With the rise of computational fluid dynamics, it is widely used techniques to solve challenging issues in the current age of Engineering, Technology, and Innovation. CFD was originally motivated by a scientific understanding of the mechanics of fluids and heat transfer. It has cut costs and improved the performance of the equipment which has culminated in greater quality discoveries through computational simulation [23,24]. It is a multidisciplinary tool that led to the evolution of computer science, mathematics, and fluid mechanics. The dedication of CFD is only for the fluids that are in movement. Mathematical simulations of any fluid flow fall under the umbrella of the computational part [25,26].

ANSYS Fluent has a built-in design tool for creating 3D sketches, which can be used to draw different geometric specifications which is known as Space-Claim. A 3.4 mm-thick sketch of a photovoltaic PV panel’s glass was drawn. Nevertheless, as shown in Fig. 1, a rectangle that resembled a duct was also constructed above the glass [15,27].

It is the important phase in CFD which arises after geometry. In this step simply, cells are built on which the flow variables are computed in a computational globe. There are distinct forms of cells, such as (Triangles, Quadrilateral, tetrahedrons, hexahedrons, etc.) out of which a fine mesh has been created of 5 mm.

Following the geometry phase, mesh generation represents a pivotal step in Computational Fluid Dynamics (CFD) as depicted in Fig. 2. During this stage, cells are intricately designed to facilitate the calculation of flow variables within a computational domain. Various cell shapes, including triangles, quadrilaterals, tetrahedral, and hexahedrals, are available for this purpose. The selection of an appropriate cell shape is contingent upon the specific characteristics of the flow under consideration. In this context, a fine mesh with a nominal size of 5 mm was employed to ensure a detailed representation of the computational domain. This meticulous mesh refinement is crucial for accurately capturing the intricacies of fluid flow and enhancing the reliability of the CFD simulations [28].

(1)qk=−kAdTdx (2)q=hcAΔT

Eqs. (1) and (2) were the basic equations to be considered for the heat transfer from PV module glass to water (Coolant). However, the following parameters for the glass were considered as a standard to calculate heat transfer. Table 2 shows data for the glass. Whereas properties of glass and water are the standard values for calculating the effect [29–31].

Boundary conditions are applied without any reluctance. Velocity in any application of equipment can be varied by the variation in Boundary conditions. Besides, in real-time applications, it gets changed by the change of equipment of higher power as in the pump for variation flow rate and velocity. Altogether the same procedure is recalled for temperature and pressure whereas for many other conditions. Above mentioned technique reduces the cost of the system. CFD helps to simulate multiple conditions at different rates and variations in different parameters [32]. However, boundary conditions are also illustrated in tabular form in Table 3.

The most useful and dynamic input variable that immediately gets affected by the flow includes velocity. Remember that a temperature of 323 K is fixed at the glass’s surface. Even variations in Reynolds number have an impact on velocity. Therefore, velocity was computed at various Reynolds numbers between 5 and 50 as an input parameter [33].

Considering the duct as a rectangular shape over the surface of the PV Glass it was considered that velocity will be the primary input variable. So, the hydraulic diameter was taken in the Reynolds number formula and calculations were done as given in following Table 4 and these calculations were carried out by Eq. (3).

(3)Dh=2aba+b

The supposed geometry was meshed, allowing for simulations in ANSYS Fluent Academic Version V18R2. The laminar flow pattern was picked for the current shape due to its transparency throughout the PV module surface, enabling maximum irradiance absorption for electricity generation. So, the framework was solved using Energy Eq. (4) under steady-state circumstances [1–3]. (4)∂∂t[ρ(e+V22)]+∇.[ρ(e+V22V→)]=ρq˙+∂∂x(k∂T∂x)+∂∂y(k∂T∂y)+∂∂z(k∂T∂z)−∂up∂x−∂vp∂y−∂wp∂z+∂uτxx∂x+∂uτyx∂y+∂uτzx∂z+∂vτxy∂x+∂vτyy∂y+∂vτzy∂z+∂wτxz∂x+∂wτyz∂y+∂wτzz∂z+ρf→.V→

The calculations were performed On ANSYS FLUENT software at different Reynolds numbers ranging from 5 to 45 as shown in Table 5. Geometry and meshing were done with the help of ANSYS workbench. Water was used as a fluid and the solid was modeled as Glass of photovoltaic. The flow was modeled as laminar and incompressible. Because of incompressible flow, the solver was used as pressure-based in ANSYS fluent. Then calculations were run on various Reynolds numbers. It was observed that with the increase of Reynolds number, the temperature change also increases. However, From Re = 35 the change in temperature becomes constant as clearly visible in Fig. 3.

