Electrical and Thermal Performances of a Single-Pass Double-Flow Photovoltaic-Thermal Collector Coupled with Nonuniform Cross-Section Rib

. The air-based photovoltaic-thermal collector (PVTC) is a system that can generate electricity and heated air simultaneously from solar energy. This study investigates the electrical and thermal performances of an air-based single-pass double-ﬂ ow photovoltaic-thermal collector (SPDFPVTC) coupled with a nonuniform cross-section rib (NUCSR) under various operating conditions. The rib is installed at the rear of the photovoltaic panel to enhance the heat transfer performance between the photovoltaic panel and the ﬂ owing air. Based on the energy balance equations, a mathematical model of the proposed SPDFPVTC is established and validated by experimental results. The solar intensity, air mass ﬂ ow rate, and wind speed are selected as operating conditions. The e ﬀ ects of these operating conditions on the electrical and thermal performance of the SPDFPVTC have been discussed. In addition, this study evaluates the daily performance of SPDFPVTC with and without NUCSR. The average electrical, thermal, and overall e ﬃ ciency were 17.59%, 43.96%, and 61.55%, respectively, for SPDFPVTC with NUCSR and 16.97%, 38.87%, and 55.83%, respectively, for SPDFPVTC without NUCSR. Consequently, installing NUCSR could enhance the daily electrical, thermal, and overall energy output of SPDFPVTC by 4.33%, 13.23%, and 10.63%, respectively.


Introduction
Photovoltaic (PV) systems are considered one of the most promising systems among renewable energy technologies with the potential to replace fossil fuels. This system converts incoming sunlight directly into useful electricity without any environmental pollution. The global penetration rate of PV systems has increased steadily as a result of its consistent increase in efficiency and decrease in prices. However, in PV systems, only a portion of incoming sunlight is converted into electrical energy, and the remainder becomes waste heat. This heat raises the PV cell's temperature, decreasing its electrical performance [1].
To address this issue, Wolf [2] proposed a photovoltaicthermal collector (PVTC) that combines a PV system and solar thermal system into a single unit. This system can recover waste heat from the PV system by using heat trans-fer mediums such as air or water, decreasing its cell temperature and preventing the reduction in electrical efficiency. Moreover, heat transfer media heated by the PVTC can be reused to heat spaces, supply hot water, and dry grains. The air-based PVTC employs air as a heat transfer medium, and owing to its simple design, this type of PVTC offers several benefits, including ease of fabrication, construction, and low operating and maintenance costs. However, this PVTC has a major drawback in terms of thermal efficiency owing to the low heat conductivity of air. Hence, there have been several studies that focus on enhancing the thermal performance of air-based PVTCs.
A general method to improve the thermal efficiency of an air-based PVTC is the addition of heat transfer enhancement devices to its air channel. Mojumder et al. [3] examined the thermal efficiency of a PVTC consisting of fins and a thin flat metallic sheet (TFMS). They reported that the PVTC with fins and TFMS performed better than the PVTC without fins, and the maximum thermal and electrical efficiencies were 56.19% and 13.75%, respectively. A PV panel with porous fins was experimentally studied by Selimefendigil et al. [4], and they found that adding porous fins could improve the electrical efficiency of PV panels. Fudholi et al. [5] estimated the energy and exergy of a PVTC using a del-groove heat exchanger. They developed a theoretical model and evaluated energy and exergy performances under various solar intensities and air mass flow rates (AMFRs). The energy and exergy performances of the PVTC investigated in their research ranged from 31.2 to 94.2% and 12.44 to 13.26%, respectively. Barone et al. [6] proposed a PVTC with hexagonal air ducts and evaluated its performance. The thermal and electrical efficiencies of the PVTC ranged from 25.8 to 31.5% and from 14.8 to 16.4%, respectively. Özakin and Kaya [7,8] analyzed the effect of cylindrical fins introduced in an air channel of a PVTC on the energy and exergy performances according to the air velocity, fin arrangement, and material. The installation of a cylindrical fin was found to improve the PVTC's electrical energy, thermal energy, and exergy performances by 48%, 109%, and 50%, respectively, and the material of the fin had a dominant effect. Tahmasbi et al. [9] employed a porous metal form for the PVTC and showed that the porous metal form improved the electrical efficiency by 3 to 4% and the thermal efficiency by 10 to 40%. Çiftçi et al. [10] estimated the thermal performance of a finned vertical PVTC used in a solar dryer and reported that the thermal efficiency ranged from 50.25 to 58.16%. Ewe et al. [11] combined a PVTC with a dual-functional jet plate reflector. They investigated its performance with various operating parameters, indicating that the optimum thermal and electrical efficiencies were 57.3% and 10.36%, respectively. Cetina-Quiñones et al. [12] examined PVTC coupled with lineal, zig-zag, and wavy fins and found that the wavy fin provided better performance than the other types of fins. Their study presented that the PVTC with a wavy fin had electrical and thermal performance ranging from 13.16 to 13.43% and 23.34 to 27.92%, respectively.
