ℎ The variable cost was Vc = 0.13 × (Fc − PV system cost), the total cost TC = Fc + Vc + SL and the total cost per year was calculated using Cy = Tc/ny.  As presented in Table 6, the Qav of DPGSAHI was calculated as 1743.5 kW/year, then the cost per one kW is 0.027 $.

For Hybrid Optimized DPGSAHM
Similarly, considering = 0.033 kg/s, the Fc = 403 $ was obtained, then TC = 403 + (0.13 × 123 × 15) + 8.06 = 650.91 $. Then, Cy is 43.39 $/year. The Qav of DPGSAHM was calculated as 1472.9 kW/year, then the cost per one kW is 0.029 $. It is worth mentioning that the maximum daily energy efficiency (82-97%) delivered by the hybrid optimized DPGSAHI and DPGSAHM at mass flow rate of 0.033 kg/s and the average cost per kW (0.028 $) of useful heat gained was comparatively higher than the baffled glazed-bladed entrance air heater (ηavd = 83.8% and 0.00733 $ at mass flow rate of 0.04 kg/s) reported by Kabeel et al. [37].

Conclusions
Double-pass perforated glazed solar air heaters (SAHs) packed with wire mesh layers (DPGSAHM), and iron wools (DPGSAHI) were experimentally investigated. The effects of air mass flow rate on the thermal efficiency, exergy efficiency and outlet temperature were surveyed. The as-fabricated SAHs exhibited a decrease in the thermal efficiency as the mass flow rate was decreased from 0.033 kg/s to 0.014 kg/s. It was found that for the same mass flow rate (0.024 kg/s), the DPGSAHI has higher efficiency (89.3%) compared to the DPGSAHM (~80%). Furthermore, the maximum temperature difference (∆T) for the DPGSAHI (29.1 • C) slightly exceeded the DPGSAHM (28.7 • C) for the identical mass flow rate (0.014 kg/s). As expected, the highest value of exergy efficiency (ηex) for various types of solar air heater was gained at the minimum rate of air mass flow. A substantial enhancement in the temperature difference (75%), thermal efficiency (1.25%) and exergy efficiency (2.4%) was achieved when the DPGSAHM and DPGSAHI were optimized by the hybrid procedure (Taguchi-artificial neural network). Notably, the average thermal efficiencies and the average cost per kW gained (0.028 $) herein are found to be comparatively higher than the double-pass SAHs with porous media (steel wool and wire mesh layers) reported in the literature.
Results herein indicate that the variation in efficiency of the ANN and Taguchi method was 1.95% and 2.14%, respectively. Importantly, under optimal conditions, the ANN and Taguchi method have an increment of 7.98-6.45% and 6.89-5.35% in thermal efficiency of DPGSAHI and DPGSAHM, respectively, when compared with physical experimental results.

Data Availability Statement:
The data presented in this study are available with the permission of authors.