1 Introduction

The growth trajectory of any developing country cannot be projected without studying the rise in its electricity requirements. India’s story of development is no more different, considering the exponential surge in power requirement over the last decade. However, the national grid infrastructure has struggled to keep pace with power generation. India is working on all fronts to reduce its reliance on traditional fossil-based fuels, replacing them with renewable energy to encounter the energy challenges.

With the upsurge in power demand over the coming decade and rapid installation of renewable power sources such as wind and solar, India’s existing grid network will require a significant expansion in a very short duration. The development in the renewable energy sector ensures reduced carbon emission, uninterrupted energy supply, job opportunities, clean energy production, and electricity in rural areas. In India, exponential growth has been observed in the generation of power using solar photovoltaic technology and reached up to 31.5 GW, which is 8.73% of the overall installed capacity as estimated at the end of June 2019 [1]. The state-wise allocation of solar PV installed capacity until September 2019 is shown in Fig. 1. Around 73% of rooftop solar installation is meant for a commercial and industrial segment, while the rest of 27% is for residential purposes [2]. The overall installed capacity of solar PV rooftop in India at the end of 2019 is 5252 MW.

Fig. 1
figure 1

State-wise allocation of solar rooftop PV-system in India [2]

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Tomar et al. [3] experimentally verified the thermo-electrical performance of five various types of PV-modules, i.e., monocrystalline silicon (m-Si), polycrystalline (p-Si), amorphous thin film (a-Si), cadmium telluride thin film (CdTe), and copper indium gallium de-selenide (CIGS) integrated with a thermal management system. Monocrystalline silicon holds the maximum market share as it offers better performance compared to various silicon-based PV technologies. The higher cost of m-Si opens the path for the commercialization of p-Si and the latest thin-film technologies. Among all the latest thin-film technologies, amorphous thin film (a-Si) technology gains significant popularity due to its low cost and its effectiveness in low-temperature regions [4].

Photovoltaic technology uses sunlight to generate electrical energy, thus eliminating the dependency on conventional energy sources. In solar thermal systems, the solar collector is an elementary element that converts the sunlight into thermal energy. The high operating temperature of the PV-module causes structural damages and reduced electrical conversion efficiency [5]. Hence, PV-modules must be coupled with a thermal management system to maintain the working temperature within the permissible limits. Previous research shows that the heat extracted using the PV-module can be reused for various domestic and commercial purposes. Thus, the hybrid PVT technology consisting of solar PV and thermal management system is used to improve the electrical output by drawing the heat from the module using air/water as a coolant in the channel below the PV-module [6]. The PVT collector is widely used for converting solar energy into thermal and electrical energy simultaneously, as shown in Fig. 2. The hybrid system is highly efficient than the solar PV-system and requires less space, material, and cost of installation.

Fig. 2
figure 2

Typical PVT air-collector

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The working temperature is reduced using both natural and forced circulation of fluid (air/water) via the channel below the PV-module. This helps in the cooling of the PV-module, resulting in increased electrical efficiency (ɳel) [7, 8].

Recently, many studies have been carried out to test the effect of glazing on the efficiency of the PVT-system, as shown in Table 1. Kazemian et al. [9] experimentally verified the impact of the additional glass cover and different working fluid (water, ethylene glycol/water, and pure ethylene glycol) on the efficiency of glazed and unglazed PVT-system. It is found that the unglazed PVT-system is preferred when electrical efficiency is the prime interest, while the glazed PVT-system has opted when higher overall efficiency is desired. The impact of solar cell emissivity on the ɳth of the PVT-system has been investigated by Lammle et al. [10] by using a selective coating on the cell. A significant reduction in heat losses has been observed by using the selective coating over the solar cell.

