Introduction

In today’s rapidly evolving world, there is a growing demand for clean energy due to concerns related to climate change, industrialization, and population growth [1,2,3]. Among renewable energy sources, solar energy stands out with its unparalleled output capacity and versatility, making it a viable option for use in virtually any location. In PVT systems, solar energy is effectively converted into both electricity and thermal power [4,5,6]. Here’s how it works: PV panels within PVT systems harness solar radiation, converting it into electrical power. Meanwhile, a cooling fluid circulates within tubes, absorbing any excess heat generated during the PV conversion phenomena [7,8,9]. While air or water can augment the efficiency, the extent of improvement is limited by their relatively low thermal conductivity. In contrast, cooling fluids based on nanotechnology offer superior thermophysical properties and heat extraction capabilities compared to conventional fluids [10,11,12]. Moreover, altering the style of the fluid channel was identified as a means to enhance the overall performance. Various studies have explored the installation of cooling channels with diverse cross-sections and the utilization of nanofluids as coolants [13,14,15]. Numerous researchers have introduced innovative ways to intensify the productivity of mechanical units [16,17,18]. They have developed numerical and optimization procedures aimed at achieving greater efficiency in these systems [19, 20]. Instead of using water, hybrid [21] and ternary [22] nanofluids can serve as the working fluids, enhancing the performance of PVT systems, particularly when used with confined jets. Additionally, a greater temperature difference across the two sides of the thermoelectric component coupled with the PV can be achieved with these testing fluids in the solar system. Madas et al. [23] scrutinized the implement of CuO nanomaterial in a PVT unit. Input parameters included fluid flow rates ranging from 60 to 120 kg h−1 and nanofluid volume concentrations from 0.1 to 0.5%. The outputs indicated a 1.36% increase in electrical efficiency when the mass flow rate increased from 60 to 120 kg h−1.

Sheikholeslami and Khalili [24] evaluated the CO2 mitigation achieved by utilizing a new solar system. Their research demonstrated that a PVT system can effectively reduce CO2 emissions when a nanofluid is used as the working fluid. In their study, Song et al. [25] investigated the feasibility of a system integrating PV technology, thermoelectric generators, and phase change materials, known as PV-TEG-PCM. Comparing the productivity of PV-TEG-PCM systems to that of TEG-PV or stand-alone PV systems, it was evident that the former outperformed the latter. Touti et al. [26] conducted a study to evaluate how six proposed designs impact the efficiency of an air-based system. Their findings indicated a decrease in TPV about 10.87 °C, with the most effective design achieving a total efficiency of 58.48%. Sheikholeslami and Khalili [27] introduced an innovative cooling duct design and used eco-friendly nanofluids to improve heat absorption from the silicon layer. They demonstrated that the productivity of the system could be meaningfully enhanced with this new duct shape and the incorporation of nanomaterials. Kandil et al. [28] investigated both experimental and theoretical analyses, exploring PVT with beam-splitting configuration. The results reveal that the average efficiency for the stand-alone system is around 13%. Sheikholeslami and Khalili [29] formulated the governing equations necessary for modeling a panel with a nanofluid filter in a concentrated PVT system. Their findings demonstrated that equipping the panel with this filter significantly enhances its performance. Studies by Cherif et al. [30] have demonstrated the benefits of using a tree-shaped duct heat sink and a rectangular channel with a water–TiO2 nanofluid for cooling. Sheikholeslami et al. [31] assessed the negative impact of dust on the performance of the system. To mitigate this, they employed a permeable duct to enhance the cooling system’s efficiency and coupled it with a heat sink. After 1 year, they refined their approach, implementing new techniques to further improve performance. In a subsequent study, Sheikholeslami et al. [32] became the first team to use sustainable material as a thermoelectric module within a PVT system. They also used a spectral filter above the panel to achieve higher electrical output. A pioneering hybrid system, as outlined by Lu et al. [33], integrates a CPVT with both a TEG and a TEC. When maximizing the performance enhancement of the hybrid system across its operational range, the energy efficiency and exergy efficiency reach 0.0251 and 0.0255, respectively. These values represent an improvement of 3.72% and 3.66% compared to the stand-alone CPVT.

