## 3 Results and Discussion
### FSCs with Graphite and Fullerene Nanofluids  
This section presents the thermophysical properties of nanofluids with respect to volume fraction. The carbon nanofluids evaluated are graphite, G, fullerene, C\({}_{60}\), and multi-walled carbon nanotubes (MWCNTs). Figure 5 shows the change in densities, viscosity and specific heat capacity for graphite and fullerene nanofluids. It is observed that the density and viscosity of nanofluids increases  
Figure 4: Useful heat and efficiency of the FSC with respect to the mass flow of the base fluid. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Range** \\ \hline FPSC inclination, \(\beta\) [\({}^{\circ}\)] data from [34] & 20 \\ Irradiance, \(G_{\rm T}\), W/m\({}^{2}\) & 750 \\ Air velocity, \(V_{\rm a}\), m/s & 5 \\ Inlet temperature, \(T_{\rm i}\) [\({}^{\circ}\)C] & 30, 40 y 50 \\ Mass flow rate, \(\dot{m}\), [kg/s] & 0.01–0.1 \\ Nanoparticle diameter, \(d_{\rm p}\), nm & 15 \\ Volume fraction, \(\phi\) & 0.001–0.1 \\ Volume fraction of carbon nanoparticles, \(\zeta_{1}\) & 0.2 \\ Volume fraction of metal oxide nanoparticles, \(\zeta_{2}\) & 0.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Varied parameters in simulation. with the volume fraction to 10.81% and 6.76% for the density and 26.62% for the viscosity for the graphite and fullerene, respectively. Specific heat capacities decrease to 16.28% and 13.93% for the graphite and fullerene, respectively, with increasing volume fraction. According to [41], the improvement in TC depends largely on the volume fraction of solids and, to some extent, on temperature. Figure 6a shows that the TC of graphite nanofluids increases with the volume fraction to 39.16% and 12.25% for the graphite and fullerene, respectively. This is true for nanofluids containing \(G\), which have higher TC levels compared to the base fluid. However, for the fullerene nanofluid, C60, TC tends to increase at a lower rate because C\({}_{60}\) nanoparticles have a TC of 0.4 W/mK (see Table 2), which is lower than that of the base fluid, which has a TC of 0.605 W/mK. In Figure 6b, the thermal diffusivity of graphite and fullerene nanofluids is shown to increase with the volume fraction to 44.53% and 19.33% for the graphite and fullerene. At a volume fraction of 0.1, carbon nanofluids such as \(G\) have diffusivity greater than 2.000 \(\times\) 10\({}^{-7}\) m\({}^{2}\)/s, while for C\({}_{60}\), the change in thermal diffusivity is minimal, with a value of 1.503 \(\times\) 10\({}^{-7}\) m\({}^{2}\)/s at a volume fraction of 0.1. Figure 5: Density, viscosity and specific heat capacity as a function of volume fraction for the graphite and fullerene nanofluids. Figure 6: (**a**) TC and (**b**) thermal diffusivity as a function of volume fraction for the graphite and fullerene nanofluids. Figure 7a presents the Reynolds numbers for the base fluid (water) and nanofluids (graphite and fullerene) as functions of mass flow rate and volume fraction, respectively. The figure demonstrates that the Reynolds number for the base fluid increases from 200 to 2100 as the mass flow rate rises. Conversely, the Reynolds number for carbon-based nanofluids decreases from 1700 to 1300 as the volume fraction increases. This discrepancy arises because the density and viscosity of the nanofluids increase. Figure 7b illustrates the Prandtl number Pr for graphite and fullerene nanofluids as a function of volume fraction. The figure shows that as the volume fraction increases, there is no significant change in the Prandtl number of the fullerene. On the other hand, the Pr of graphite nanofluids decreases. This discrepancy arises because the conductivity of the fullerene decreases. Figure 8 illustrates the Nusselt number (\(Nu\)) and the convection heat transfer coefficient (\(h\)) for graphite, fullerene and multiple-walled carbon nanotube nanofluids as a function of volume fraction. The figure shows that as the volume fraction increases, both the \(Nu\) and \(h\) increase.