Introduction

The importance of energy in global economic progress and industrialization has grown significantly over time. However, due to the dwindling reserves of fossil fuels, there is an increasing focus on the development of non-conventional renewable energy sources. Among the many options available, geothermal, solar, biomass, wind, tidal, and hydroelectric power stand out [1, 2], with solar energy being one of the most popularly utilized sources of energy worldwide. Solar energy is a non-polluting, freely accessible fuel source. The most effective way to utilize solar energy is by converting it to thermal energy for use in SAH, as it ensures optimal utilization of this valuable resource.

Solar air heaters (SAHs) are the cheapest and most commonly used solar collectors due to their inherent simplicity. SAHs are primarily used for timber seasoning, industrial product curing, and space heating [3, 4], and they are also used in the field of building corruption side such as drying concrete, curing, and clay building components. SAHs play a vital role in solar heating systems due to their low material and cost requirements.

In a standard solar air heating system, the components include a collector frame with support structures, insulation, collector, and glass cover. The effectiveness of the system depends on several factors, including the design, tilted angle, material of collector, surface area, environmental conditions, MFR of the fluid heat transfer, and more, as detailed in references [5]. Therefore, achieving a cost-effective and efficient operation for many applications requires an optimal design of these components.

A solar collector, also known as the absorber plate, is the essential part of a SAH. It converts solar energy into thermal energy, which is then sent through a duct to the air that is moving. However, conventional SAHs function less well because of the absorber surface’s low heat absorption capacity and the low thermal conductivity of the moving air. In order to address these issues, researchers have used various techniques, including extended surfaces [6,7,8,9], porous/packed beds [10,11,12,13], and artificial roughness [14,15,16], to increase the heat transfer coefficient and boost SAH’s overall efficiency. Air-type collectors have a number of advantages, such as lower construction costs and overall weight as well as no worries about boiling, freezing, or pressure-related issues. To get around SAH’s limitations, various kinds of theoretical models and experimental data have been used to verify the design parameters. Several factors, including depth, shape, collection length, number of glass covers, kind of absorber plate, and wind speed, affect the efficiency of SAH [17, 18]. In order to enhance the effectiveness of SAH, scientists have investigated various collector kinds, modified design parameters, and broadened their uses [19]. Though thermal analysis has been the primary approach used in earlier research to evaluate SAH performance [20], this approach overlooks internal losses. Thus, when assessing and contrasting solar thermal systems, exergy analysis—which measures the greater potential work feasible from energy—offers more thorough information and ought to be taken into account [21]. In order to maximize their effectiveness and achieve optimal exergy performance under certain operating and system settings, this study intends to investigate the thermal and exergy performance of various PSAHs in detail. According to Dincer and Rosen [22], exergy analysis is a strong thermodynamic approach that supports the development and analysis of thermal systems by fusing the principles of mass and energy conservation with the second law of thermodynamics. An effective technique for identifying and measuring inefficiencies in thermal systems is exergy analysis, which makes it possible to create designs that are more efficient. Exergy analysis identifies places where energy is wasted or lost by analyzing the movement of matter and energy inside a system. The system can then be optimized using this data, improving both its performance and energy efficiency. To put it briefly, exergy analysis is an essential tool for researchers and engineers who want to improve the efficiency and sustainability of thermal systems. A wide range of study has made use of the first and second laws of thermodynamics [23,24,25,26,27,28,29]. Kurtbas and Durmus [30] developed and evaluated five distinct SAC types based on their exergy and thermal efficiency. According to their findings, performance evaluations of SAH ought to focus on factors such as temperature differential (Tfo-Tfi), pressure loss, roughness geometry, and collector efficiency. Kurtbas and Turgut [31] conducted an investigation to examine the exergy and thermal analysis performance of SAH with both fixed and free fins. Their study’s findings showed that the collector with free fins performed less well than the absorber plate with fixed fins. They also observed that exloss and heat transfer both