Table 1 Impact of glazing on the PVT-system
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Air as a cooling fluid in the channel ensures simplicity in the design, along with greater safety. Still, at the same time, it offers low thermal conductivity and specific heat, which results in low ɳth. That’s why most of the researchers diverted their studies towards the use of water along with nano-fluids as a heat transfer medium. The inclusion of nanoparticles with the base fluid in the channel raises the thermal efficiency of the PVT-system. A number of research works are performed to examine the effect of size, volume fraction, and a suitable concentration of nanoparticles with base fluid. Abbas et al. [13] presented a detailed analysis to show the effect of nanoparticles upon the PVT-system’s efficiency. It is observed that the organic fluids offer better thermal conductivity concerning water when used as a base fluid. A comparative study on PVT, PVT with nano-fluid, and PVT-PCM system have been conducted by Sardarabadi et al. [14]. The outcomes showed that \({\eta _{Ex}}\)of the PVT with nano-fluid is better as compared to other PVT- systems. Ali et al. [15] examined the impact of carbon-based nanoparticles, especially SiC, on the ɳth of the PVT-system.

Singh et al. [16] formulated a mathematical model of the PVT-system considering the effect of the absorber plate shape factor and mass-flow rate. From the analysis, it has been concluded that the absorber plate shape factor is an important factor that influences the efficiency of the PVT-system. Jones et al. [17] presented a novel mathematical model on a two-node approach to estimate the thermal and electrical efficiencies of the PVT-collector.

Exergy analysis is a useful technique for estimating the efficiency of PVT-systems as it helps in suppressing the inefficiencies in the system and enables to estimate the amount of loss in the system. Fudholi et al. [18] investigated the exergetic performance of ∇- groove absorber installed in the channel of the PVT-system. Salem et al. [19] presented an experimental description of the hybrid PVT-system with straight and helical aluminium plates for cooling. The average ɳEx of the hybrid system was 11.1% and 13.5% for experimental and theoretical studies, respectively. Tadesse [20] experimentally examined the PVT air-collector with a V-groove absorber in a channel below the module. The performance of the PVT-collector is significantly enhanced by using V-groove in the channel. A comparison of the present work with the existing state-of-art is shown in Table 2.

Table 2 Comparison of the present work with current state-of-art
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Dust and pollution significantly affect both the productivity and conversion efficiency of a PV module. Accumulation of the dust on the upper surface of PV modules results in energy loss and damage of the upper layer [31]. Dust includes bird droppings, sand, microfiber, hair, and plant products. The dust accumulation on the upper surface of the PV module is a function of the physical and chemical properties of dust particles such as size, weight, and shape. Ecological factors such as temperature, moisture, wind direction, wind speed, and rainfall also affect the dust deposition to a large extent [32]. The optical, thermal, and electrical characteristics of the PV module are also affected by the amount of dust deposition. Molki [33] conducted an experimental study to investigate the impact of the deposition of ground clay (bentonite) over the performance and efficiency of the PV module. The outcomes show that the overall efficiency decays with a rise in the deposition of bentonite. Kazem et al. [34] investigate the effect of sand, ash, silica, and calcium carbonate deposition on the performance of the PV module. The study reveals; maximum loss in PV voltage occurs with the deposition of ash over the surface of the PV module.

Dust deposition not only affects the thermal and electrical performance of the PV module but also reduces its lifetime. Therefore, the cleaning of dust is necessary for the performance and lifetime enhancements of the PV modules. There are various methods of cleaning, such as natural cleaning (rainfall, wind), manual cleaning (washing), and automated cleaning. In the present work, manual cleaning (water and soft cloth) has been opted to clean the PV module.

1.1 Main contribution

  • In this study, V-groove is inserted in the PVT air collector channel to raise the thermal conductivity.

  • The efficiency of the PVT air-collector is evaluated in terms of ɳth, ɳel, and ɳT.

  • The energy balance equation has been derived with the help of the matrix inversion method to predict the PV and air output temperatures.

  • The exergy efficiency of the proposed system is analyzed based on real-time data.

  • The experimental results are compared with theoretical results based on mathematical modeling using the same weather conditions to validate the proposed model.

