## 4 Results and Discussions
### Thermal Performance Results and Discussions  
Through this research, an appropriate flow rate was determined for several cases, based on the relationship of efficiency versus different flow rates for different inlet temperatures. When the beam radiation intensity was taken to be 1000 W/m\({}^{2}\), and the ambient temperature was 300 K (as described in Figure 3), the results showed a decrease in the thermal efficiency with the inlet temperature increase. The flow rate after 150 L/min did not deliver a significant change in efficiency, as such there was no need to further increase the flow rate because as it required more input pumping power. Therefore, in this study, the thermal performance of the PTC was simulated under a constant flow rate equal to 150 L/min. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Cases**} & \(G_{p}\) & \multirow{2}{*}{\(T_{amb}\) (**C**)} & \multirow{2}{*}{\(T_{in}\) (**C**)} & \multirow{2}{*}{\(V_{f}\) (**L/min**)} & \multicolumn{2}{c}{\(T_{out}\) (**C**)} & \multicolumn{2}{c}{\(\eta_{eff}\)\%} & \\ \cline{5-10}  & & & & & **Dudley** [21] & & **Model** & **Deviation** [21] & **Model** & **Deviation** [21] & **\%** \\ \hline
1 & 933.7 & 21.2 & 102 & 47.7 & 124 & 124.36 & 0.29 & 72.51 & 73.6 & 1.51 \\
2 & 968.2 & 22.4 & 151 & 47.8 & 173 & 174.04 & 0.6 & 72.1 & 72.91 & 1.13 \\
3 & 962.3 & 24.3 & 197 & 49.1 & 219 & 219.28 & 0.13 & 71.6 & 72.06 & 0.65 \\
4 & 909.5 & 26.2 & 250 & 54.7 & 259 & 268.99 & 3.86 & 70.4 & 70.74 & 0.48 \\
5 & 937.9 & 28.8 & 297 & 55.5 & 316 & 316.52 & 0.16 & 69.1 & 69.3 & 0.29 \\
6 & 880.6 & 27.5 & 299 & 55.6 & 317 & 317.24 & 0.08 & 68.7 & 68.99 & 0.42 \\
7 & 920.9 & 29.5 & 379 & 56.8 & 398 & 398.43 & 0.11 & 64.8 & 65.64 & 1.02 \\
8 & 903.2 & 31.1 & 355 & 56.3 & 374 & 373.92 & 0.02 & 66.1 & 66.63 & 0.8 \\ Mean & & & & & & & 0.64 & & 0.78 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Validation model with SNL outlet temperature and efficiency results [44]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Property/Nanoparticles** & **Aluminum Oxide Nanoparticle Al\({}_{2}\)O\({}_{3}\)** & **Tungsten Oxide Nanoparticle WO\({}_{3}\)** \\ \hline Specific heat \(Cp_{np}/\text{J}\cdot\text{kg}^{-1}\) K\({}^{-1}\) & 765 & 315.4 \\ Density \(\rho_{np}/\text{kg}\) m\({}^{-3}\) & 3970 & 7160 \\ Thermal conductivity \(k_{np}/\text{W}\) m\({}^{-1}\) K\({}^{-1}\) & 40 & 16 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Nanoparticle thermal properties [42,46]. In order to explain the advantage of using the hybrid nanofluid in the PTC and the sensitivity of our model compared to previous work, Figure 4 depicts the thermal efficiency change using variable inlet temperatures for the mono and hybrid nanoparticles used in our research. The mono and hybrid nanoparticles obtained by [PERSON] and [PERSON] in their study using Therminol VP1 were used for comparison [43]. The evaluated results presented an increase in the thermal efficiency of both hybrid nanofluids compared with the monotypes. Moreover, the thermal efficiency of using nanofluid of Al2O3 and WO3/VP1 showed a slight increase compared with the nanoparticles used in the literature. The solar radiation intensity that was used in this study was obtained using the Hottel model. The ambient temperatures were obtained from the weather station of the Budapest University of Technology and Economics for typical sunny and winter days. These conditions were utilized to examine the thermal performance of the PTC under those weather conditions using different HNF concentrations. The preprocessing of the cosine of incident angle considering the sun-tracking approach, which was continuously tracked along the E-W direction was used, as shown in Equation (3). Thus, Figure 5 shows the variance between the radiation affecting the PTC on those days. Figure 5a presents a typical sunny day when the maximum radiation intensity was obtained at midday and was recorded at 880 W/m2.