2.1. Model Description

The pilot’s focus is on enhancing the electrical efficiency of a monocrystalline PV module, specifically on the specific hot day of the summer (summer solstice [June 21, 2023]). The chosen site is the Sunder Industrial Estate in Lahore, known for its vast industrial zone with a prevailing trend of PV system installations. There is a significant concern about the loss of electrical potential due to elevated PV surface temperatures during operational conditions [24]. The selected model, featuring 120 half-cut cells, is depicted in Figure 1a, with panel dimensions (length: 2172.00 ± 0.50 mm, width: 1303.00 ± 0.50 mm) provided by the manufacturer [32]. The half-cell dimensions (length: 210.00 ± 0.50 mm, width: 102.00 ± 0.50 mm) can be observed in the same figure as well. The CAD modeling of this PV system is finalized using SolidWorks software. In Figure 1b, the quarter of the entire PV panel is designated and agreed for SSTA, aimed at managing computational time. The dimensions for this segment are specified as 1086.00 ± 0.50 mm for length and 651.00 ± 0.50 mm for width of the selected PV system with 30 half-cut cells. Further approximation is approved, reducing the number of cells to only 10 in a row, facilitating the examination of forced and natural heat conduction and convection and their impact on the complete PV system’s performance. The electrical properties of the monocrystalline PV panel are detailed in Table 1. Solar flux value of 957.33 W/m², calculated analytically using equations from the previous article [33], for solving the concerned problem of temperature profile visualization at mid-day of summer solstice. According to the manufacturer’s directions, only 22.33% of the radiation is converted into electricity while the remaining solar radiation generates heat on the surface of the panel, thereby reducing its available electrical potential. Although the recommended PV surface temperature range given by the manufacturer is between approximately −40 and 85°C, the aim to maintain this surface temperature around 25.0°C is a potential driver behind this study. Figure 2a further illustrates the design with module length and width of 1086.00 ± 0.50 mm and 220.00 ± 0.50 mm on a respective note with a subsequent detail of single and dual-layer MCHSs in Figure 2b,c. These MCHSs are provided at the end of the panel to absorb generated heat at the PV layer which is a source of heat generation among other layers of the PV module. Only six layers are selected from top to bottom as glass, encapsulated ethylene-vinyl acetate (EVA) front layer, PV cells layer followed by the encapsulated back EVA layer, absorber plate, and finally aluminum MCHSs. These two-layer configurations of MCHSs are introduced with squared design to maintain the temperature uniformity of the cell, which otherwise deteriorates the PV cells material. Their thermophysical and configuration properties are also given in Tables 1 and 2, respectively. Regarding coolant selection, water is selected because of higher thermal management capability, and economical availability as compared to other working fluids.

2.2. Hypothetical Analysis

2.3. Governing Equations

2.4. LCOE

The degradation rate d is incorporated into the equation to account for the gradual decline in the PV system’s output over time due to environmental and climatic factors. The financial parameters used in this calculation, including capital initial investment and operational costs, were sourced from the studies [29, 34] and listed in Table 3. Moreover, a 4.36 kWh/m² irradiance value [38] on the average scale for a Lahore-based location and a performance ratio of 80% are considered.

2.5. Grid Sensitivity Test

All CFD domains underwent testing with varying numbers of elements using linear meshing order, and the final counts of elements and nodes are presented in Table 4. The SSTA achieved a temperature profile with 923,869 elements, and meshing elements for MCHSs and working fluid streams (WFSs) were suppressed during setup. In subsequent single-layer MCHSs arrangement within the SSTA domain, the meshing elements were 789,283, which suppressed the WFS. Only WFSs were allowed in the Fluent domain, resulting in 118,374 elements. Similarly, in dual settings of MCHSs, the agreed-upon number of elements was 1,242,053 and 947,864 for SSTA and Fluent domains, respectively.

