## 3 Results and Discussion
The results also show that both models demonstrate good performance in terms of all metric values. However, some geometries gave better results with small differences. Correlation coefficients and performance measurements for the Nusselt number based on M1 are given in Table 3. According to the M1 model results, the best result in both GRG and HFO-1 algorithms was obtained with data taken from the solar air heater with a semi-circular section geometry. In addition, the HFO-1 algorithm gave about 42% more accurate results than GRG with respect to average RMSE. The lowest percentage error (MAPE) was obtained with the semicircular section geometry. With the equation obtained using the HFO-1 algorithm based on M1, the Nusselt number value was calculated with a percentage error of 2.15%. [PERSON] et al. [4], who used similar equations to calculate the Nusselt number, calculated it with a 12% error, and [PERSON] et al. [10] calculated it with a 6% error value. It can be seen that the equations whose coefficients are determined using the HFO-1 algorithm give better results. \begin{table}
\begin{tabular}{c c} \hline \hline
**Model** & **Equations** \\ \hline M1 & \(Nu_{r}=C_{0}Re^{C_{1}}.(P/e)^{C_{2}}.exp\Big{\{}C_{3}[\ln(P/e)]^{2}\Big{\}}\) \\ M2 & \(Nu_{r}=C_{0}Re^{C_{1}}.(P/e)^{C_{2}}+C_{3}exp\Big{\{}C_{4}.(P/e)^{C_{5}}\Big{\}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Proposed models for Nusselt number. Figure 4: CFD results for smooth and corrugated absorber plates of types ((**a**) square; (**b**) semicircular; (**c**) triangular). Correlation coefficients and performance measurements for the Nusselt number based on M2 are given in Table 4. Upon examining the M2 results, it can be seen that better results are obtained for all geometries. Again, the best results in both GRG and HFO-1 algorithms were obtained with the data taken from the solar air heater with a semi-circular section geometry. With the equation obtained using the HFO-1 algorithm based on M2, the Nusselt number value was calculated with an error of 0.86%. When we compare GRG and HFO-1 based on M2, HFO-1 gave approximately 58% better results than GRG. The highest R\({}^{2}\) was 0.9930 (semicircular type), while the lowest R\({}^{2}\) was 0.9792 (mix type) based on M1. R\({}^{2}\) being close to 1 is an indication that the established model is successful. The independent variables used in the equation established for the model with a semicircular section geometry explain 99.3% of the variation in the Nusselt number (Figure 5). The highest R\({}^{2}\) was 0.9986 (semicircular type), while the lowest R\({}^{2}\) was 0.9870 (mix type) based on M2. Using the M2 model for all geometries, the Nusselt number is obtained with approximately 99.5% accuracy (Figure 6). \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline  & **Geometry** & **C\({}_{0}\)** & **C\({}_{1}\)** & **C\({}_{2}\)** & **C\({}_{3}\)** & **MAE** & **MAPE** & **MSE** & **RMSE** & **R\({}^{2}\)** \\ \hline \multirow{4}{*}{HFO-1} & Square & 0.176871 & 0.675233 & \(-\)0.41475 & 0.091569 & 1.2695 & 0.0263 & 2.2641 & 1.5047 & 0.9903 \\  & Semircular & 0.206126 & 0.683402 & \(-\)0.50035 & 0.095602 & 1.1042 & 0.0215 & 1.8445 & 1.3581 & 0.9930 \\  & Triangle & 0.205957 & 0.620256 & \(-\)0.04692 & 0.00961 & 1.3683 & 0.0268 & 2.6859 & 1.6389 & 0.9877 \\  & Mix type & 0.196928 & 0.659367 & \(-\)0.3225 & 0.065971 & 1.8450 & 0.0345 & 4.9573 & 2.2265 & 0.9792 \\ \hline \multirow{4}{*}{GRG} & Square & 0.102491 & 0.674964 & 0.080736 & \(-\)0.013104 & 1.9220 & 3.7481 & 5.7662 & 2.4013 & 0.9900 \\  & Semircular & 0.128679 & 0.675530 & 0.003350 & \(-\)0.013209 & 1.9580 & 3.6420 & 5.4926 & 2.3436 & 0.9930 \\ \cline{1-1}  & Triangle & 0.184195 & 0.622564 & 0.056879 & \(-\)0.011458 & 2.1623 & 3.9154 & 7.4613 & 2.7315 & 0.9882 \\ \cline{1-1}  & Mix type & 0.149880 & 0.659976 & \(-\)0.059758 & 0.012898 & 3.4332 & 6.1657 & 16.5008 & 4.0621 & 0.9796 \\ \hline \end{tabular}
\end{table} 
Table 3: Correlation coefficients and performance measurements for Nusselt number based on M1.