The study presented in this article focuses on an innovative environmental and economic analysis of a solar PV panel system combined with a finned paraffin container. This system incorporates advanced materials and design modifications to enhance its performance. The paraffin, used as a PCM (phase change material), is enhanced with a mixture of lauric acid and MWCNT nanomaterial to improve its thermal conductivity. The study examines three different fin shapes to optimize the melting rate of the PCM, which is crucial for maintaining the operational efficiency of the PV panels. Additionally, the system incorporates a nanofluid duct, containing water mixed with MWCNT nanoparticles, to facilitate better cooling of the PV panels. The design is further optimized by placing flat mirrors beneath the panel to reflect additional sunlight, thereby increasing the overall solar irradiance received by the PV cells. The novelty of this research lies in its comprehensive approach to integrating advanced thermal management solutions with solar PV technology. The previous studies have explored various methods to enhance PV panel efficiency, such as using PCM and nanomaterial independently. However, this study is unique in its combined use of finned PCM containers, nanofluids, and reflective mirrors, creating a synergistic effect that significantly boosts the system’s overall performance. The homogeneous mixture formulation used to determine the properties of the working materials, along with the detailed mathematical modeling and simulation using ANSYS FLUENT, further underscores the innovation in this approach. The research gap addressed by this study involves the lack of integrated solutions that combine multiple advanced materials and design strategies to enhance solar PV efficiency. While the previous publications have focused on individual enhancements, such as using PCMs for thermal regulation or nanofluids for cooling, there has been limited exploration into how these elements can be synergistically combined. This study fills that gap by demonstrating how integrating finned PCM containers, nanofluid cooling ducts, and reflective mirrors can lead to substantial improvements in both thermal management and electrical output. The importance of this research is underscored by its potential impact on the renewable energy sector. By improving the efficiency and sustainability of solar PV systems, this study addresses both economic and environmental concerns. Compared to the previous publications, this study provides a more holistic solution to the challenges faced by solar PV technology, offering a promising pathway toward more efficient and sustainable energy systems. In summary, this research represents a significant advancement in solar PV technology by integrating multiple innovative strategies to enhance system performance. It addresses existing gaps in the literature by combining advanced materials and design modifications in a novel manner. The results demonstrate substantial improvements in both economic viability and environmental impact, highlighting the potential for these integrated solutions to contribute meaningfully to the global transition to renewable energy.

Assessment of present solar system

In this article, an environmental and economic analysis of a PVT combined with a finned paraffin container is presented. The paraffin, used as the PCM, is enhanced with a mixture of lauric acid and multi-walled carbon nanotube (MWCNT) nanoparticles to improve thermal conductivity. To optimize the melting rate of the PCM, three different fin geometries are examined. The PV panel system includes a nanofluid duct containing a mixture of water and MWCNT nanoparticles, alongside the PCM container. Additionally, the system is enhanced by the strategic arrangement of flat mirrors beneath it, which reflect sunlight onto the panel, thereby increasing its exposure to solar radiation. To accurately determine the properties of the working materials, a homogeneous mixture formulation is applied. The mathematical model developed for this study deliberately neglects the impact of gravity to simplify the analysis. ANSYS FLUENT is employed for the numerical modeling of the system. The primary objectives of this study are to evaluate four key performance metrics: payback period, carbon credit, CO2 mitigation, and electrical power output. These metrics are calculated for all three fin geometries at two different inlet velocities of the nanofluid within the circular duct. The other geometric parameters are consistent with those outlined in Reference [34]. The system configurations explored in this study include three distinct cases, as illustrated in Fig. 1. The MWCNT–paraffin mixture utilized as the nano-enhanced PCM (NEPCM) adheres to the properties specified in Reference [34]. Similarly, the details regarding the arrangement of mirrors follow the same parameters as outlined in the aforementioned reference. This research aims to bridge the gap in current solar PV technology by integrating advanced materials and design innovations to enhance system performance. The previous studies have explored the use of PCMs and nanofluids individually; however, this study uniquely combines these elements with a finned enclosure and reflective mirrors, creating a more efficient and sustainable solar energy system. By investigating the environmental and economic impacts of this novel cooling system, this research contributes to the advancement of solar energy technology, offering practical solutions for improving energy efficiency and reducing carbon emissions.