2.6. Validation

To validate results, a comprehensive analysis of the validation and errors between the experimental work of Shittu et al. [39] and the current model has been done, specifically regarding PV average temperature under varying solar irradiance values. The validation process illustrated in Figure 3 demonstrates the thermal management of a PV module under 500 W/m² irradiance. Figure 3 shows the distinguishing temperature gradients/contours among various views inclusive of (Figure 3a) top, (Figure 3b) back, (Figure 3c) front, (Figure 3d) left, (Figure 3e) isometric complete unit, and (Figure 3f) isometric (PV only), confirming consistent energy absorption and the simulation’s reliability in capturing generated heat. Moreover, Figure 3 is the continuation of the model by displaying the average temperature distribution on the PV surface and temperature contours across the computational domain in isometric view, enhanced by forced convection using water flowing at 1 L/min through the microchannel. This forced convection cooling system efficiently reduces the PV module’s temperature by enhancing heat transfer through the microchannel, which can be assessed. The water mass flow rate (1 L/m) significantly reduces the heat while stabilizing the PV temperature. This stabilization improves PV efficiency by reducing the effect of temperature on power output. Apart from that, the validation graph in Figure 4 displays a comparison between the experimental and current work data. The results of both studies closely overlap, indicating that the validation is highly germane, with minimal deviations. As solar irradiance increases, the average temperature increases steadily, consistent with physical expectations. Moreover, the high degree of agreement between the experimental work and the current one demonstrates that the current work effectively replicates the temperature deviations seen in the experimental modeling. The slight differences between the results also suggest only minor experimental uncertainties or potential limitations of the model. In Table 5, absolute and relative errors are provided to strengthen the agreement between the findings. The absolute errors vs. solar irradiance relationship provides additional context regarding the scale of discrepancies between both works. The absolute error values range from 0.07 to 0.89°C, indicating minor differences. The slightest absolute error occurs at 700 W/m², while the largest occurs at 1000 W/m². At the same time, the relative errors are generally relatively low, below 2% across all irradiance levels. The highest relative error occurs at 600 and 1000 W/m², reaching around 1.40%, while the lowest error occurs at 700 W/m², below 0.2%. This trend reveals that the model’s performance is most accurate at moderate irradiance levels and shows slightly larger deviations at the lower and higher extremes of irradiance. Finally, this validation of the current model is reliable for predicting PV temperatures under various irradiance levels, which is effective for designing and optimizing PV systems.

3.1. Solar Flux Profile

The solar flux profile is derived through analytical analysis, and Figure 5 provides a detailed representation. The data presentation is straightforward, showcasing diffuse, beam, and total radiation values from 5:00 a.m. to 7:00 p.m. As an illustration, at 6:00 a.m., the beam and diffuse irradiance values stand at 73.03 and 54.21 W/m², resulting in a total of 127.25 W/m². These values exhibit an ascending trend, assuming clear sky conditions, and peak at 846.73, 110.55, and 957.33 W/m² for beam, diffuse, and total irradiance, respectively. Subsequently, a symmetrical trend persists until 6:00 p.m., reflecting the morning values. However, this study emphasizes the values at solar noon to simulate and analyze temperature contours and additional results, as elaborated below as a profound exegesis.

3.2. SSTAs

In SSTA, the approach involves selecting only three layers of half-cut silicon solar cells, comprising 30 cells, instead of the entire module with 120 cells. This selection is based on the understanding that these cells exhibit lower computational time (approximation). Although the complete monocrystalline unit with 120 half-cut solar cells is the prime focus of this study, the computational efficiency considerations lead to the adoption of a reduced scale, representing only 30 half-solar cells, as illustrated in Figure 6. All the panel layers are examined under the fluent domain, and temperature contours are available for the day of the summer solstice. In Figure 6a, the maximum, minimum, and average temperature can be observed for only the solar cells layer at the values of 63.96°C, 62.22°C, and 63.76°C, respectively. On the other hand, for the complete chosen model in Figure 6b, the maximum, minimum, and average values of the temperature profile at 63.96°C, 61.50°C, and 63.46°C are given, respectively. Minimum and maximum temperature highlights are the assumed direction of the wind on a selected day from a minimum temperature pointer to a maximum temperature one. Data points gathered from this comprehensive analysis are utilized to assess the subsequent performance of the panel’s efficiency and power output. Despite the manufacturer’s datasheet, which indicates a rated efficiency of ~22.33%, the presence of radiation that cannot be converted into electrical output induces heat on the silicon solar cell layer, reducing efficiency. This study’s observed efficiency drop is ~1/5th (~4.0% out of 22.33% = ~18.33%) of the maximum achievable efficiency. While temperature uniformity under no forced convection conditions remains acceptable at 1.7°C, the study considers implementing forced convection to regain maximum possible efficiency. This involves restricting the number of half-cut solar cells to 10, accompanied by two MCHSs, including single-layer and double-layer configurations. Further insights into the study’s findings are elaborated in the subsequent detailed description.

