## 1 Introduction
Their results were conducted under volume concentrations of up to 4%, with a constant flow rate of 0.005 kg/s, and a constant temperature equal to 303 K. The results showed an increase in the thermal performance and efficiency of the evacuated tube in the simulations, particularly when using CuO/water nanofluid at a high concentration. [PERSON] and [PERSON] [23] experimentally assessed the effect of graphene nanoplatelet-based methanol in evacuated tube collectors under various conditions. Their results showed that using 0.1% wt of graphene-methanol nanofluid leads to an improvement in the thermal efficiency of the ETSC system of 95%. [PERSON] et al. [24] numerically compared the performance enhancements of PTC receiver tubes, which was achieved by adding various nanoparticles (TiO\({}_{2}\), Al\({}_{2}\)O\({}_{3}\), CuO and Cu) to water under a uniform heat flux boundary. The key result showed that the maximum enhancement reached 21.5% using a TiO\({}_{2}\)/water nanofluid at a 6% volume concentration and a Reynold number equal to 70,000. In other research, [PERSON] et al. [25] numerically investigated the impact of realistic heat flux boundary conditions on the PTC receiver tube. In detail, the thermal performance of the PTC for six metallic oxides dispersed in three base fluids as monononofluids were compared under a wide range of conditions. Regardless of the choice of the base fluid, silicon dioxide is the most efficient nanoparticle tested and the most efficient concentrations. Recently, [PERSON] et al. [26] numerically investigated the effect of utilizing swirl inserts, with and without SiO\({}_{2}\)/Therminol VP-1 nanofluid, on the thermal hydraulic performance of PTCs. Their results showed that the large swirl inserts with a 6% nanofluid concentration were considered to be the optimal configuration; this can be attributed to the high improvements achieved in terms of the exergy and energy efficiencies of the PTC, which reached 14.47%, and 14.62%, respectively. Applying a nanofluid or base fluid, on the theoretical side, remained to be understood, which was accomplished by analyzing the thermal energy balance equation and heat transfer methods, which have been explained in detail by several researchers (i.e., [PERSON] and [PERSON] in their book [27], and [PERSON] in his research [28]). [PERSON] solved the energy balance equations for the receiver part of the LS2 model using Engineering Equation Solver (EES) software. In conclusion, the obtained results were compared with the experimental ones of the PTC-type LS2 in various cases [28]. Different kinds of metallic and nonmetallic nanoparticles have been used to improve the thermal properties of different types of base fluids, such as water, ethylene glycol (EG), and oil. Moreover, these nanoparticles and their improvement effects have been examined in various studies, and were conducted experimentally or theoretically. From the theoretical side, enhancement results of using nanofluids in PTC applications were based on solving the energy balance equation of the heating collecting element (HCE) using various software programs [29; 30]. Table 1 presents and summarizes the specifications and the results of several theoretical studies that used oil as a base fluid. According to Table 1, various nanoparticles were examined using different oil types and showed varying enhancement results. Most of the previous studies used LS2 PTC as a study model due to its relevant experimental results [44]. Using nanofluid as an enhancement method has received great interest in recent years, especially those that use nanoparticle samples from Al\({}_{2}\)O\({}_{3}\) and CuO, despite the effects of metallic nanoparticles and other nanoparticles. Results showed minor thermal efficiency enhancements compared with the convection heat transfer coefficient. A few studies presented the effects of using nanofluids on exergy efficiency [31; 42].