The Section 1 includes the latest research conducted in the PVT air-collector accompanied by the impact of channel modifications on the PVT-system performance. The Section 2 incorporates the mathematical modeling of the proposed system with the energy balance equation. In the Section 3, the specifications of the PVT-module have been discussed in detail. In the Section 4, the experimental and theoretical results have been analyzed. The Section 5 concludes the paper with justified references.

2 Mathematical modeling

The energy balance equation to predict the PV and air output temperature in the proposed system has been developed based on the following assumptions:

  1. 1)

    The system is assumed in a steady-state.

  2. 2)

    The specific heat of the fluid remains invariable in the channel.

  3. 3)

    The convective heat transfer coefficients across the air channel, and the air remains constant and equal.

  4. 4)

    Ohmic losses from the PV-module remain constant.

  5. 5)

    The useful heat gained by the fluid remains constant throughout the channel length.

The cross-sectional view of the PVT air-collector with V-groove absorber in the air channel is shown in Fig. 3.

Fig. 3
figure 3

Schematic representation of heat transfer characteristics across PVT air-collector

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The energy balance equation can be derived as:

  • For PV-module

    $$\alpha \tau I={H_t}({T_p} - {T_a})+{h_A}({T_p} - {T_f})+{h_{rpb}}({T_p} - {T_b})+{\eta _{pv}}I+{Q_t}$$
    (1)

  • Energy balance equation for the channel

    $$m{C_f}({T_o} - {T_i})={h_A}({T_p} - {T_f})+{h_B}({T_b} - {T_f})+{Q_t}$$
    (2)

  • At the back surface

    $${h_{rpb}}({T_p} - {T_b})={h_B}({T_b} - {T_f})+{H_b}({T_b} - {T_a})$$
    (3)

Where,

$${H_b}=\frac{k_t}{l_t}$$
(4)
$${H_t}={\left( {\frac{1}{{{h_w}+{h_{rpa}}}}} \right)^{ - 1}}$$
(5)
$${h_{rpb}}=\frac{{\sigma \left( {{T_p}+{T_b}} \right)\left( {T_{p}^{2}+T_{b}^{2}} \right)}}{{\left( {\frac{1}{{{\varepsilon _p}}}+\frac{1}{{{\varepsilon _b}}} - 1} \right)}}$$
(6)
$${h_{rpb}}={\varepsilon _p}\sigma (T_{p}^{2}+T_{s}^{2})\left( {{T_p} - {T_s}} \right)$$
(7)
$${T_s}=0.0522T_{a}^{{1.5}}$$
(8)

The equation for convective heat transfer coefficients was calculated according to the formula used by Fudholi et al. [35].

$$h=\frac{k}{{{D_c}}}{N_u}$$
(9)
$${D_c}=\frac{{4Wd}}{{2\left( {W+d} \right)}}$$
(10)

The Nusselt number (Nu) depends on the Reynolds number (Re) and can be calculated as:

  • Laminar flow region (Re < 2300)

    $${N_u}=5.4+\frac{{0.00190{{\left[ {\operatorname{Re} \Pr \left( {\frac{{{D_c}}}{L}} \right)} \right]}^{1.71}}}}{{1+0.00563{{\left[ {\operatorname{Re} \Pr \left( {\frac{{{D_c}}}{L}} \right)} \right]}^{1.17}}}}$$
    (11)

  • Transition flow region (2300 < Re < 6000)

    $${N_u}=0.116({\operatorname{Re} ^{2/3}} - 125){\Pr ^{1/3}}\left[ {1+{{\left( {\frac{{{D_c}}}{L}} \right)}^{2/3}}} \right]{\left( {\frac{\mu }{{{\mu _w}}}} \right)^{0.14}}$$
    (12)

  • Turbulent flow region (Re > 6000)

    $${N_u}=0.018{\operatorname{Re} ^{0.8}}{\Pr ^{0.4}}$$
    (13)

Where Re and Pr are the Reynolds number and Prandtl number respectively and calculated as:

$${R_e}=\frac{{m{D_c}}}{{{A_c}\mu }}$$
(14)
$${P_r}=\frac{{\mu {C_f}}}{k}$$
(15)