Fig. 1
figure 1

The studied PVT-NEPCM system

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The equations for modeling layers of PV are as follows [34]:

$$ \chi^{*} + \nabla (k_\text{s} T) = \left( {\rho C_\text{p} } \right)_\text{s} \frac{\partial T}{{\partial t}} $$
(1)
$$ \chi_\text{g}^{*} = \alpha_\text{g} A\,G $$
(2)
$$ \chi_{{{\text{EVA1}}}}^{*} = \alpha_{{{\text{EVA}}}} A\,\tau_\text{g} G $$
(3)
$$ \chi_{{{\text{PV}}}}^{*} = \alpha_{{{\text{pv}}}} A\,\tau_{{{\text{EVA}}}} F\,G\,\tau_\text{g} \left( {1 - \eta_{{{\text{ele}}}} } \right) $$
(4)
$$ \chi_{{{\text{EVA2}}}}^{*} = \alpha_{{{\text{EVA}}}} \,\tau_{{{\text{EVA}}}} A\,\tau_\text{g} \left[ {\tau_{{{\text{pv}}}} F + (1 - F)} \right]G $$
(5)

For simulating the nanofluid zone, below formula has been solved [35]:

$$ \frac{{\partial \rho_{{{\text{nf}}}} }}{\partial t} + \nabla .(\rho_{{{\text{nf}}}} \vec{V}_{{{\text{nf}}}} ) = 0 $$
(6)
$$ \nabla .(\mu_{{{\text{nf}}}} \nabla \vec{V}_{{{\text{nf}}}} ) - \nabla P = \left[ {(\vec{V}_{{{\text{nf}}}} .\nabla )\vec{V}_{{{\text{nf}}}} + \frac{{\partial \vec{V}_{{{\text{nf}}}} }}{\partial t}} \right]\left( {\rho_{{{\text{nf}}}} } \right) $$
(7)
$$ \nabla .(k_{{{\text{nf}}}} \nabla T_{{{\text{nf}}}} ) = \left[ {\frac{{\partial T_{{{\text{nf}}}} }}{\partial {\text{t}}} + (\vec{V}_{{{\text{nf}}}} .\nabla )T_{{{\text{nf}}}} } \right]\left( {\rho C_\text{P} } \right)_{{{\text{nf}}}} $$
(8)

For PCM zone, the following equations have been applied [36]:

$$ \frac{{\partial \rho_{{{\text{NEPCM}}}} }}{\partial t} + \nabla .(\rho_{{{\text{NEPCM}}}} \vec{V}_{{{\text{NEPCM}}}} ) = 0 $$
(9)
$$ \begin{gathered} \left[ {\frac{{\partial \vec{V}_{{{\text{NEPCM}}}} }}{\partial {\text{t}}} + (\vec{V}_{{{\text{NEPCM}}}} .\nabla )\vec{V}_{{{\text{NEPCM}}}} } \right]\rho_\text{NEPCM} = \nabla .(\mu_{{{\text{NEPCM}}}} \nabla \vec{V}_{{{\text{NEPCM}}}} ) - \nabla P \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - \underbrace {{\frac{{\left( {1 - \lambda } \right)^{2} }}{{\left( {\lambda^{3} - 0.001} \right)}}A_{{{\text{mush}}}} \vec{V}}}_\text{S} \hfill \\ \end{gathered} $$
(10)
$$ \left[ {\frac{{\partial T_{{{\text{NEPCM}}}} }}{\partial t} + \nabla .(\vec{V}_{{{\text{NEPCM}}}} .T_{{{\text{NEPCM}}}} )} \right]\left( {\rho C_\text{p} } \right)_{{{\text{NEPCM}}}} = \nabla .(k_{{{\text{NEPCM}}}} \nabla T_{{{\text{NEPCM}}}} ) - \frac{{\partial \left( {\lambda \rho L} \right)_{{{\text{NEPCM}}}} }}{\partial t} $$
(11)
$$ \lambda = \left\{ \begin{gathered} \frac{{T_\text{s} - T}}{{T_\text{s} - T_{\text{l}} }}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,T_\text{s} \, < T < T_{\text{l}} \hfill \\ \hfill \\ 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,T < T_\text{s} \hfill \\ \hfill \\ 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,T > T_{\text{l}}\hfill \\ \end{gathered} \right. $$
(12)