show increases with an increase in pressure drop (∆P). Karslı [17] evaluated the energetic and exergetic efficiency of a built Solar Air Collector used for drying applications. In order to do this, a system comprising four different types of absorber plate variations that have been experimentally examined was built. According to the findings, Collector Type A’s thermal efficiency (ηI) varied from 26 to 80%, Type B’s from 26 to 42%, Type C’s from 60 to 70%, and Type D’s from 26 to 64%. Moreover, it was shown that the exergetic efficiency (ηII) ranged from 0.27 to 0.64 for all collectors. Chand et al. [9] examined the thermal performance of LFSAH under the experimental investigation. The result reveals that the LFSAH performed better as compared with PSAH. Chand and Chand [32] analyzed the thermal performance of LFSAH at different louvered parameters. The results indicated that the thermal performance enhances from 43.14 to 76.79% with the use of louvered fines in solar collectors. Esen [33] performed an experiment on a DFSAH with absorber surfaces of two types: with and without obstacles. The author used flow rates of 0.015, 0.02, and 0.025 kg/s during the experiments. The results found by applying the concepts of energetic and exergetic efficiencies showed that the SAHs with obstacles outperformed the SAHs without obstacles under the similar operating conditions. Gupta and Kaushik [34] aimed to optimize the performance of a PSAH by investigating its exergy efficiency. They looked into the energetic performance of various factors such as MFR per unit collector area, aspect ratio, and duct depths. Their findings revealed that the maximum exergy output can be achieved when MFR is at its minimum and the inlet fluid temperature is low. Gupta and Kaushik [35] examined the effects of various roughness types on exergy, energy efficiency, and effective efficiencies. They looked at six different sorts of arrangements: metal mesh, wedge-shaped ribs, circular ribs, enlarged chamfered rib-groove, and V-shaped ribs. They developed a program with correlations to calculate ηI, ηII, and ηeff using MATLAB software. The results showed that adding roughness to the surface enhanced the efficiency when compared to a smooth one. Experiments were carried out by Akpinar and Kocyigit [19] to investigate the efficacy of a SAH fitted with barriers. They found that the thermal efficiency ranged from 20 to 82% using MFR of 0.0052 kg/s and 0.0074 kg/s. Exergetic performance, on the other hand, ranged from 8.32 to 44% in comparable operating conditions. The energy and energetic efficiency of a recently developed finned SAH and PSAH were studied by Alta et al. [20]. Using both single and double glass covers, they evaluated the collector’s thermal and energy performance at different mass flow rates (MFR) and tilt angles (0 to 30°). They observed that the finned SAH with DGC outperformed the PSAH in terms of efficiency. The energy and exergetic performance of PBSAH integrating round capsules was investigated by Bouadila et al. [36]. The study participants observed that the daily energy efficiency (ηI) varied between 32 and 45%, and the daily energetic efficiency (ηII) varied between 13 and 25%. In an alternative study, Benli [37] conducted experimental investigations on the exergetic and energy efficiency of five distinct collector types, which included reverse trapeze and corrugated, corrugated trapeze, and flat plate collectors. Bayrak et al. [38] assessed the exergetic and energy efficiency of a collector plate with a porous baffled design. The experiments were carried out with MFR of 0.016 kg/s and 0.025 kg/s. They observed that the maximum values of ηth and ηII, along with temperature difference, were attained with a porous material thickness of 6 mm at an MFR of 0.025 kg/s in case III. However, for case I, they observed the lowest values for the PSAH at MFR of 0.016 kg/s. Velmurugan and Kalaivanan [39] established an energy balance equation to assess the exergy and energy analysis of single, double, and triple pass SAH. They used MATLAB software to program a simulation code for calculating the thermal and exergy efficiency, and studied the effect of MFR on exergetic performance, energetic performance, improvement potential, temperature rise, and irreversibility. They concluded that the triple pass solar collector performs better compared with double pass and PSAH. Acır et al. [40] investigated the exergy and energy performance of a novel SAC with circular turbulator collectors. They conducted studies with four copper tubes painted black and having varied obstacle relief angles (45°, 90°, and 135) with MFR range from 0.0023 to 0.0055 kg/s. According to their findings, the ηII varied from 8.1 to 42.4% and the ηI ranged from 28.6 to 79.5%. For MFR 0.0055 kg/s with a 45° obstacle relief angle, the highest ηI and ηII values were recorded. Ghritlahre and Prasad [41] implemented a neural model to estimate the energetic and exergetic performance of SAH with roughened surfaces. They performed