The equations for physical properties of fluid circulated in the channel (air) is taken from Fudholi et al. [35]

$$\rho =1.1774 - 0.00359(T - 27)$$
(16)
$${C_f}=1.0057+0.000066(T - 27)$$
(17)
$$k=0.02624+0.0000758(T - 27)$$
(18)
$$\mu =[1.983+0.00184(T - 27)]{10^{ - 5}}$$
(19)

The temperature of the fluid (Tf) is the mean of inlet air temperature and outlet air temperature.

$${T_f}=\frac{{\left( {{T_{in}}+{T_{out}}} \right)}}{2}$$
(20)

To calculate the temperature vector, the Eq. (2)-(3) can be written in the form of a matrix

$$\left[ A \right]\left[ T \right]=\left[ B \right]$$
(21)
$$\left( {\begin{array}{*{20}c} {{Z_1}} &{ - {Z_2}} &{ - {h_{rpb}}} \\ {{Z_4}} &{{Z_5}} &{{h_2}} \\ {{h_{rpb}}} &{{h_2}} &{{Z_7}} \end{array}} \right)\left[ {\begin{array}{*{20}c} {{T_p}} \\ {{T_f}} \\ {{T_b}} \end{array}} \right]=\left[ {\begin{array}{*{20}c} {{Z_3}} \\ {{Z_6}} \\ {{Z_8}} \end{array}} \right]$$
(22)

Where

$${Z_1}={H_t}+{h_A}+{h_{rpb}}+(N{A_n}{h_c}{\eta _n})$$
(23)
$${Q_t}=N{A_n}{h_c}{\eta _n}\left( {{T_p} - {T_f}} \right)$$
(24)
$${Z_2}={h_A}+(N{A_n}{h_c}{\eta _n})={Z_4}$$
(25)
$${Z_3}=\tau \alpha I+{H_t}{T_a} - {\eta _{pv}}I$$
(26)
$${Z_5}= - [{h_A}+{h_B}+2m{C_f}+(N{A_n}{h_c}{\eta _n})]$$
(27)
$${Z_6}= - 2m{C_f}{T_{in}}$$
(28)
$${Z_7}= - ({h_B}+{h_{rpb}}+{H_b})$$
(29)
$${Z_8}= - {H_b}{T_a}$$
(30)
$${\eta _n}=\frac{{\tanh MH}}{{MH}}$$
(31)

Where,

$$M={\left( {\frac{{2{h_c}}}{{{k_n}{A_{cn}}}}} \right)^{1/2}}$$
(32)
$${h_A}={h_B}={h_c}$$
(33)

At first, the heat transfer coefficients are estimated based on initial predicted values of temperature across various layers of PVT air-collector, i.e., ambient, air, PV, and backplate. The temperature vector is calculated according to Eq. (20).

$$\left[ T \right]={\left[ A \right]^{ - 1}}\left[ B \right]$$
(34)

The numerical values of designed parameters used in the study were: L = 53.7 cm, W = 45.7 cm, α = 0.9, τ = 0.92, ϵp= 0.7, ϵb = 0.9, Ta = Ti = 27oC and Vf = 1 m/s. The temperature matrix obtained from Eq. (34) can be named as matrix [T1] and compared with the initial predicted values of temperature [T]. The value of the iteration is set by comparing the previous matrix with a new matrix. If the difference between the two sets of values is lower than 0.001, then the iteration stops, and the old temperature values are changed by new values of Ta, Tf, Tp, and Tb. The iterative process used to obtain the theoretical results has been shown in Fig. 4. Further, it has been observed that adequate convergence for the temperatures was accomplished in three to four iterations.