Another common method is to change PVTC's configuration. Hegazy [13] numerically analyzed the performance of four different PVTC configurations. This study investigated glazed single-pass single-flow PVTC (GSPSFPVTC) with air flowing above the PV panel, GSPSFPVTC with air flowing under the PV panel, single-pass double-flow PVTC (SPDFPVTC) with air flowing above and under the PV panel in the same direction, and double-pass single-flow PVTC (DPSFPVTC) with air flowing above the PV panel, returning, and flowing under the PV panel. Based on the results obtained, the SPDFPVTC provided the highest overall energy efficiency of about 56.4% compared to the other types of PVTCs. Raman and Tiwari [14] analyzed the performance of unglazed single-pass single-flow PVTC (UGSPSFPVTC) and DPSFPVTC configurations and showed that DPSFPVTC performed better in terms of thermal, electrical, and exergy efficiencies. According to their study, the thermal, electrical, and exergy efficiencies of the investigated DPSFPVTC were higher than those of the UGSPSFPVTC by 40 to 45%, 10 to 12%, and 13 to 17%, respectively. Amori and Abd-AlRaheem [15] experimentally compared GSPSFPVTC, SPDFPVTC, and DPSFPVTC configurations and indicated that the SPDFPVTC had a higher overall efficiency and a lower blowing power than the other PVTCs. Slimani et al. [16] evaluated the daily and annual energy outputs of UGSPSFPVTC, GSPSFPVTC, and DPSFPVTC configurations and reported that the highest energy output was found for the DPSFPVTC, followed by GSPSFPVTC and UGSPSFPVTC. Their study reported the electrical and thermal efficiencies of a DPSFPVTC as 10.65% and 44.41%, respectively. Fan et al. [17] established a dynamic simulation model combining a PVTC with a solar air heater and fins to increase outlet air temperature. This study reported that the PVTC, which was proposed in their study, provided the highest primary energy efficiency when the PV cells occupied 50% of its total surface area. Huang and Markides [18] fabricated a PVTC using a semitransparent PV cell and solar thermal absorber to produce low-and high-temperature fluids simultaneously in a single system. Their research proved that the proposed PVTC successfully generated low-and high-temperature fluids, and the electrical efficiency and thermal efficiencies for low-and high-temperature heats were 13.8%, 22.5%, and 21.5%, respectively. Al-Damook et al. [19] optimized SPDFPVTC using CFD analysis and found that the electrical and thermal efficiencies were 50.1% and 10.5%, respectively, with optimized parameters. Gupta et al. [20] developed a solar dryer using the PVTC having a wavy-shaped absorber plate. This study presented the daily performance of the proposed PVTC and reported that the electrical and thermal efficiencies varied from 12.28 to 14.27% and 23.89% to 62.37%, respectively. Shahsavar and Aıcrı [21] evaluated a sensible rotary heat exchanger coupled with PVTC with and without glass. This research showed that the PVTC with glass generated higher thermal energy than PVTC without glass. A summary of the literature review on air-based PVTCs is presented in Table 1.