experiments with roughness solar collector with various MFR range from 0.010 to 0.0175 kg/s to calculate the ηI and ηII. They analyzed a neural model with study of 2 output and 6 input variables and usage of 60 sets data of experimental in neural model. The optimal neural model for prediction was found to be the 6–6-2 neural model trained using the Levenberg–Marquardt (LM) training algorithm. Abuşka [42] experimentally analyzed the exergetic and energetic performance of conical surface SAH with various MFR range from 0.04 to 0.01 kg/s. The result indicated that the thermal and exergy efficiency were obtained at 63.2–57.2%, 71.5–61.7%, 74.6–64.0%, and 19.3–16.1%, 15.1–11.5%, 12.5–9.2% for MFR of 0.04 kg/s, 0.08 kg/s, and 0.10 kg/s respectively for conical and PSAH. They also observed that the thermal performance was enhanced by 10% compared to PSAH. Matheswaran et al. [43] conducted an analytical investigation of ηI and ηII for a SAC with a double duct jet surface with single pass. They developed a MATLAB program to calculate exergy and energy efficiency, and also they developed a correlations for using various factor like jet plate design parameters and Reynolds number. Aktaş et al. [44, 45] established a designed a multi-pass solar collector (MPSAC) with perforated fins and investigated its thermal and exergetic performances through experiments conducted under the MFR of 0.0069 kg/s and 0.0087 kg/s. The results revealed that the thermal efficiency of DPSAC and MPSAC were varied from 30.37 to 69.03% and 48.88 to 83.47%, respectively. Furthermore they observed that the exergy performance of DPSAC and MPSAC varied from 2.10 to 17.12% and 8.74 to 23.97%, respectively. According to the literature study, it was observed that the second law analysis of the SAH provides a clear understanding of the efficient utilization of solar energy to heat the air. It is also observed that no research has been performed on the exergetic performance analysis of LFSAH. Therefore, the present study aims to examine the exergetic performance analysis of LFSAH. Kumar and Layak [46] investigated the analytical approach to enhance the energy and exergy performance of a twisted-rib roughness absorber collector. They observed that the enhancement in thermal efficiency (ηth), exergy efficiency (ηexergy), and overall efficiency (ηeff) were 1.81, 1.81, and 1.79 times higher, respectively, compared to PSAH. Amit and Layak [47] designed a novel winglet-type roughness SAH and conducted experiments to analyze its performance using thermal, effective, and exergetic analysis concepts. The analysis results indicated a notable improvement in performance for the SAH with a winglet-type roughness absorber surface in comparison to a smooth plate absorber. Specifically, the optimum values for thermal, effective, and exergetic efficiencies were found to be 2.12, 1.99, and 2.03 times higher than PSAH. Kumar et al. [48] conducted a SAH that incorporated copper tubes with a zig-zag design. When tested under comparable weather circumstances, they discovered that the SAH with copper tubes had greater thermal and energy efficiency than one without. In natural convection conditions, the energy efficiency of the SAH with copper tubes fluctuated between 14.53 and 20.36%, with an average of 18.26%. In contrast, the absorber without copper tubes exhibited efficiency ranging from 12.45 to 17.53%, with an average of 16.29%. The exergetic efficiency for both types of SAH ranged between 0.95 and 1.939% and 1.2 and 1.53%, with an average of 1.41% and 1.69%, respectively. Das [49] conducted an experiment to examine the performance of a stationary SAH versus a movable one. The movable SAH proved to be superior in several aspects based on two assessment methods. Notably, the movable SAH displayed double the average heat transfer value, 47.8% thermal efficiency, 2.4 times exergetic efficiency, 20% higher performance coefficient, and 23.8% higher average collector outlet temperature than the stationary SAH. Prakash et al. [50] studied the performance of a hybrid mode double-pass solar air heater (DPSAH) using exergy and thermal analysis. According to their findings, the average exergy and energy efficiency for natural convection mode were 2% and 11.47%, respectively. For the induced forced convection mode, the exergetic and energetic performance were 10.43% and 56%, respectively. However, the addition of a reflector increased the exergy and energy efficiency to 17.617% and 86.19%, respectively. In their study, Khanlari et al. [51] investigated a vertical SAH that utilized a perforated baffle plate and an absorber coated with nanoparticles. Using both analytical and experimental techniques, they evaluated the heaters’ performance and found that the heaters with nanoparticles had a thermal efficiency range of 58.10 to 76.22% and the heaters without nanoparticles had a range of 54.96 to 72.05%. Moreover, they observed that the application of a nanoparticle-embedded coating raised exergy efficiency by 9.25 to 10.58%.