Fig. 4
figure 4

Flowchart representing the process of theoretical solution

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2.1 Performance parameters of PVT air-collector

The performance of the PVT air-collector is measured in the form of electrical (ɳele), thermal (ɳth), and exergy efficiency (ɳEx). The overall efficiency of the PVT is the aggregate of electrical and thermal efficiencies [36]

$${\eta _{overall}}={\eta _{th}}+{\eta _{ele}}$$
(35)

The ɳth of the PVT-collector is written as

$${\eta _{th}}=\frac{{{Q_t}}}{{I{A_c}}}$$
(36)

Where Qt is the collected heat, which may be written as

$${Q_t}=m{C_f}({T_o} - {T_i})$$
(37)

The ɳele of PVT air-collector depends upon the temperature of the solar cell, temperature coefficient of efficiency, and the ambient temperature

$${\eta _{el}}_{e}={\eta _0}\left[ {1 - {\beta _0}({T_{cell}} - {T_a})} \right]$$
(38)

Apart from these, exergy efficiency (ɳEx) is also taken as a parameter for evaluating the efficiency of the PVT-system as it helps in reducing the inefficiencies of the system [37].

$${\eta _{Ex}}=\frac{{E{x_{out}}}}{{E{x_{in}}}} \times 100$$
(39)

The exergy balance in a PVT air-collector is calculated according to Das et al. [30].

$$E{x_{out}}=\sum\limits E{x_{th}}+\sum E{x_{el}}$$
(40)

Where,

$$\sum {E{x_{th}}={Q_t} - m{C_f}{T_a}} \ln \frac{{{T_o}}}{{{T_i}}}$$
(41)
$$\sum {E{x_{el}}} =\left[ {\frac{{\eta I{A_c}}}{{1000}}} \right]$$
(42)

The input exergy is calculated according to the relation presented by Kalogirou et al. [38]

$$\sum {E{x_{in}}={A_c}{N_c}} I\left[ {1 - \left( {\frac{4}{3}} \right)\left[ {\frac{{{T_a}}}{{{T_{sun}}}}} \right]+\left( {\frac{1}{3}} \right)\left[ {\frac{{T_{a}^{4}}}{{T_{{sun}}^{4}}}} \right]} \right]$$
(43)

3 Methodology

3.1 Study area

The experimental study is conducted in Ghaziabad City, India, with the coordinates of 28.667856o N and 77.4538o E. It resides close-in location and latitude to New Delhi. The climatic conditions of Ghaziabad are similar to the national capital of New Delhi. The estimated ambient temperature ranges between 21 and 40oC, with an average wind speed of 2.4 m/s and approximate humidity of 67.7%. The city receives its maximum rainfall in July and August, with an average of 236.2 mm of precipitation. The approximated hour of sunshine ranging between 200 and 300 h. Since the city receives good sunshine hours throughout the year, steady growth in solar photovoltaic projects has been observed in the last decade. The climatic conditions are favorable for performing the experimental investigation on PVT technology.

3.2 PVT air-collector description

Figure 5 represents the schematic of the experimental set-up of PVT air-collector with the V-groove absorber in the channel. The experimental set-up consists of a PV-module, V-groove, low power brushless DC fan, and data acquisition unit to record the observations. The PV-module employed in the fabrication of PVT air-collector was developed by Central Electronics Limited (CEL) India. The size of the module is 537*457*35 mm with open-circuit voltage and short circuit current of 21.8 V and 2.74 A, respectively. The other specifications of the PV- module are mentioned in Table 3.

Fig. 5
figure 5

Schematic diagram of the Experimental set-up of PVT air-collector with V-groove absorber

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Table 3 PV-module Specifications
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The V-groove used in the channel of the PVT air-collector works as an absorber and installed at the backside of the 40 W PV-panel. The length, vertex angle, and height of each side of the individual groove is 53.2 cm, 60o, and 3.5 cm, respectively. Thermal grease was used to fix the V-groove in the channel to avoid the heat loss into the surroundings. Experiments were performed on 7th June 2019 for the climatic condition of Ghaziabad, India.

3.3 Measuring instruments

The solar radiations were measured using a class 2 pyranometer; A J-type thermocouple was employed to estimate the temperature across the various layers. The solar radiations and ambient temperature are recorded at 30 minutes interval, and the experiment performed between 07:00 a.m. to 5:30 p.m. An anemometer (PCE-VA 11) is employed to estimate the air velocity at the inlet and outlet of the channel. The measuring instruments used for the experiment are specified in Table 4.