The efficiency of PV can be measured as [34]:

$$ \eta_{{{\text{ele}}}} = \eta_{{{\text{ref}}}} \left[ {1 - 0.0045\,(T_{{{\text{PV}}}} - 298.15)} \right],\,\,P_{{{\text{out}}}} = \eta_{{{\text{ele}}}} {\text{GA}} $$
(13)

To calculate the required functions for assessment of system, below equations have been applied [37]:

$$ \begin{gathered} {\text{Embodied}}\,{\text{energy}} = \frac{{{\text{Capital}}\,{\text{cost}}}}{0.14} \hfill \\ {\text{Pyaback}}\,{\text{period}} = \frac{{{\text{Embodied}}\,{\text{energy}}}}{{P_{{{\text{out}}}} }} \hfill \\ {\text{CC}}({\text{Carbon}}\,{\text{credit}}) = {\text{Net}}\,{\text{CO}}_{2} \,{\text{mitigation}} \times \,{\text{price}}\,{\text{per}}\,{\text{tons}}\,{\text{of}}\,{\text{CO}}_{2} \,{\text{mitigation}} \hfill \\ \end{gathered} $$
(14)

Results and discussion

This article presents a comprehensive environmental and economic analysis of PVT combined with a finned paraffin container. The paraffin used as the PCM is enhanced with a mixture of lauric acid and multi-walled carbon nanotube (MWCNT) nanoparticles to improve thermal conductivity. The study examines three different fin shapes to optimize the melting rate of the PCM, which is crucial for maintaining the operational efficiency of the PV panels. Additionally, the system incorporates a nanofluid duct, containing water mixed with MWCNT nanoparticles, to facilitate better cooling of the PV panels. The design is further optimized by placing flat mirrors beneath the panel to reflect additional sunlight, thereby increasing the overall solar irradiance received by the PV cells. The properties of the working materials are determined through a homogeneous mixture formulation, and a detailed mathematical model has been developed to simulate the system, with the impact of gravity being neglected for simplification. The simulations are carried out using ANSYS FLUENT, a robust software for handling complex fluid and thermal analyses. The primary objectives of this research are to calculate four key functions for each fin geometry at two different nanofluid inlet velocities: payback period, carbon credit, CO2 mitigation, and electrical power output. This analysis helps in understanding the economic viability and environmental impact of the proposed solar PV system. By integrating finned paraffin containers and using nanofluid ducts, the study aims to improve heat management, which is critical for maintaining the performance of PV panels. Additionally, the use of flat mirrors to increase sunlight exposure further boosts the unit’s efficiency. This work is crucial in the context of renewable energy advancements, as it addresses both economic and environmental concerns associated with solar energy units. The primary aim of this study is to evaluate the payback period, carbon credit, CO2 mitigation, and electrical power for the three fin geometries and two nanofluid inlet velocities. The payback period refers to the time required for the system to recover its initial investment through savings and earnings. Carbon credit quantifies the amount of carbon dioxide emission reduction credited to the system, while CO2 mitigation measures the total amount of carbon dioxide emissions prevented by using the system. Electrical power output indicates the power generated by the PV unit. These metrics are essential for assessing the economic feasibility and environmental benefits of the planned PV unit. The findings from this study provide valuable insights into how advanced materials and innovative design modifications can significantly enhance the performance and sustainability of solar energy systems. By addressing these aspects, the research contributes to the broader field of renewable energy, offering a promising solution to intensify the efficiency and environmental impact of solar PV technology. This work is crucial for advancing renewable energy technologies, providing both economic and environmental benefits, and supporting the global transition to cleaner energy sources.