From the literature review, it is evident that numerous studies have been conducted by various researchers to assess the exergetic performance of different types of SAH, including roughened, extended surface, packed/porous bed, and finned absorber SAHs. However, there is a notable lack of research on finned absorbers, particularly those with louvered fins. For LFSAH, only theoretical investigations have been conducted thus far, with no experimental studies on louvered fins SAHs being conducted yet. This study was undertaken to analyze the performance of a SAH equipped with louvered fins, considering outdoor conditions and conducting exergy analysis.

The current investigation is centered on the design of a novel LFSAH absorber plate, with a focus on assessing its exergetic performance through experiments conducted in Jamshedpur, India. The study seeks to accomplish the following objectives: Conduct experiments with different MFR using a louvered fin absorber plate.

  1. (i)

    Evaluate the performances based on second law efficiency.

  2. (ii)

    Analyze the SAH performances with different parameters of fin space and MFR.

  3. (iii)

    Evaluate the potential for exergy destruction and improvement at various parameters.

This objective aims to evaluate the magnitude of exergy destruction within the system and identify potential enhancements to improve the system’s performance. In summary, the primary goal of this study is to offer insights into the performance of a SAH featuring a louvered fin collector plate and to identify potential avenues for optimizing the system’s efficiency.

Methods

Experimental setup description

Figure 1 illustrates the schematic representation of a single-pass SAH. In this setup, both the louvered finned and smooth collectors were situated 5 cm above the base. Throughout the experiment, the air circulation through the collectors followed the converging segment, leading into the orifice meter for the measurement of airflow rate. Figure 2 presents the picture of both the finned and flat SAH. The collector’s outlet was linked to the wooden convergent section using GI pipes, an orifice meter, a flow control valve, and a 3-hp blower. Various flow rates were achieved by adjusting the flow control valve.

Fig. 1
figure 1

Diagram of the experimental arrangement

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Fig. 2
figure 2

Pictorial view of experimental arrangement

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Twenty-four thermocouples were fitted in order to measure the intake temperature (Tin), plate temperature (Tp), and exit temperature (Tout). To be more precise, each absorber plate’s temperature was monitored by five thermocouples (Fig. 3), and the air temperature inside the ducts was monitored by seven thermocouples that were positioned in a strategic manner. The locating of thermocouples across the test section for monitoring air and plate temperatures is depicted in Fig. 4. Furthermore, a pyranometer, as depicted in Fig. 5, was employed to gauge insolation levels throughout the experiment. The outdoor experiments were conducted from 9 am to 3 pm in January and February of 2018 on clear-sky days. A flow control valve was utilized in order to regulate the MFR inside the duct. Both channels were permitted to circulate air for a minimum of 120 min before data recording commenced. Subsequently, the flow was maintained at a constant rate, and data collection was initiated. Measurements of manometer, inlet temperature, wind speed, outlet temperature, and insolation were recorded at 30-min intervals, spanning from 9:00 am to 3:00 pm.

Fig. 3
figure 3

Absorber plates

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Fig. 4
figure 4

Thermocouple position in absorber and duct

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Fig. 5
figure 5

Pyranometer with digital display unit

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The airflow measurement in the duct is achieved using an orifice meter connected to a digital manometer, which is installed in line with the mild steel pipe. The orifice meter was calibrated by installing it in series with a calibrated orifice plate of known coefficient of discharge. The MFR of air was calculated based on the observed pressure drop in centimeters of water (cm H2O). The investigation’s MFR has been documented in Table 1.

Table 1 Measurement of MFR of air
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The pressure drop across the test length was measured using a digital micro manometer. J-type thermocouples coupled to a digital data recorder were used to monitor the temperature of the absorber plate, the exit and inlet air, and both. The data loggers from Countron have an accuracy of ± 1 °C. The thermocouples were calibrated under similar environmental conditions. A calibration test demonstrated that the thermocouple readings were accurate to within ± 1 °C.

The positions of the thermocouples for measuring air and plate temperatures over the test section are illustrated in Fig. 4. The pyranometer was also used to measure sun radiation.