3.3. Single Layer of Heat Sinks

A focused approach is undertaken to minimize computation time, selecting a simplified configuration with a single layer consisting of 10 PV half-cut cells. Thermal management employs the Ansys Fluent domain, incorporating SSTA, which is aesthetically and numerically justified. Figure 7a presents an isometrical view of the cooled PV layer with a minimum temperature of 40.22°C at the inlet side. Simultaneously, the outlet region indicates a computed maximum allowable temperature of 62.70°C. Contrastingly, in the complete model, the figure’s temperature contour distribution is examined in Figure 7b, spanning the entire domain with temperatures ranging from 37.07 to 62.82°C at a working fluid velocity of 0.01 m/s. Likewise, elevating the velocity to 0.05 m/s results in a prominent reduction in the maximum temperature of the PV layer (Figure 7c) and the complete model (Figure 7d) to 46.86°C and 48.55°C, respectively, indicating enhanced temperature reduction with increased velocity. Further simulations at the velocity of 0.1 m/s reveal that the overall domain experiences a decrease in temperature, with the difference between maximum and minimum temperatures for the PV layer (Figure 7e) and module (Figure 7f) calculated at 10.10°C and 12.80°C, respectively. At 0.2 m/s, the maximum and minimum temperature values for the PV layer (Figure 7g) and entire model (Figure 7h) are in proximity, recording 30.0°C and 33.33°C as maximum values and 25.98°C and 26.0°C as minimum values, respectively. Figure 7i–l illustrates a further decline in temperature for the PV cells and the complete unit with an increase in coolant velocity. If opting for a velocity of 0.5 m/s, the PV layer (Figure 7i) demonstrates a maximum temperature of 27.0°C and a minimum of 25.93°C at the outlet and inlet side, respectively. The complete model (Figure 7j) exhibits these values at 30.66 and 25.91°C, marking a significant achievement in the thermal management of the PV module. Finally, at the highest velocity of 1.0 m/s, chosen to examine flow behavior and temperature contours, it becomes evident that this velocity is optimal. The maximum and minimum temperature values are only 0.58°C apart for the PV layer (Figure 7k), and for the entire domain (Figure 7l), this temperature difference is computed at 4.31°C.

3.4. Double Layer of Heat Sinks

Dual MCHSs were designed and implemented meticulously to conduct an in-depth analysis of fluid flow, temperature profiles, and associated results. These findings are elaborated on in comprehensive detail below. The temperature contours derived from the dual MCHS scheme are evident, particularly at an initial velocity of 0.01 m/s with laminar flow boundary conditions. In Figure 8a, PV layer depicts a maximum temperature of 62.02°C at the outlet side, while at the inlet, the minimum temperature approaches the applied working fluid inlet temperature. This is attributed to using two parallel heat sink arrangements, which resulted in a minimum temperature roughly 37% lower than that achieved in the earlier single-layer setup. For the complete geometry (Figure 8b), since the maximum and minimum values are computed at 62.22°C and 25.82°C, respectively. At the subsequent velocity of 0.05 m/s, the temperature values exhibit a substantial drop in the surface temperature of the PV module (Figure 8c) and the entire working domain (Figure 8d), displaying maximum and minimum temperatures of 34.36°C and 37.28°C and 25.55°C and 25.52°C, respectively. The temperature contours indicate minimal gaps between maximum and minimum temperature values in further velocity examinations. At 0.1 and 0.2 m/s velocities, the maximum temperature at PV layers (Figure 8e,g) shows a difference of just 1.27°C, with a nearly identical variance in minimum temperatures. The complete module domains (Figure 8f,h) highlight the same temperature difference as the PV cells. Furthermore, the PV layer and complete unit exhibit further temperature reduction below or equal to 30.0°C in Figure 8i,j. Finally, at the highest velocity of 1 m/s, the temperature profiles align closely with the input temperature of the working domain, that is, 25°C. Finally, both thermal management approaches showed the potential to lower surface temperatures; however, the dual induction of microchannels proved to be the most efficient case.