Figure 2 shows the validation test presented for the current computational code. The outcomes obtained by the code are compared with the results obtained from Reference [36], focusing on the liquid fraction at different time stages. The comparison reveals a high level of agreement between the outputs, indicating good alignment between the computational models used in this study and the established reference. This validation confirms the capability of the code to accurately model the phenomena under investigation in the present study. It instills confidence in the reliability and accuracy of the computational approach adopted for analyzing the solar photovoltaic panel system with the integrated cooling system. The electrical power outputs for various cases are depicted in Fig. 3. Electrical power generation is the primary objective of a photovoltaic (PV) system, and this factor can be significantly influenced by the inclusion of a cooling system. Over time, from 15 to 90 min, the electrical power output for Case B at Re = 750 changes from 211.8 to 194.66 W. Similarly, for Case A at Re = 750, the power output changes from 210.94 to 190.76 W, and for Case C at Re = 750, it changes from 210.82 to 190 W. Increasing the Re enhances the productivity, leading to an increase in electricity production. In fact, the amount of power approximately doubles with an increase in Re. Case B demonstrates the highest electrical power output, indicating the superior performance of its cooling system. This suggests that the design and efficiency of the cooling system play a crucial role in maximizing electrical power generation in the PV system. By optimizing the cooling system design and flow conditions, significant improvements in electrical power output can be achieved, contributing to the economic viability and sustainability of solar energy systems.

Fig. 2
figure 2

Validation of PVT-PVM system [36]

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Fig. 3
figure 3

Variation of the electrical power versus time

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The variation of CO2 mitigation (CM) over time for various cases is illustrated in Fig. 4. Utilizing this solar system significantly reduces CO2 emissions, offering substantial environmental benefits. As time progresses with a Reynolds number (Re) of 750, the amount of CM decreases by approximately 9.56% for Case A, 8.09% for Case B, and 9.87% for Case C. Increasing the Reynolds number generally enhances CM, with Case B showing an increase of about 1.89% in CM. Among the cases analyzed, Case B is the most effective in terms of CM, while Case C is the least effective. Transitioning from Case C to Case B results in a 2.44% improvement in CM. These results underscore the importance of optimizing the solar PV system’s design and operational parameters to maximize environmental benefits. Case B’s superior performance highlights its potential for significantly reducing CM, making it the most environmentally friendly configuration. Conversely, Case C’s lower performance suggests that its design is less effective in promoting CM. Increasing the Reynolds number positively impacts CM across all configurations, emphasizing the need for optimized flow conditions to maximize environmental gains. Careful selection of fin geometry and adjustment of the nanofluid flow rate are crucial for enhancing the system’s ability to mitigate CO2 emissions. Overall, these findings highlight the critical role of advanced design and operational strategies in achieving both economic and environmental objectives in solar energy systems.

Fig. 4
figure 4

Variation of CO2 mitigation versus time

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The variation of carbon credit (CC) over time for various cases is depicted in Fig. 5. Case B shows the highest carbon credit, ranging from $420.69 to $386.65 as time increases from 15 to 90 min when Re = 750. Over time, the carbon credit for Case C declines by approximately 9.87%, representing the lowest value among all cases. An increase in Reynolds number (Re) generally enhances the carbon credit for all cases; for instance, there is an increase of about 2.07% for Case A. When the geometry is changed from Case B to Case C, the carbon credit decreases by approximately 2.39% at Re = 750. These results highlight the critical role of system configuration and flow conditions in determining the environmental benefits of the solar PV system. Case B consistently demonstrates superior performance in terms of carbon credit, indicating its effectiveness in reducing CO2 emissions over time. The decline in carbon credit for Case C suggests that its design is less efficient in promoting environmental benefits. Increasing the Reynolds number positively impacts carbon credit across all configurations, emphasizing the importance of optimizing flow conditions to maximize environmental benefits. By carefully selecting the fin geometry and adjusting the flow rate of the nanofluid, it is possible to enhance the system’s carbon credit, thereby contributing more significantly to CO2 mitigation efforts.