Uncertainty analysis

A method for analyzing design and experimental measurement error is uncertainty analysis. Moreover, the error analysis shows a correlation between the error interval and the recorded experimental results. Kline and Mc Clintock [52] presented the uncertainty analysis. The experimental error measurement is shown in Table 2. The error in measurement of “\(\psi\)” may be stated as follows if the uncertainty of any criterion is determined using specific quantities:

$$\frac{\delta \psi }{\psi } = \left[ {\left( {\frac{\delta \psi }{{\partial y_{1} }}\delta y_{1} } \right)^{2} + \left( {\frac{\delta \psi }{{\partial y_{2} }}\delta y_{2} } \right)^{2} + ............. + \left( {\frac{\delta \psi }{{\partial y_{n} }}\delta y_{n} } \right)^{2} } \right]^{1/2}$$
(1)

where \(\delta \psi\) and \(y_{1}\), \(y_{2}\)……..\(y_{n}\). \(\frac{\delta \psi }{\psi }\) and \(\delta y_{1}\), \(\delta y_{2}\)……..\(\delta y_{n}\). The measurement errors are recognized as absolute uncertainty and relative uncertainty, respectively.

Table 2 Uncertainty analysis of different parameters
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Flow rate (\(\mathop m\limits^{.}\))

$$\mathop m\limits^{.} = C_{d} A_{o} \left[ {\frac{2\rho \Delta P}{{1 - \beta^{4} }}} \right]^{0.5}$$
(2)
$$\frac{{\delta \mathop m\limits^{.} }}{{\mathop m\limits^{.} }} = \left[ {\left( {\frac{{\delta C_{d} }}{{C_{d} }}} \right)^{2} + \left( {\frac{{\delta A_{o} }}{{A_{o} }}} \right)^{2} + \frac{1}{4}\left( {\frac{\delta \Delta P}{{\Delta P}}} \right)^{2} + \frac{1}{4}\left( {\frac{\delta \rho }{\rho }} \right)^{2} + \frac{1}{4}\left( {\frac{\delta \beta }{\beta }} \right)^{2} } \right]^{1/2}$$
(3)

Thermal efficiency (η)

$$\eta = \frac{{\mathop m\limits^{.} C_{p} (T_{o} - T_{i} )}}{{I \times A_{c} }}$$
(4)

Equation (1) shows the uncertainty analysis of efficiency calculation as a function of \(\mathop m\limits^{.}\), \(\Delta T\), and I where Ac and Cp are taken as constants.

$$\frac{\delta \eta }{\eta } = \left[ {\left( {\frac{{\delta \mathop m\limits^{.} }}{{\mathop m\limits^{.} }}} \right)^{2} + \left( {\frac{\delta \Delta T}{{\Delta T}}} \right)^{2} + \left( {\frac{\delta I}{I}} \right)^{2} } \right]^{1/2}$$
(5)

The uncertainty of η and ṁ are 0.0290 and 0.0278, respectively.

Exergetic performance analysis

The optimal utilization of energy can be achieved through the analysis of a system’s exergy, which is a highly useful concept. Such an analysis can facilitate the efficient operation and design of thermal systems. The 2nd law efficiency of a system is determined by the ratio of exergy gained to exergy input. It should be noted that the current analysis is subject to the following assumptions:

  1. 1.

    It is assumed that the system is in a state of steady-state.

  2. 2.

    The effects of potential energy (PE) and kinetic energy (KE) can be disregarded.

  3. 3.

    The system is assumed to be homogenous.

  4. 4.

    Air-specific heat always remain constant so we can consider it as ideal fluid.

  5. 5.

    The system experiences positive work transfer and heat transfer.

In general, the energy and exergy balance equations (Fig. 6), which usually neglect potential and kinetic energies, can be formulated in the form of rate equations [53,54,55]:

$$\sum {\dot{E}}_{i}=\sum \dot{{E}_{o}}$$
(6)
$$\left( {\sum {\mathop {Ex_{i} }\limits^{.} } - \sum {\mathop {Ex_{o} }\limits^{.} } } \right) = \sum {\mathop {Ex_{Loss} }\limits^{.} }$$
(7)

where

$$\sum {\mathop {Ex_{Loss} }\limits^{.} } = \left( {\sum {\mathop {Ex}\limits^{.}_{Loss(external)} + } \sum {\mathop {Ex}\limits^{.}_{{Dest({\text{int}} ernal)}} } } \right)$$
(8)
$$\sum {\mathop {Ex}\limits^{.}_{Dest} } = \sum {\mathop {Ex}\limits^{.}_{Heat} } - \sum {\mathop {Ex}\limits^{.}_{Work} } + \sum {\mathop {Ex}\limits^{.}_{Mass,in} } - \sum {\mathop {Ex}\limits^{.}_{Mass,out} } - \sum {\mathop {Ex}\limits^{.}_{Loss(external)} }$$
(9)
Fig. 6
figure 6