Therefore, the value of Reynolds is suggested as 35 at hydraulic diameter 0.04786 for maximum heat transfer.

After calculating optimum Reynolds number 35, for maximum heat transfer. Secondly, the optimum thickness was calculated. For the calculation of optimum thickness, different values of thickness were taken ranging from 5 to 50 mm. Based on thickness, the hydraulic diameter was calculated. Wherein the Change in temperature between the inlet and outlet was calculated on different thickness values as shown in Table 6. It can be observed from Fig. 4 and Table 6 that the maximum change in temperature occurs at 5 mm thickness of water. Moreover, as the value of thickness is increased the change of temperature is decreased. The maximum heat transfer occurs at Re = 35 and thickness = 5 mm in comparison to Re = 30, thickness = 30 mm. Therefore, it has been selected as the optimum value of Reynolds and the optimum value of thickness.

The rapid cooling of photovoltaic (PV) modules is essential for enhancing overall performance as shown in Fig. 5a–d, particularly electrical output during midday operations at peak temperatures. Various methods are employed to reduce working temperature, including the use of water as a cooling medium above the module’s front transparent glass to extract surface temperature generated by irradiance. Water flow is regulated using the fundamental principles of the Reynolds number and hydraulic diameter as drawn in Table 6. Importantly, empirical observations reveal that the most significant temperature reduction occurs at a Reynolds number of 35 and a film thickness (T) of 5 mm demonstrated in Fig. 5c. The analysis in Fig. 5a–d implies a marked advancement in electrical efficiency by reducing the surface temperature of the PV Glass. Fig. 5b,d is the contours of the Glass surface and Fig. 5a,c is the contours of the Duct. when these optimal cooling parameters are applied, confirming the efficacy of this cooling strategy. Additionally, Table 6 focuses on the correlation between hydraulic parameters and cooling performance, providing a comprehensive framework for optimizing PV module cooling under varying operational conditions.

Fig. 6a,b displays the CFD study of the system including duct and PV glass. It is observed that the flow of water extracts the heat from the solar PV glass. From Fig. 6b, the contours of PV glass and interaction surface are illustrated. At Point 1, PV glass has the highest temperature, but water is very cold as compared to glass. However, with the optimal parameters the same contour shifts and takes place in opposite directions. At Point 2, the water is very hot, and the PV glass becomes very cold by achieving the standard temperature and pressure (STP) condition and maintaining room temperature at 25°C or 298 K.

Our study molded the optimal cooling conditions for photovoltaic (PV) modules, with a Reynolds number of 35 and a water film thickness of 5 mm. Which ultimately increases the electrical power of the PV module [34]. This discovery aligns with previous research by Hosseini et al. [35] which also identified water cooling as an effective method for temperature control in PV modules. However, our study extends this research by pinpointing specific optimal parameters, whereas Smith et al. provided a broader range of effective Reynolds numbers (500–1500) without specifying the exact optimal point, and his study concluded the turbulent flow. Whereas, our study focused on laminar flow.

In contrast, Raju et al. [36] suggested a three-dimensional computational model for water spray cooling of photovoltaic panels, which reduced operating temperatures and enhanced performance, validated by an average deviation of 1.4 K from experimental data. The optimal flow rate of 170 L/h achieved an electrical efficiency of 15.73%, a panel power output of 40.25 W, and a pump power requirement of 0.77 W, with a maximum system power output of 39.48 W.

However, Patil et al. [12] disclosed the operating temperature of the PV panel significantly impacts its conversion efficiency, with high temperatures reducing output power under identical solar radiation conditions. His CFD Analysis with ANSYS Fluent software presents a solar PV/T system with a bottom active air-cooling system, finding that at an airflow rate of 0.1 kg/s and 800 W/m² irradiance, the maximum temperatures of the PV/T system’s top surface, cell, bottom surface, and air inlet/outlet were 48.8°C, 48.4°C, 47.3°C, and 24.5°C, respectively. So, the discrepancies between our findings and those of Martin Raju and Malagouda Patil may be attributed to differences in experimental setups, such as the Martin Raju sprayed water with sprinklers, and we used free flow. Malagouda Patil tested the system with air as a fluid, but we used water as the fluid. Our study’s improvements in cooling efficiency underscore the importance of fine-tuning cooling parameters, which had not been as precisely addressed in previous research.