## 5 Conclusions  
In this paper, the radiation intensity in Budapest was used and simulated using the Hottel model, while ambient temperatures were obtained from a weather station at the energy laboratory. The simulations of the thermal performance were based on solving the analytical expression using MATLAB symbolic tools. Moreover, the results were validated with experimental results from the literature [44, 63]. Finally, the thermal model performance of the LS-2 PTC was used to display the effects of using HNFs of Al\({}_{2}\)O\({}_{3}\)-WO\({}_{3}\)/based Therminol VP1 under different concentrations and weather conditions. The key findings obtained in this study are summarized as follows:  
* Utilizing concentrated solar applications (PTC) under Budapest's weather conditions showed their ability to produce energy, especially in summer. The maximum intensity of the beam radiation reaching the parabolic reflectors approached 880 W/m\({}^{2}\) on typical sunny days, and it reaches 260 W/m\({}^{2}\) on typical winter days.
* In order to explain the effect of the dimensionless Nusselt number and heat transfer coefficient in increasing exergy and energy efficiencies, experiments were performed for HNFs under different concentrations (0-4%) and temperatures (300-600 K) at a constant volume flow rate of 150 L/min. Using a 2% volume concentration yielded  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Therminol VP1** & **1\%** & **2\%** & **3\%** & **4\%** \\ \hline \(\eta_{eff,summer}\) & 71.065 & 71.224 & 71.238 & 71.246 & 71.255 \\ \(\eta_{eff,winter}\) & 63.528 & 63.66 & 63.672 & 63.682 & 63.688 \\ \(\eta_{ex,summer}\) & 32.64 & 32.712 & 32.718 & 32.72 & 32.728 \\ \(\eta_{ex,winter}\) & 30.65 & 30.718 & 30.724 & 30.728 & 30.732 \\ \(Heat_{loss}\) W & 1306 & 1249 & 1245 & 1241 & 1239 \\ \(Heat_{gain}\) W & 25,300 & 25,357 & 25,360 & 25,365 & 25,371 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Major found results.  
Figure 14: Exergy efficiency of the base fluid and HNFs for sunny and winter days in Budapest.  
1402 W/m\({}^{2}\cdot\)K for the Nusselt number and 2060 W/m\({}^{2}\cdot\)K for the heat transfer coefficient. In comparison, a maximum Nusselt number of 1427 W/m\({}^{2}\cdot\)K and a heat transfer coefficient of 2236 W/m\({}^{2}\cdot\)K were obtained using a 4% volume concentration with a maximum temperature of 600 K.
* Thermal and exergy efficiencies achieved the highest improvement using high concentrations and high temperatures, reaching 68.384% and 37.828%, respectively; this means that the enhancement ratio equaled 0.39% for the thermal efficiency and 0.38% for the exergy efficiency.
* For HNFs, the maximum exergy and energy values were recorded at midday under Budapest's summer climatic conditions, and reach 32.728% and 71.255%, respectively, under the optimum temperature of 500 K and flow rate 150 L/min. These results and the low impact of increasing the concentrations, in this case, can be attributed to simulating the effects under high volume flow rates and using a highly efficient commercial PTC (which has an evacuated tube). Despite the low enhancement results (0.25%), which were attributed to the reasons mentioned above, it was acceptable and justified [31]. On the other hand, there were promising findings on the financial feasibility in the literature for the effects of nanofluid prices. For example, [PERSON] et al. [64] found that nanofluid use did not contribute to a major increase in the overall cost of PTCs. In addition, [PERSON] et al. [38] found in their research that the payback period of nanofluid-based PTC usage is lower than the payback period of nanofluid-free PTCs.