3.5. Temperature Profile

Figure 9a illustrates the disparity in maximum temperature among PV cells at a velocity of 0.01 m/s, where the values surpass 60°C (maximum value) for both cases involving single and dual MCHS layers. As velocities progress, the most substantial difference in surface temperature occurs at 0.05 m/s, with a temperature difference exceeding 10°C between single-layer and dual-layer heat sinks. This temperature profile, concerning the maximum temperature, attains optimum values with further increases in velocity while maintaining laminar flow. At the ultimate velocity (1.0 m/s), the maximum temperature appears to have nearly identical values above the defined room temperature of 25°C. On the other hand, PV cells’ minimum temperature follows a similar pattern from 0.1 to 1.00 m/s velocity, slightly above 25°C, except for the initial case of 0.01 m/s velocity. In this case, the minimum surface temperature for single MCHSs is determined at 40°C, while it is 27°C for dual heat sinks arrangements. Furthermore, the average temperature of PV cells indicates remarkable temperature reduction achievements, a crucial parameter for computing electrical efficiency and subsequent results. Initially, the average surface temperature of a PV layer is observed at 61.12°C and 44.38°C, respectively, for single and dual-layer settings of MCHSs at 0.01 m/s velocity. In the subsequent simulation at 0.05 m/s velocity, the average temperature values are above and below 30.0°C for both heat sinks. For further simulations, the minimum temperature trend and the average temperature are observed between 25.0 and 30.0°C. Finally, the temperature uniformity for all cases is presented in Figure 9d. In this segment, a higher temperature value but lower temperature uniformity is obtained by two layers of heat sinks. Specifically, a temperature uniformity value of 36.06°C is achieved by the two layers of heat sinks at the initial velocity, whereas, with a single arrangement of microchannels, its value remains at 22.5°C. As velocity increases, at 0.05 m/s, for example, the temperature uniformity improves to 20.6 and 8.8°C, and at 0.1 m/s, its value is nearly 10.0°C and 3.1°C for single and dual layers of MCHSs, respectively. Moreover, at 0.2, 0.5 , and 1.00 m/s, the temperature uniformity is below 5.0°C, with an optimum value of around 0.5°C at higher velocity.

3.6. Electrical Efficiency

Electrical efficiency enhancement constitutes the focal point of this case study, which assessed the efficiency gain following the implementation of forced convection through varying MCHSs. In Figure 10a, the maximum efficiency of the agreed panel and the operating efficiency at our location are highlighted, showing 22.3% and 18.3% as the maximum and operating efficiency without applying heat transfer through forced convection, respectively. Subsequent Figure 10b presents the efficiency increment concerning changing velocities. Initially, at a velocity of 0.01 m/s, the efficiency of the PV layer reaches 18.55% and 20.3% for single- and double-layer MCHS arrangements, employing water as a coolant. Similarly, with an increased velocity of 0.05 m/s, the efficiency profile reaches around 22.0%, considering both cases of the geometries. Furthermore, efficiency approaches its maximum value with further changes in working fluid velocities. For instance, negligible variations in the new efficiency profile can be observed from 0.1 to 1.0 m/s velocities. At the final velocity of 1.0 m/s, the electrical efficiency improvement reaches the maximum value, with 22.22% and 22.27% for single and dual MCHS arrangements, respectively. In Figure 10c, an enhanced efficiency range is observable, ranging from 0.25% to precisely 4.0%. At 0.01 m/s, the efficiency gain is 0.25% and 2.0% for single and double-layer MCHSs, with a subsequent surge of 3.2% and 3.5% at 0.05 m/s velocity, respectively. However, further examination of velocities between 0.1 and 1.0 m/s reveals gradual and minor upward changes in improved efficiency between 3.5% and 4.0%. Also, regarding the power output, the diagram reflects the same trend as the new (after cooling) electrical efficiency. At the initial velocity value of 0.01 m/s, the system’s power output reaches exactly 500 W and roughly 550 W for single and double-layer MCHSs, respectively, as can be seen in Figure 10d. A notable improvement is evident at the next velocity of 0.05 m/s, where the power has 578 and 994 W values for dual MCHS configurations. Finally, from 0.1 to 1.0 m/s velocities, there is a minimal difference in the power of the PV panel, which nearly reaches its maximum value of ~600 W.