From the above literature, however, it was found that very few studies addressed the thermal and electrical performances of SPDFPVTC, despite its superior performance over other types [13,15,19]. In particular, there is very limited study regarding the influence of operating conditions on the performance of SPDFPVTC. In addition, most previous researches have focused primarily on the use of fins, which extend the heat transfer surface, as a heat transfer enhancement device. A heat transfer enhancement device generally increases the thermal performance of the PVTC in two ways: extending the heat transfer surface or improving the heat transfer coefficient. An increase in the heat transfer coefficient can be achieved by installing turbulators, such as ribs, baffles, and protrusions, at the heated wall, which breaks the viscous sublayer and generates additional turbulence near the wall [22,23]. A further advantage of attaching the turbulators is that this method has a lower pressure drop than that caused by extending the heat transfer surface [24]. This technique has been more widely used in solar air heaters than PVTC. Many researchers have investigated the heat transfer enhancement in solar air heaters using ribs with various shapes, including equilateral triangular rib [25], square rib [26], circular rib [27], reverse L-shaped rib [28], 2 International Journal of Energy Research  [29], and quarter-circular rib [30]. The ribs in these studies were of different shapes, but all of the investigated ribs had uniform cross-sections. Singh et al. [31] proposed a nonuniform cross-section rib and compared its heat transfer enhancements and friction factors with those of the rib having a uniform cross-section. Their study found that the nonuniform cross-section rib has better heat transfer and lower friction factor than the uniform crosssection rib by reducing eddy formation at the downstream of the rib. Other types of tabulators, such as protrusion [32], multiple broken ribs [33], and multistaggered ribs [34], also have been extensively studied, and more details can be found in relevant review papers [23,35]. These tabulators can also enhance the PVTC's performance because the solar air heater and air-based PVTC have a similar structure of two parallel plates with constant heat flux on one side and insulated on the other side. However, to the best of the authors' knowledge, no study has examined the SPDFPVTC coupled with turbulators such as ribs. Thus, it will be interesting to prove how the operating conditions and installation of the rib affect the electrical and thermal behaviors of SPDFPVTC.
This study numerically investigated the performance of SPDFPVTC coupled with a nonuniform cross-section rib (NUCSR). Figure 1 presents a schematic of SPDFPVTC investigated in the current research. As shown in the figure, the PVTC has two air channels above and below the PV panel. In addition, the rib was installed on the rear of the PV panel to increase the heat transfer coefficient. This study employed a NUCSR that has been reported to perform better than a uniform cross-section rib and has a simple structure [31]. To develop the mathematical model for    International Journal of Energy Research SPDFPVTC with NUCSR, the correlation for the Nusselt number between the ribbed surface and air was derived using computational fluid dynamics (CFD) simulations. The developed model was solved by the matrix inversion technique and validated using the experimental values obtained from previous research. Using the developed model, the effect of operating conditions on the electrical and thermal behaviors of the proposed SPDFPVTC was analyzed. Furthermore, the daily performance of the SPDFPVTC with and without NUCSR was compared to evaluate how much more energy could be produced with the addition of the NUCSR.

System Description
The SPDFPVTC with NUCSR was experimentally tested in a previous study by the authors [36]. Figure 2 shows the composition of SPDFPVTC used in the previous experiment and the present numerical study. It is composed of a top glass, PV glass, PV cell, tedlar, rib, and insulator. This PVTC has upper and lower air channels above and below the PV panel, respectively, and the air flows in these two air channels simultaneously. Figure 3 illustrates the rib located at the rear of the PV panel. This rib was composed of several triangles and therefore had a nonuniform cross-section. The detailed dimensions of a PVTC and rib used in both the previous experiment and the present numerical study are listed in Table 2.

CFD Simulation
To develop the mathematical model for the SPDFPVTC with NUCSR, the AMFR in the upper and lower air channels should be determined. Furthermore, the heat transfer coefficient from the ribbed surface to the flowing air should be   known. In this study, a CFD simulation was conducted using ANSYS Fluent R17.2 to obtain the above values. Figure 4 shows the three-dimensional (3D) model used for the simulation. As the airflow characteristics in the PVTC are symmetrical about its center, half of the PVTC was designed in a 3D model, and the symmetry boundary condition was applied. The dimensions of the designed 3D model are identical to those of the PVTC used in the experimental study.