Table 4 List of instruments used for measurement
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3.4 Uncertainty analysis

To ensure accurate results and avoid errors in the measurement, it is essential to conduct the uncertainty analysis. During experiments, while measuring air velocity, temperature, and sunlight intensity, specific errors and uncertainties can occur in the results due to the selections of the instrument, calibration, handling of instruments, and recordings. These uncertainties may slightly alter the experimental results from the theoretical results obtained from mathematical modeling. The uncertainties can be estimated by using the relation:

$${X_R}={\left[ {{{\left( {{x_1}} \right)}^2}+{{\left( {{x_2}} \right)}^2}+{{\left( {{x_3}} \right)}^2}+ \cdots \cdots +{{\left( {{x_n}} \right)}^2}} \right]^{1/2}}$$
(44)

Where,

XR is the uncertainty in the experimental result.

\({x_1},{x_2},.......{x_n}=\) Uncertainties in the individual variables.

The error analysis (e) was performed to validate experimental and theoretical models.

$$e=\sqrt {\frac{{\sum {{{\left( {{e_i}} \right)}^2}} }}{N}}$$
(45)

Where,

$${e_i}=\left( {\frac{{{x_i} - {y_i}}}{{{x_i}}}} \right) \times 100$$
(46)

Xi, Yi are the theoretical and experimental figures of the variable.

The accuracy among the theoretical and experimental outcomes was measured according to Eq. (45).

4 Results and discussion

In this paper, the performance of PVT air-collector with low-cost V-groove absorber in the channel is experimentally as well as theoretically investigated for the climate of Ghaziabad City (28.667856o N, 77.4538o E), India in June 2019. To justify its applicability and acceptability, various parameters such as ɳele, ɳth, ɳoverall, and ɳEx have been calculated for the proposed model. A mathematical model is formulated to predict the thermal and electrical efficiencies of the proposed system, and the outcomes are verified with the experimental results. The parameter of proposed PVT-setup, such as solar radiations (W/m2), ambient temperature, fluid temperature, and inlet-outlet temperatures of the channel has been measured regularly at an interval of 30 minutes. Therefore, the analysis of experimental observations relied on a half-hour average measurement.

The deviation in climatic parameters, viz. global solar radiations, and ambient temperature during 07:00 a.m. to 5:30 p.m. for a day in June 2019 is shown in Fig. 6. The data for solar radiations and ambient temperature is recorded for a particular day (7th June 2019) at an interval of 30 minutes.

Fig. 6
figure 6

Global solar radiations and ambient temperature on an hourly basis

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As demonstrated in Fig. 6, the ambient temperature (Ta) increases with time. The average Ta is 35.40oC. The solar radiation is maximum at around 12:30 p.m., which is 907 W/m2. The PV-cell temperature is an important parameter that directly affects the performance of PV-systems. It has been mentioned that the electrical efficiency (ɳele) of the PV-system decreases on the rise in temperature of cells [37]. Therefore, it is always essential to keep the cell temperature within limits. Figure 7 shows the hourly variation of ɳele with time on 7th June 2019. It has been observed from the figure that a reasonable value of ɳele is obtained, although the conditions are not very favorable. The proper functioning of the channel below the PV-module ensures that the rise in PV-cell temperature is not very high and still within the acceptable limits. A noticeable decrement in ɳele is observed from 3:00 p.m. to 4:00 p.m., and during that particular period, the cell temperature reached its highest value.

Fig. 7
figure 7

Electrical efficiency variation with temperature

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It has been observed that the average ɳele is 10.39% and 10.26% for theoretical and experimental analysis. Hence, the theoretical results are coherent with experimental results with an accuracy of 98.8%, as illustrated in Table 5.

Table 5 Comparison of theoretical and experimental results for electrical efficiency
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Figure 8 provides a comparison of PV, outlet, and inlet temperatures obtained from both the theoretical and experimental models. It has been observed that the theoretical results obtained using the mathematical model were coherent with experimental results obtained in real outdoor conditions with an accuracy of greater than 90% in each case.