Exergy flow diagram for a solar air heater with louvered fins

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The Eq. (9) can also be simplified as:

$$\sum {\mathop {Ex}\limits^{.}_{Dest} } = \sum {\mathop {Ex}\limits^{.}_{Heat} - \mathop W\limits^{.} + } \sum {\mathop {m_{i} }\limits^{.} \psi_{i} } - \sum {\mathop {m_{o} }\limits^{.} \psi_{o} } - \sum {\mathop {Ex}\limits^{.}_{Loss(external)} }$$
(10)

From the Petela equation, exergy of insolation falling on glass cover, \(\sum {Ex_{Heat} }\) can be given as [56]:

$$\sum {Ex_{i} } = \sum {Ex_{Heat}} = IA_{c} \left[ {1 - \frac{4}{3}\left( {\frac{{T_{amb} }}{{T_{sun} }}} \right) + \frac{1}{3}\left( {\frac{{T_{amb} }}{{T_{sun} }}} \right)^{4} } \right]$$
(11)

Therefore, at the inlet and outlet, the specific exergy can be expressed as:

$${\Psi }_{o}=\left({h}_{o}-{h}_{e}\right)-{T}_{a}\left({S}_{o}-{S}_{e}\right)$$
(12)
$${\Psi }_{i}=\left({h}_{i}-{h}_{e}\right)-{T}_{a}\left({S}_{i}-{S}_{e}\right)$$
(13)

In Eq. (10), the external loss is calculated by the following equation [54]:

$$\sum {\mathop {Ex}\limits^{.}_{Loss(external)} = } \sum {\mathop {Ex}\limits^{.}_{Loss(optical)} } = (1 - \tau \alpha )IA_{c} \left[ {1 - \frac{4}{3}\left( {\frac{{T_{amb} }}{{T_{sun} }}} \right) + \frac{1}{3}\left( {\frac{{T_{amb} }}{{T_{sun} }}} \right)^{4} } \right]$$
(14)

From Eqs. (11), (12), (13), and (14), put in Eq. (10) and the resulting equation becomes:

$$\left[ {1 - \frac{4}{3}\left( {\frac{{T_{amb} }}{{T_{sun} }}} \right) + \frac{1}{3}\left( {\frac{{T_{amb} }}{{T_{sun} }}} \right)^{4} } \right]\mathop {Q_{c} }\limits^{.} - \mathop m\limits^{.} \left[ {(h_{o} - h_{i} ) - T_{a} (s_{o} - s_{i} )} \right] - (1 - \tau \alpha )IA_{c} \left[ {1 - \frac{4}{3}\left( {\frac{{T_{amb} }}{{T_{sun} }}} \right) + \frac{1}{3}\left( {\frac{{T_{amb} }}{{T_{sun} }}} \right)^{4} } \right] = \sum {\mathop {Ex}\limits^{.}_{Dest} }$$
(15)

where

$$\dot{Q}_{c} = IA_{C} \;{\text{and}}\;\dot{W} = 0$$
(16)

The variations in the entropy and enthalpy of the air can be written as:

$$\Delta s_{air} = s_{o} - s_{i} = C_{pf} ln\frac{{T_{fo} }}{{T_{fi} }} - Rln\frac{{P_{o} }}{{P_{i} }}$$
(17)
$${\Delta h}_{air}={h}_{o}-{h}_{i}={C}_{pf}\left({T}_{fo}-{T}_{fi}\right)$$
(18)

The following expression is obtained by putting the Eqs. (16), (17), and (18) in Eq. (15).

$$\begin{array}{ll}\left[1-\frac{4}{3}\left(\frac{T_{amb}}{T_{sun}}\right)+\frac{1}{3}\left(\frac{T_{amb}}{T_{sun}}\right)\right]IA_c-mC_{pf}(T_{fo}-T_{fi})+mT_a\left(C_{pf}mathrm{ln}\frac{T_{fo}}{T_{fi}}-R\mathrm{ln}\frac{P_o}{P_i}\right)-\\(1-\tau\alpha)IA_c\left[1-\frac{4}{3}\left(\frac{T_{amb}}{T_{sun}}\right)+\frac{1}{3}\left(\frac{T_{amb}}{T_{sun}}\right)^4\right]=\sum Ex_{dest}\end{array}$$
(19)