3.7. LCOE

This section underscores the performance and cost-effectiveness of the energy system utilizing MCHS, evaluated under varying conditions of velocity, MCHS configuration (one-layer and two-layer MCHS), operational lifespan (30 years and 20 years), and the presence of cooling mechanisms given in Figure 11. The critical parameters analyzed are the annual energy output (kilowatt-hour) per year (kWh/year) and the LCOE in Pakistani Rupees per kilowatt-hour (PKR/kWh). For example, in the 30-year operational lifespan scenario (Case-B), increasing the velocity from 0.01 to 1 m/s led to significant changes in annual energy output for MCHS configurations. For the one-layer MCHS, the annual energy output increased from 1,056,564 kWh/year at 0.01 m/s to 1,266,281 kWh/year at 1 m/s, marking an improvement of ~19.85% (an increase of 209,717 kWh/year). The corresponding LCOE rose from 5.73 to 6.86 PKR/kWh, indicating that higher velocities enhance energy production and slightly increase the cost per unit of energy. However, the two-layer MCHS exhibited a similar trend, with annual energy output rising from 1,156,864 kWh/year at 0.01 m/s to 1,269,131 kWh/year at 1 m/s, an improvement of about 9.7% (a rise of 112,267 kWh/year). At 0.01 m/s, the two-layer configuration recovered 100,300 kWh/year more than the one-layer MCHS, but this advantage narrowed to 2,850 kWh/year at 1 m/s. The LCOE for the two-layer MCHS increased from 6.27 to 6.88 PKR/kWh over the same velocity range. Moreover, the impact of operational lifespan on LCOE was also significant. Reducing the lifespan from 30 to 20 years led to an increase in LCOE for both MCHS configurations due to the shorter amortization period of the initial investment. For the one-layer MCHS at 0.01 m/s, the LCOE rose from 5.73 PKR/kWh (30 years) to 6.49 PKR/kWh (20 years), an increase of almost 13.26%. The two-layer configuration experienced a similar LCOE increase from 6.27 to 7.11 PKR/kWh, ~13.40% higher. This pattern was consistent across all velocities, underscoring the importance of a longer operational lifespan for improved cost-effectiveness. The introduction of active cooling mechanisms profoundly affected the performance of both MCHSs. Without cooling, both the one-layer and two-layer MCHSs produced an annual energy output of 1,041,177 kWh/year. Initially, introducing cooling at 0.01 m/s increased the annual energy output to 1,056,564 kWh/year for the one-layer configuration and 1,156,864 kWh/year for the two-layer configuration. This represents improvements of 15,387 kWh/year (~1.48%) and 115,687 kWh/year (around 11.11%) for the one-layer and two-layer MCHSs, respectively, compared to the no-cooling scenario. At 1 m/s, the benefits of forced convection were even more pronounced. The one-layer MCHS’s annual energy output increased by 225,104 kWh/year (around 21.62%) to 1,266,281 kWh/year, while the two-layer configuration’s output rose by 227,954 kWh/year (almost 21.89%) to 1,269,131 kWh/year compared to the no-cooling situation. These substantial gains highlight the significant role of cooling mechanisms in enhancing energy production using MCHS configurations. In addition, while considering the annual energy output at rated efficiency, which is 1,273,120 kWh/year, both MCHS approached this maximum output at higher velocities with cooling. The LCOE at rated efficiency was 6.90 PKR/kWh for the 30-year lifespan and 7.82 PKR/kWh for the 20-year lifespan. At 1 m/s, the one-layer MCHS’s LCOE was 6.86 PKR/kWh, slightly below the LCOE at rated efficiency, indicating cost-effectiveness at high velocities. Finally, optimal operational conditions were identified between 0.2 and 0.5 m/s with cooling. Within this range, the one-layer MCHS produced between 1,258,303 and 1,264,572 kWh/year, with LCOE values ranging from 6.82 to 6.85 PKR/kWh. On the other hand, the two-layer configuration’s annual energy output was slightly higher, between 1,266,851 and 1,268,561 kWh/year, with LCOE values from 6.87 to 6.88 PKR/kWh. The marginal increases in energy output and minimal changes in LCOE at velocities beyond 0.5 m/s suggest declining returns, making this velocity range the most cost-effective for operation.