As a turbulence model, renormalization-group (RNG) enhanced wall treatment, which has been widely used in related studies, was chosen [10,31,37]. An AMFR value ranging from 0.0198 to 0.14 kg/s was set as the inlet boundary condition. For the outlet boundary condition, constant pressure (101,325 Pa) was considered. A uniform heat flux of 800 W/m 2 was appointed to the ribbed surface, the other walls were assumed to be adiabatic, and a no-slip condition was considered for all solid surfaces. A coupled algorithm is used to link pressure and velocity, and a second-order upwind scheme is employed to discretize the continuity, momentum, and energy equations. For the energy equation, a convergence criterion of 10 -6 was used, and for the other equations, a convergence criterion of 10 -4 was used. ANSYS ICEM CFD was utilized to generate nonuniform mesh, and relatively fine tetrahedron mesh was created near the ribs to resolve the boundary layer while the hexahedron mesh was applied for the upper air channel. For the gridindependent test, cell numbers varied from 793,339 to 3,410,534 by changing the minimum cell size from 5 to 0.5 mm with a growth ratio of 1.2. Table 3 presents the variation in the Nusselt number with different cell numbers. The results indicated that after 1,835,158, further increases in cell numbers resulted in a variation of less than 1% in the Nusselt number. In this study, a mesh cell number of 2,867,995 was taken for the CFD simulation. The orthogonal quality of a cell with the selected cell number averaged 0.869 and had a minimum value of 0.195. Figure 5 shows the meshed domain of the SPDFPVTC with NUCSR for a selected number of cells.
From the CFD simulation, the AMFRs for the upper and lower air channels were obtained as a function of the total AMFR and are, respectively, given as follows: In addition, the simple correlation for the Nusselt number between the ribbed surface and air was derived as follows: Nu rib = 0:0385 Re 0:7902 : ð3Þ All of the correlations were derived using a power regression model. Figure 6 shows simulation results along with regression lines. The figure apparently shows that the obtained correlations can predict simulation results well, with the R 2 values of 0.9969 for the Nusselt number and 1 for the AMFRs for upper and lower air channels.
The purpose of CFD analysis is to derive correlations, and this study is aimed at evaluating the performance of

Mathematical Modeling and Methods
The current study developed a mathematical model for SPDFPVTC with NUCSR based on the energy balance equations. To simplify the mathematical model, several assumptions have been considered [17,38].
(i) A steady-state condition is considered for the PVTCs (ii) Heat loss at the side surface of the PVTCs is ignored due to its sufficient insulation

Energy Balance Equation.
The SPDFPVTC with NUCSR consists of a top glass, upper air channel, PV glass, PV cell, tedlar, lower air channel, and insulator. From the thermal resistance network presented in Figure 8, the following equations can be derived for each component of PVTC.
For the top surface of the top glass, For the top glass, For the air flowing in an upper air channel, Equation (6) The temperature of the outlet air of an upper air channel can be expressed by using the boundary conditions, T fu ðx = LÞ = T fu,out , as follows:  The average temperature of the air in an upper air channel can be determined by integrating Equation (7) over the distance (x) from 0 to L and is given as follows: where For the PV glass, For the PV cell, In Equation (14), the electrical output of the PVTC was calculated using Equation (15) [39,40].
where η el is the empirical equation for the electrical efficiency of a PV cell. It is given as follows [39,41]: where η stc , δ, and T cell are the standard electrical efficiency of the PV panel, temperature coefficient, and cell temperature, respectively. For the tedlar, For the air flowing in a lower air channel, Similar to Equations (8) and (9), the outlet and average air temperature in a lower air channel can be, respectively, expressed as follows: T fl,avg = X 4 T ted + where For the insulator, The radiative heat transfer coefficient between the top surface of the top glass and the sky is calculated by using Equation (26) [17,44].
T sky = 0:0552T am 1:5 : The heat transfer coefficient for the conductive heat transfer between the top surface and the middle of the top glass is obtained from the following equation [38]:  The heat transfer coefficient between the top glass and flowing air in an upper air channel was determined from Equation (29) [38].
In Equation (29), the Nusselt number for laminar and turbulence flows in an air channel with a smooth surface was obtained using the following empirical correlations [17,46]: To calculate the radiative heat transfer coefficient from plate i to j, Equation (32) was used [16,17].
