## 3 Results and Discussion
### Standardized Efficiency of Low Temperature Solar Collectors  
To evaluate the relevance of using heat pipes in flat plate solar collectors, this section presents the efficiency with respect to specific environmental conditions, ambient temperature, \(T_{a}\), and radiation, \(I\), represented by the Hottel-Willier-Biss coefficient \((T_{i}-T_{a})/G_{T}\). This coefficient helps to visualize the efficiency of solar collectors throughout the operating range of a day, typically where the three parameters that affect the collector vary: ambient temperature, radiation, and fluid temperature. For this, the values of radiation, ambient temperature, and fluid temperature from [30] have been used, presented in [32] and in Table 5.  
Figure 10 illustrates the efficiency of three types of low-temperature solar collectors--FPCs, HPETCs, and HPFPCs--throughout a typical day in relation to the Hottel-Willier-Biss coefficient. The analysis was conducted at a mass flow rate of 0.05 kg/s, consistent with the methodology of [32]. From the figure, it can be seen that, as the temperature difference between the fluid inlet and the ambient temperature increases, the collector's efficiency decreases. This occurs because overall losses increase when the temperature of a hot body is higher than the ambient temperature. This is true for all three collectors evaluated. As depicted in Figure 10a, the efficiency of the evacuated tube collector surpasses that of the flat plate collector by up to 15%. Additionally, the integration of heat pipes within a flat plate collector can enhance its efficiency by as much as 9%, particularly noticeable around 14:00 h. During this evaluation, solar radiation levels ranged from approximately 360 to 800 W/m\({}^{2}\). Figure 10b further demonstrates that the efficiency of flat plate solar collectors can increase by up to 6.5% when heat pipes are incorporated. \begin{table}
\begin{tabular}{c c c c} \hline
**Time (h)** & **Radiation, \(G_{T}\) (W/m\({}^{2}\))** & **Ambient Temperature, \(T_{a}\) (\({}^{\circ}\)C)** & **Fluid Temperature, \(T_{i}\) (\({}^{\circ}\)C)** \\ \hline
9 & 398 & 27 & 38.8 \\
10 & 560 & 28.5 & 38.5 \\
11 & 700 & 30 & 39.2 \\
12 & 780 & 31.9 & 40.2 \\
13 & 800 & 32.98 & 43 \\
14 & 790 & 33.9 & 44.17 \\
15 & 710 & 34 & 45.1 \\
16 & 560 & 34.4 & 45 \\
17 & 362 & 34.15 & 46 \\ \hline \end{tabular}
\end{table} 
Table 5: Environmental and fluid values used for standardized efficiency [32]. Figure 9: Efficiency and useful heat with respect to the fluid temperature, for the three types of solar collectors and the five antifreeze working fluids: (**a**) efficiency, (**b**) useful heat. The results imply that the integration of heat pipes in flat plate collectors can improve efficiency by up to 13%. The comparative evaluation of heat transfer fluids, including varying concentrations of ethylene glycol and propylene glycol, provides valuable guidance for engineers in selecting suitable fluids that not only achieve efficiency standards but mitigate the risk of freezing in colder climates. The variations in operational conditions, such as fluid temperature and flow rates, were found to impact efficiency. This information can be utilized by engineers to design systems that operate under specific conditions, leading to better energy resource management. It is fundamental to consider the synergistic effects between fluid properties--such as thermal conductivity, viscosity, and specific heat capacity--and the physical design of HPFPCs on the overall efficiency of the solar collector system. Water has higher thermal conductivity and specific heat capacity than most antifreeze solutions, enhancing the overall heat transfer process and improving the thermal performance of the HPFPC. By contrast, antifreeze solutions typically have higher viscosity, particularly at lower temperatures, which can reduce heat transfer efficiency.