# Numerical Investigation of Thermal Efficiency of a Solar Cell
## 1 Introduction
An active cooling having a thermal resistance of less than 10\({}^{-4}\) m\({}^{2}\)K/W is necessary for the proper functioning of densely packed solar PV cells (>150 suns). It was proved that such a low thermal resistance is possible only by using micro-channels and impinging jets. [PERSON] [27] found that with per unit temperature increase in PV cells, the temperature of water decreases by 0.4%. Using the water flow over the front surface of the PV cells, the temperature of the cell drops up to 22 \({}^{\circ}\)C. This magnitude of temperature drops yields a 10.3% rise in electrical power output. [PERSON] and [PERSON] [28] reported cooling of the PV array by circulating water from the front surface and studied its efficiency. It was concluded that up to 15% increase in efficiency could be achieved at peak irradiations using this technique. Furthermore, a vast amount of heat loss (50%) was observed due to the direct contact of PV cells with water. It was also found that water cooling keeps the module free from dust and dirt particles. This leads to some increase in electrical efficiency. [PERSON] and [PERSON] [29] found out various correlations to understand the dependency of the electrical performance of PV cells on operating temperature. It was concluded that output voltage and efficiency both are indirectly proportional to the operating temperature and they decrease with an increase in the temperature in all conditions. [PERSON] and [PERSON] [30] analyzed the performance of 5.28 kW capacity PV cells installed at KFUPM, Saudi Arabia. It was clearly visible that energy yield was highest at 35.8 \({}^{\circ}\)C and it decreased with an increase in temperature. [PERSON] et al. [31] used the water spray impingement technique to enhance the performance of PV arrays. Because of the cooling of modules, an enhancement of 12% in the electric power output was observed. Overall, a gain of 215 W in output power was reported because of cooling. Additionally, the temperature decrease from 60.5 \({}^{\circ}\)C to 28.5 \({}^{\circ}\)C in 5 min was observed due to water impingement. [PERSON] et al. [32] performed experiments on a PV cell, with and without air cooling, and found a linear relationship between the temperature of modules and its efficiency. Without cooling the PV cells, only 8-9% of conversion efficiency was possible. However, with active cooling, the temperature decreased gradually, and a 12-14% enhancement in conversion efficiency was observed. Furthermore, using an air blower to cool down the PV cells reduced the temperature of the cell significantly. The validation of the numerical model of the PV panels cooling system with an experimental setup was carried out in the present study. Experiments were carried out for determining the thermal efficiency by measuring the temperature at the outlet. This was done at two mass flow rates (0.025 kg/s and 0.5 kg/s). Energy balance was conducted for the heat losses in order to calibrate the setup. The validation of the computational domain was successfully managed by specifying the boundary conditions. Simulations were carried out at different values of the velocity inlet in order to develop a correlation between the Re at the inlet and the thermal efficiency. The correlations were developed as semi-empirical relations. Last, the semi-empirical relation developed was validated with other literature work.