For the calculation of the heat transfer coefficient between the flowing air in an upper air channel and the PV glass, the following equation was used [38]: The heat transfer coefficient between two adjacent solids i and j was calculated from Equation (34) [38].    The heat transfer coefficient between the tedlar and flowing air in a lower air channel was obtained using Equation (35) [38].
In Equation (35), the Nusselt number for the ribbed surface was obtained from Equation (3).
The heat transfer coefficient between the flowing air in a lower air channel and the insulator was obtained from Equation (36) [38].
The heat transfer coefficient for the combined heat transfer between the insulator and the ambient was obtained from the following: The U v,ins−am is determined from Equation (25).
The following empirical correlations were used to obtain the properties of air [45,47]:  where To find the temperature of each component, the initial temperatures were first assumed and used to calculate air properties and heat transfer coefficients. After that, the new temperatures were obtained by solving ½T = ½A − 1½B with the calculated heat transfer coefficients. If the difference between the new and initial temperatures exceeded 0.1%, the initial temperatures were replaced by the new temperatures, and the previous process was repeated until the difference was below 0.1%.
Using the obtained temperature, the thermal energy output ( _ q f ) of SPDFPVTC was calculated as follows [13]: The thermal efficiency was obtained from Equation (62) [15,48].
The electrical output and efficiency were obtained from Equations (15) and (16) using the calculated cell temperature. The overall efficiency of the SPDFPVTC was obtained by combining the electrical and thermal efficiencies as follows [9,15,49]: The MATLAB R2022a was used to develop and solve the mathematical model for SPDFPVTC with NUCSR. Figure 9 illustrates the flow chart for the solution procedure.

Validation
In this section, a comparison of experimental values with simulated results was performed to validate the developed model. As previously mentioned, the tested SPDFPVTC with NUCSR in the previous study was composed of a top glass, PV panel, ribs, air channel, and insulator. The PV panel was a commercially available product (Model: Q.PEAK BFR-G4.4), and the actual view of the fabricated PVTC is presented in Figure 10. The design parameters of the SPDFPVTC with NUCSR are listed in Table 4, and Table 5 summarizes the material properties employed in the validation setup.
To obtain the numerical results, the solar intensity and ambient temperature were taken from the previous research as input values of the developed model. At the same time, the wind speed was fixed at 0 m/s. The electrical and thermal outputs predicted by the mathematical model with corresponding experimental values are shown in Figure 11. As seen in the figure, the predicted values by the mathematical model are in close agreement with the corresponding experimental data, with mean absolute percentage errors (MAPEs) of 5.34% and 5.12% for electrical and thermal outputs, respectively.

Methodology
In this study, the performance of the SPDFPVTC with NUCSR was investigated under various operating conditions. The solar intensity, AMFR, and wind speed were chosen as operating parameters. The ambient temperature was set to 10°C. Table 6 summarizes the ranges of the operating conditions selected in the present work. The design parameters and material properties employed in the validation setup were used for the simulation.   14 International Journal of Energy Research In addition, this research estimated the daily performance of the SPDFPVTC with NUCSR and compared it to the SPDFPVTC without an NUCSR (smooth channel). The daily performance of the SPDFPVTC was assessed on winter days (3 rd , Jan.), and as weather data, the typical meteorological year data for Seoul, Korea, were considered.

Results and Discussion
7.1. Effect of Operating Conditions. Figure 12 presents the effect of solar intensity on different parameters of the SPDFPVTC with NUCSR for various AMFR values. The increment in solar intensity increases the cell temperature, as shown in Figure 12(a). However, the electrical efficiency declined with an increment in solar intensity because the electrical efficiency is inversely proportional to the cell temperature. A decrease of about 0.59% and 0.31% in electrical efficiency was observed for every 100 W/m 2 at AMFR values of 0.02 kg/s and 0.14 kg/s, respectively. Figure 12(c) shows the variation in the outlet air temperature of the SPDFPVTC. The outlet air temperature rises with increasing solar intensity because, for a given AMFR and wind speed, the increase in incident solar energy increases heat transfer to the air. In addition, the higher outlet air temperature was observed at low AMFR for a given solar intensity. Similar to the outlet air temperature, a higher solar intensity results in a higher thermal efficiency. For a given solar intensity, a higher AMFR results in a higher thermal efficiency. This is because an increment in AMFR increases the heat transfer from the PV panel to the flowing air. The average 15 International Journal of Energy Research increase in thermal efficiency for every 100 W/m 2 of solar intensity was 0.48% and 1.1% at AMFR values of 0.02 and 0.14 kg/s, respectively. Figure 13 presents the overall efficiency of the SPDFPVTC with various solar intensities and AMFR. At an AMFR of less than 0.06 kg/s, the overall efficiency first increases and then decreases with increasing solar intensity as the reduction in electrical efficiency outweighs the increase in thermal efficiency. However, when the AMFR exceeded 0.6 kg/s, the overall efficiency steadily rises with increasing solar intensity because the improvement in thermal efficiency was larger than the reduction in electrical efficiency.