The exergetic efficiency of SAH [51]:

$$\eta_{2nd} = \left( {\frac{{\sum {\mathop {Ex}\limits^{.}_{o} } }}{{\sum {\mathop {Ex}\limits^{.}_{i} } }}} \right) = \left( {1 - \frac{{\sum {\mathop {Ex}\limits^{.}_{Loss} } }}{{\sum {\mathop {Ex}\limits^{.}_{i} } }}} \right)$$
(20)

In the context of exergetic analysis of different processes or systems, Van Gool [57] proposed the concept of “Improvement Potential,” which is expressed as follows:

$$\mathop {IP}\limits^{.} = (1 - \eta_{2nd} )\mathop {Ex}\limits^{.}_{Dest}$$
(21)

Results and discussion

Experimental research on the effects of LFSAH at various fin spacings has been conducted in Jamshedpur, India, during the winter months of January and February 2018. Jamshedpur, an Indian city, is situated at the geographical coordinates of 22.77° N and 86.14° E. The experiment involved testing different louvered fin spacings, with MFR from (0.007 to 0.0158) kg/s. Table 3 presents the design and operating parameters that were taken into account for the analysis.

Table 3 System and operating parameters
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Figure 7 illustrates how insolation changes throughout the day for varying fin spacing ranging from 2 to 5 cm, and the range of MFR 0.007 to 0.015 8 kg/s, at which the experiment is performed. In solar collectors, the quantity of instantaneous radiation serves as a crucial parameter. The intensity of solar radiation begins to rise at dawn and reaches its peak at noon, followed by a gradual decline. In February, the peak insolation value is 866.37 W/m2 at 12:30 pm. Compared to February, January exhibited the lowest ambient temperature. Furthermore, the average solar intensity for experiments conducted on louvered fins with pitch of 2 to 5 cm were 650.03, 600.62, 565.66, and 589.06 W/m2, respectively.

Fig. 7
figure 7

Variation of solar Intensity with standard daytime for fins pitch of a 2 cm, b 3 cm, c 4 cm, and d 5 cm at different MFR from 0.007 to 0.0158 kg/s

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Figure 8 displays the correlation between exergy efficacy and various time periods, and different MFR (0.007–0.0158) kg/s, and fin spacings ranging from 2 to 5 cm for both LFSAH and PSAH. The outcomes indicate that the highest exergy efficiency is achieved between 12:00 to 1:00 h, following which it gradually decreases. It has been observed that LFSAH outperforms PSAH in terms of exergy efficiency across all fin spacings. Exergy efficiencies of 3.31%, 2.3%, and 0.93% were achieved for fin spacings of 2 cm, 5 cm, and PSAH, respectively, at an MFR of 0.007 kg/s. Moreover, there were observed exergy efficiency variations of around 2.5 and 1.47 times compared to PSAH for fin spacings of 2 cm and 5 cm, respectively.

Fig. 8
figure 8

Variation in exergy efficiency at different MFR for various fin spacings, namely a 2 cm, b 3 cm, c 4 cm, d 5 cm, and e PSAH

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In Fig. 9, the exergetic performance pattern for all experiments conducted that day is displayed for PSAH, 2 cm and 5 cm fin spacings. The results indicate that as the MFR increased from 0.007 to 0.0158 kg/s, the exergetic performance of all collector types decreased. Additionally, compared to the PSAH and LFSAH with a spacing of 5 cm, 2 cm displayed superior exergy efficiency.

Fig. 9
figure 9

The variation on exergy efficiency for entire days of experiments at fin spacing 2 cm, 5 cm, and PSAH

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The comparison between the exergy efficiency of louvered fins with varying spacing and PSAH at different MFR is presented in Fig. 10. The graph highlights that the exergy efficiency decreases with increasing MFR. A fin spacing of 2 cm exhibits a significantly higher exergy efficiency of 3.3% compared to 2.3% and 0.93% for fin spacings of 5 cm and PSAH, respectively. This trend remains consistent even at a lower MFR of 0.007 kg/s. The cause of this effect is the absorption of insolation by the collector, resulting in higher exergy loss and lower exergy efficiency values, regardless of the MFR values. This trend is particularly evident at higher MFR, where the high pump work required outweighs the exergy of heat energy collected.

