In this study, the heat transfer and fluid flow behavior of an arrow-ribbed absorber plate under turbulent conditions Reynolds number ( \(Re\) ) ( \(3800 \le Re \le 18,000\) ) is examined using computational techniques. The influence of the \(Re\) and relative roughness pitch ( \(P/e\) ) ( \(7.50 \le P/e \le 18.75)\) on the thermal energy extraction from the absorber plate is systemically investigated. Throughout the investigation, the non-dimensional height remained constant in the present study. The average Nusselt number \(\left( {\overline{{Nu_{{\text{r}}} }} } \right)\) is increased with Reynolds number across all relative roughness pitches, whereas the average friction factor \(\left( {\overline{{f_{{\text{r}}} }} } \right)\) is decreased accordingly. Results from the numerical evaluation show that the highest \(\overline{{Nu_{{\text{r}}} }}\) , approximately 5.33 times the smooth duct value, is achieved at \(P/e\) = 7.50 for \(Re\) = 3800. Meanwhile, the maximum growth in \(\overline{{f_{{\text{r}}} }}\) , about 2.53 times the smooth case, is obtained for the same configuration. Additionally, the optimal thermal–hydraulic performance parameter (THPP) is determined to be 3.91 at \(P/e\) = 7.50 for \(Re\) = 8000. Additionally, empirical correlations for the \(\overline{{Nu_{{\text{r}}} }}\) and \(\overline{{f_{{\text{r}}} }}\) have been proposed, achieving an accuracy of ± 6% and ± 8%, respectively, with a coefficient of determination ( \(R\) 2 = 0.98). These empirical correlations provide valuable guidance for both academic research and industrial applications in optimal design of the solar air heater duct (SAHD). The findings establish a reliable foundation for enhancing the solar air heater system.