The impact of AMFR on the electrical and thermal behaviors of the SPDFPVTC with NUCSR for various wind speed values is presented in Figure 14.
As the AMFR increases, the cell temperature is reduced, resulting in a higher electrical efficiency, as can be seen in Figures 14(a) and 14(b). For a given AMFR, the higher wind speed results in a higher electrical efficiency. This is because increased wind speeds boost the heat loss between the PVTC and its surroundings, resulting in a lower cell temperature. The most significant increment in electrical efficiency was observed when the AMFR was changed from 0.02 to 0.04 kg/s. The corresponding increase in electrical efficiency was approximately 1.02% at a wind speed of 0 m/s and 0.7% at a wind speed of 20 m/s. In all ranges of AMFR, the average increase of about 0.25% and 0.19% in electrical effi-ciency was observed for every 0.01 kg/s of AMFR at wind speeds of 0 m/s and 20 m/s, respectively.
The outlet air temperature is reduced with increasing AMFR as presented in Figure 14(c). For a given AMFR, it decreases with an increment in wind speed because of the increment in heat loss of the PVTC. The thermal efficiency increased with an increase in AMFR, as mentioned previously. For a given AMFR, the thermal efficiency declined with an increment in wind velocity owing to the increment in heat loss of the PVTC. The average increase in thermal efficiency was 1.58% and 1.82% for every 0.01 kg/s of AMFR at wind speeds of 0 m/s and 20 m/s, respectively.
As shown in Figure 15, the overall energy efficiency was improved with increasing AMFR because both the electrical and thermal efficiencies increased. Figure 16 illustrates the impact of wind speed for various solar intensity values. The increase in wind speed leads to a higher electrical efficiency owing to the decrement in PV cell's temperature. However, the effect of wind speed was insignificant compared with the impact of solar intensity and AMFR. The electrical efficiency was raised by only about 0.04% at a 400 W/m 2 solar intensity and 0.31% at a 1000 W/ m 2 solar intensity when the wind speed increased from 0 to 20 m/s. On the contrary, higher wind speed results in lower outlet air temperature and thermal efficiency. The reduction in thermal efficiency owing to the increment in wind speed

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International Journal of Energy Research was more significant than the increment in electrical efficiency. The thermal efficiency decreased by 2.87% at a 400 W/m 2 solar intensity and 7.67% at a 1000 W/m 2 solar intensity as the wind speed increased from 0 to 20 m/s. Consequently, increasing the wind speed reduces the overall efficiency as seen in Figure 17. In Hegazy's previous study [13], SPDFPVTC exhibited electrical and thermal efficiencies of about 6.85 to 8.1% and 29 to 55%, respectively. A recent study by Al-Damook et al. [19] reported that the electrical and thermal efficiencies of the optimized SPDFPVTC were 10.5% and 50.1%, respectively. The SPDFPVTC investigated in this study achieved thermal efficiency ranging from 26.78 to 54.86% and relatively higher electrical efficiency of 13.71 to 19.16% due to the use of high-efficiency PV panel. In addition, among the investigated conditions, the highest overall efficiency was found to be 71.54% when the solar intensity, AMFR, and wind speed were 1000 W/m 2 , 0.14 kg/s, and 0 m/s, 25 Figure 17: Effect of wind speed on overall efficiency for various solar intensity values.   