Fig. 8
figure 8

Theoretical and experimental variation of temperature

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The thermal efficiency (ɳth) of the PVT-system depends upon the temperature difference between the PVT-collector output and input (T0-Ti), as mentioned in Eq. (36)-(37). T0-Ti also indicates that temperature in the PVT-collector is successfully absorbed by the air. Figure 9 shows the deviation of ɳth with the temperature difference between the input-output of the collector. It has been observed that the ɳth is high when an appreciable temperature difference T0-Ti is obtained.

Fig. 9
figure 9

Thermal efficiency variation with temperature difference

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Table 6 depicts the theoretical calculation of temperatures along with thermal efficiency variations. The average ɳth is 41.78% and 41.57% for theoretical and experimental studies, respectively. The mathematical modeling results are coherent with the experimental results with an accuracy of 99.43%.

Table 6 Experimental and theoretical variation of thermal efficiency
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Figure 10 shows the hourly variation of overall efficiency (ɳoverall) obtained both theoretically and experimentally.

Fig. 10
figure 10

Variation in overall efficiency with time

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The average value of ɳoverall obtained for the theoretical and experimental model were 52.21% and 51.88%, respectively. Further, it has been observed that the accuracy between both models is greater than 95%. It is noticed that minimal variation is observed in ɳoverall as compared to thermal and electrical efficiencies because of the compensating effect of one parameter over the other. i.e., when one parameter shows increasing behaviour, the other shows decreasing behaviour.

The electric power output from the experimental set-up varies linearly with solar radiation. Based on the analysis, the maximum electrical power obtained from the experimental set-up is 37.96 W, obtained when the intensity is 890 W/m2. Figure 11 demonstrate the deviation in voltage and current of the proposed experimental set-up. It is evident that the voltage of the PV-collector drops sharply with the rise in solar radiation and PV temperature. The numerical value of Voc and Imax obtained from the experimental set-up were 19.62V and 2.25A, respectively.

Fig. 11
figure 11

Voltage and current variation of PV-collector with time

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The thermal and electrical efficiencies are not the only performance parameters for hybrid PVT- systems; an exergy analysis is also performed to evaluate the overall efficiency of the system. The exergy efficiency is evaluated by calculating the thermal and electrical exergies separately. Figure 12 shows the exergy efficiency (ɳEx) of the PVT-system with V-groove in the channel evaluated both theoretically and experimentally.

Fig. 12
figure 12

Exergy efficiency variation with time

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The average ɳEx of the PVT air-collector with V-groove absorber is 12.94% and 12.70% for theoretical and experimental studies, respectively, as shown in Table 7. It has been concluded that the results obtained using mathematical modeling were coherent with the experimental results obtained in real outdoor conditions with an accuracy of approximately 98.17%.

Table 7 Theoretical and experimental results of exergy efficiency
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5 Conclusion

In this paper, a PVT air-collector is designed with V-groove in the air channel and investigated experimentally in real outdoor conditions with detailed mathematical modeling. The manuscript is best concluded as:

  • A matrix-inversion method has been adopted to solve the temperature equations.

  • Mathematical model results are validated with the experimental results with the help of error analysis.

  • The average overall efficiency of the proposed system is 52.21% and 51.88% for theoretical and experimental studies, respectively.

  • The theoretical and experimental values of exergy efficiency are 12.94% and 12.70%, respectively, with an accuracy of 98.17%.

  • A significant improvement has been observed in the energy and exergy efficiencies of the PV-panel using the proposed set-up.

  • The temperature of the PV-cell was highest among all other components of the PVT-setup. Also, the overall efficiency and exergy efficiency is maximum on optimum solar intensity.

  • The thermal efficiency of the proposed system is 41.78% and 41.57% for theoretical and experimental studies, respectively.

  • The overall efficiency of the proposed PVT-system has been considerably improved with the V-groove in the channel.