Fig. 5
figure 5

Variation of carbon credit versus time

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The variation of the payback period over time is illustrated in Fig. 6. As time progresses, the payback period increases, with higher Reynolds numbers (Re) yielding greater outputs. Specifically, Case C exhibits the most significant increase in payback period over time, with an increase of approximately 10.95% at Re = 750 and 9.14% at Re = 1250. As Re increases, the payback period decreases by approximately 2.03% for Case A, 1.85% for Case B, and 2.98% for Case C. Among the cases studied, Case B has the shortest payback period, whereas Case C has the longest. Transitioning from Case B to Case C results in an increase in payback period of about 2.44% at Re = 750 and 2.2% at Re = 1250. These results indicate that the system’s economic efficiency is influenced by the Reynolds number and the specific case configuration. Higher Reynolds numbers generally improve the economic feasibility by reducing the payback period, thus leading to quicker returns on investment. However, the effectiveness of this reduction varies between different configurations, with Case B consistently showing better performance in minimizing the payback period. This analysis highlights the importance of optimizing the cooling system design and flow conditions to achieve the most economically viable solar PV system. By carefully selecting the fin geometry and managing the flow rate of the nanofluid, significant improvements in both payback period and overall system efficiency can be achieved. These findings emphasize the need for detailed evaluation of design parameters to maximize the economic benefits of advanced solar energy systems.

Fig. 6
figure 6

Variation of payback period versus time

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Conclusions

Current article demonstrates an environmental and economic assessment of a solar PVT combined with a finned paraffin container. The paraffin, used as the PCM, is enhanced with a mixture of lauric acid and multi-walled carbon nanotube (MWCNT) nanoparticles to improve thermal conductivity. The study examines three different fin shapes to optimize the melting rate of the PCM, which is crucial for maintaining the operational efficiency of the PV panels. Additionally, the system incorporates a nanofluid duct containing water mixed with MWCNT nanoparticles to facilitate better cooling of the PV panels. The design is further optimized by placing flat mirrors beneath the panel to reflect additional sunlight, thereby increasing the overall solar irradiance received by the PV cells. The properties of the working materials are determined through a homogeneous mixture formulation, and a detailed mathematical model has been developed to simulate the system, with the impact of gravity being neglected for simplification. The simulations are carried out using ANSYS FLUENT, a robust software for handling complex fluid and thermal analyses. The primary objectives of this research are to calculate four key functions for each fin geometry at two different nanofluid inlet velocities: payback period, carbon credit, CO2 mitigation, and electrical power output. By integrating finned paraffin containers and using nanofluid ducts, the study aims to improve heat management, which is critical for maintaining the performance of PV panels. Additionally, the use of flat mirrors to increase sunlight exposure further boosts the system’s efficiency. This work is crucial in the context of renewable energy advancements, as it addresses both economic and environmental concerns associated with solar energy systems. The primary aim of this study is to evaluate the payback period, carbon credit, CO2 mitigation, and electrical power for the three fin geometries and two nanofluid inlet velocities. The payback period refers to the time required for the system to recover its initial investment through savings and earnings. Carbon credit quantifies the amount of carbon dioxide emission reduction credited to the system, while CO2 mitigation measures the total amount of carbon dioxide emissions prevented by using the system. Electrical power output indicates the power generated by the PV system. These metrics are essential for assessing the economic feasibility and environmental benefits of the proposed PV system. The findings from this study provide valuable insights into how advanced materials and innovative design modifications can significantly enhance the performance and sustainability of solar energy systems. In conclusion, this research contributes significantly to the broader field of renewable energy by offering a promising solution to improve the efficiency and environmental impact of solar PV technology. The integration of advanced nanomaterials and intelligent design strategies marks a significant step forward in the development of more efficient and sustainable solar energy systems. The results demonstrate that the proposed system not only enhances the productivity of the PV panels but also provides substantial environmental benefits by reducing CO2 emissions and earning carbon credits. This work supports the global transition to cleaner energy sources, offering economic and environmental advantages that align with the goals of sustainable development. The innovative approach presented in this study could pave the way for future advancements in solar energy technologies, contributing to a more sustainable and energy-efficient world.