Fig. 10
figure 10

Demonstrates the relationship between exergy efficiency and MFR for various louvered fin spacings

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Figure 11 shows that the exergy destruction of louvered fins pitch at 2 to 5 cm and PSAH at varying MFR. This result leads to the increasing nature of the exergy destruction with MFR. This behavior is similar to compared with PSAH. The reason for this is that at higher values of MFR, the exergy losses due to friction and pressure also increase, resulting in the exergy input not being able to overcome these losses. To increase the amount of useful work that can be obtained from the system and reduce exergy destruction, the performance of the collector can be improved.

Fig. 11
figure 11

MFR versus exergy destruction for various louvered fin spacings

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Figure 12 shows that the improvement potential of louvered fins pitch at 2 to 5 cm and PSAH at varying MFR. This result leads to the increasing nature of the improvement potential with MFR. This behavior is similar to compared with PSAH. From Fig. 12, it can be observed that as the MFR increases, the system needs to have more improvement potential.

Fig. 12
figure 12

Effect on improvement potential at various MFR for different fin spacing

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To ensure the precision of the outcomes, it is necessary to validate the results, a comparison was conducted between the exergy efficiency of the present PSAH and the LFSAH proposed by Sabzpooshani et al. [58]. Figure 13 illustrates this comparison, with the mean deviations of exergy efficiency between the two systems calculated to be 13.8%. The results revealed that, for an MFR ranging from 0.007 to 0.0158 kg/s, the average enhancement in exergy efficiency for the LFSAH was 3.7 times higher than that of the PSAH. These findings suggest that the current experimental work is consistent with the findings of Sabzpooshani et al. [58], which provides greater confidence in the extension of the present research of louvered fin discussed in this research.

Fig. 13
figure 13

Comparison between the exergy efficiency of this study and that of Sabzpooshani et al. [58]

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The current study is contrasted with prior research in Table 4. The experimental results from both the present investigation and the earlier study indicate that the LFSAH demonstrates superior performance.

Table 4 Comparison of current work with preceding works
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The exergy analysis results for LFSAH, acquired in Jamshedpur, Jharkhand, during the months of January and February 2018, are displayed in Table 5. From Eq. (11) to Eq. (13), exergy inlet and exergy outlet were calculated. In addition to this, the exergy optical losses, exergy destruction and second law efficiency and improvement potential (IP) were calculated from Eq. (14), Eq. (19), Eq. (20), and Eq. (21), respectively. Exergy losses were computed across different fin spacings and Flow Rates. It is crucial to emphasize that the maximum exergy loss occurred with a fin spacing of 5 cm at a flow rate of 0.0158 kg/s, whereas the minimum exergy loss was noted with a fin spacing of 2 cm at a flow rate of 0.007 kg/s. Furthermore, the exergetic performance of each fin spacing was assessed, revealing that the highest exergetic efficiency was attained with a fin spacing of 2 cm at a flow rate of 0.007 kg/s. Conversely, the minimum exergetic efficiency was noted for the fin spacing of 5 cm at a flow rate of 0.0158 kg/s.

Table 5 Exergy analysis of louvered fin SAH
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Conclusions

This study entails conducting experimental investigations to evaluate the exergy efficiency of LFSAH under various operating conditions. The experimental assessments cover different MFR and fin spacings varying from 0.007 to 0.0158 kg/s and 2 to 5 cm, respectively.

The results have led to the following conclusions.

  1. 1.

    The experimental findings lead to the conclusion that the louvered fin spacing outperforms the PSAH.

  2. 2.

    The addition of louvered fins leads to a significant improvement in exergy efficiency when compared to PSAH for all MFR ranges.

  3. 3.

    The result revealed that the fin spacing of 5 cm in which the exergy loss is maximum for MFR of 0.0158 kg/s and the fin spacing 2 cm exergy loss is minimum at MFR of 0.007 kg/s.

  4. 4.

    The highest exergetic efficiency has been observed for the fin spacing 2 cm at 3.94% for MFR of 0.007 kg/s and the lowest exergetic efficiency has been found in fin spacing 5 cm at MFR of 0.0158 kg/s.

  5. 5.

    The exergy efficiency is improved by the attachment of louvered fins at the lower MFR, but as the MFR and fin spacing increased, the percentage of exergy efficiency decreases.

  6. 6.

    The exergy performance is enhanced by increasing the insolation, and the variations in exergy efficiency with MFR remain unchanged irrespective of the insolation.

  7. 7.

    In this study, various system and operating parameters have been addressed. However, there remain some aspects that could be explored in further studies. Investigating different geometries of louvered fins, such as corrugated or wavy louvered fins, could provide additional insights into enhancing heat transfer characteristics.