Figure 18. Figure 19 illustrates the cell and outlet air temperature. The cell and outlet air temperatures increase in response to the increasing solar intensity and then decrease with a decrement in solar intensity. The maximum cell and outlet air temperatures are, respectively, 55.93°C and 16.84°C for SPDFPVTC with NUCSR and 67.52°C and 15.84°C for SPDFPVTC without NUCSR. Thus, it was confirmed that adding NUCSR reduces the cell temperature and increases outlet air temperature. Figure 20 illustrates the electrical, thermal, and overall efficiency of the SPDFPVTC with and without NUCSR. The electrical efficiency decreases with increasing solar intensity and then increases again with decreasing solar intensity. With respect to the thermal efficiency, it rises with an increment in solar intensity until 11:30. Then, after 11:30, the thermal efficiency exhibited little change in spite of the 19 International Journal of Energy Research increment in solar intensity owing to the increment in wind speed, and then decreased after 15:00 with decreasing solar intensity and increasing wind speed. The average electrical, thermal, and overall efficiency are, respectively, 17.59%, 43.96%, and 61.55% for SPDFPVTC with NUCSR and 16.97%, 38.87%, and 55.83% for SPDFPVTC without NUCSR during the operation period. Figure 21 presents the daily energy output of SPDFPVTC with and without an NUCSR. The electrical, thermal, and overall energy outputs are, respectively, 0.916 kWh/m 2 , 2.407 kWh/m 2 , and 3.323 kWh/m 2 for the SPDFPVTC with NUCSR and 0.878 kWh/m 2 , 2.126 kWh/ m 2 , and 3.004 kWh/m 2 for the SPDFPVTC without NUCSR.
The addition of NUCSR improved the daily electrical, thermal, and overall energy output of the SPDFPVTC by 4.33%, 13.23%, and 10.63%, respectively. The results clearly show that more useful energy can be recovered from the incident solar energy by incorporating the NUCSR into SPDFPVTC.

Conclusions
In the current research, a mathematical model of a noveltype PVTC that uses a single-pass double-flow air channel and NUCSR was developed and validated with experimental values. The effects of various operating conditions on the electrical and thermal behaviors of the SPDFPVTC were discussed. Moreover, the daily performance of SPDFPVTC with NUCSR was evaluated and compared with SPDFPVTC without NUCSR to confirm how much more solar energy can be retrieved by the NUCSR. From the results, the following conclusions were made: (i) An increase in solar intensity had an unfavorable impact on SPDFPVTC's electrical efficiency, but there was a beneficial effect on its thermal efficiency. The overall efficiency increases and then decreases with increasing solar intensity when the AMFR was less than 0.06 kg/s, while it steadily increases as the solar intensity increases when AMFR was more than 0.08 kg/s (ii) A higher AMFR resulted in higher electrical and thermal efficiencies. Therefore, the overall efficiency improved with an increment in AMFR (iii) An increase in wind speed led to increased electrical efficiency and decreased thermal efficiency. Because the decrease in thermal efficiency outweighs the rise in electrical efficiency, the overall efficiency decreases with increasing wind speed (iv) In the investigated conditions, the SPDFPVTC with NUCSR had the highest overall efficiency of 71.54% when the solar intensity, AMFR, and wind speed were 1000 W/m 2 , 0.14 kg/s, and 0 m/s, respectively (v) On a winter day in Seoul, Korea, the average electrical, thermal, and overall efficiency were, respectively, 17.59%, 43.96%, and 61.55% for SPDFPVTC with NUCSR and 16.97%, 38.87%, and 55.83% for SPDFPVTC without NUCSR (vi) The daily energy outputs of SPDFPVTC with and without NUCSR were compared under the same weather conditions. Based on the results, it was confirmed that the installation of NUCSR could improve the daily electrical, thermal, and overall energy output of SPDFPVTC by 4.33%, 13.23%, and 10.63%, respectively In the current research, the performance of the SPDFPVTC has been evaluated using fixed geometric parameters, including the height of the upper and lower air channels, the length of the PVTC, and the height and pitch of the NUCSR. Therefore, future studies should focus on evaluating the impact of these parameters on the SPDFPVTC's performance and optimizing them accordingly. Additionally, the primary purpose of enhancing the thermal efficiency of the PVTC is to reduce energy consumption in various