# Energy-Based Thermo-Hydraulic Performance of Roughened Absorber in Solar Air Heater Duct
## 4 Result and Discussions
### The Effect of Relative Height  
The exergy efficiencies of the SAH absorber with conical protrusion ribs are studied for all combinations of relative rib height and relative rib pitch when the solar insolation is exploited from 600 W/m\({}^{2}\) to 1000 W/m\({}^{2}\). The exergy efficiency of conventional SAH is also assessed for comparison considerations. The exergy efficiencies for fixed rib pitch (\(P/e=10\)) at 1000 W/m\({}^{2}\) of solar insolation is shown in Figure 7. The exergy efficiency improves with increasing temperature rise parameter, then falls continuously for all relative rib heights, as seen in the graphs. However, differing temperature increase parameters, which are dependent on the relative rib height, produce distinct exergy efficiency peaks. Table 2 shows the range of temperature parameters at which increased exergy efficiency is seen. Smooth SAH exhibits the highest exergy efficiency for temperature increase parameters smaller than 0.0076 K\(\cdot\)m\({}^{2}\)/W. When the temperature increase parameter increases, the parameter for relative rib height takes precedence. The largest exergy efficiency is achieved for relative rib heights of 0.020, 0.0289 and 0.036 when the respective temperature increase parameters are 0.0076-0.0087 K\(\cdot\)m\({}^{2}\)/W, 0.0087-0.0101 K\(\cdot\)m\({}^{2}\)/W and 0.0104-0.0111 K\(\cdot\)m\({}^{2}\)/W. For a temperature increase parameter larger than 0.0111 K\(\cdot\)m\({}^{2}\)/W, the optimum exergy efficiency is achieved with a relative rib height of 0.044. At 1000 W/m\({}^{2}\) of solar insolation, Figure 8 illustrates the fluctuation of exergy efficiency for a conical rib pitch value of \(P/e=10\). The exergy efficiency increases with the Reynolds number, reaches a maximum value, and subsequently decreases, as seen in the graphs. The maximum exergy efficiency  
Figure 6: Absorber temperature variation, air heat gains and pumping power.  
has been observed for varying Reynolds numbers, which depend on the relative rib height. Similarly, Table 2 reports the optimal values of relative rib heights with respect to the ranges of the Reynolds number for which the maximum energetic efficiency is achieved. When the Reynolds number is larger than 10760, the solar air heater with smooth duct achieves the highest exergy efficiency. The solar air heater with conical protrusion ribs achieves the highest effectiveness when the Reynolds number is smaller than 10760. In the following ranges of the Reynolds number, 9700-10760, 7530-9700 and 6910-7530, the relative rib height of 0.020, 0.0289 and 0.036 exhibit the highest exergy efficiency. When the Reynolds number is less than 6910, the relative rib height of 0.044 provides optimum exergy efficiency. Table 3 reports the enhancement factor of the exergy efficiency achieved by conical protrusion ribs over varying relative rib height.  
\begin{table}
\begin{tabular}{c c c c c} \hline  & \multicolumn{3}{c}{\(\eta\)/\(\epsilon\) = 10 and \(I\) = 1000 W/m\({}^{2}\)} \\ \hline
**Parameter** & **Optimum Value** & \(\Delta T\)/\(I\) & **Re** \\ \hline  & Smooth & \(\Delta T\)/\(I\) \(<\) 0.0076 & \(Re>\) 10760 \\  & \(e/D\) = 0.0200 & 0.0076 \(<\Delta T\)/\(I\) \(<\) 0.0087 & 9700 \(<Re<\) 10760 \\ \(e/D\) & \(e/D\) = 0.0289 & 0.0087 \(<\Delta T\)/\(I\) \(<\) 0.0104 & 7530 \(<Re<\) 9700 \\  & \(e/D\) = 0.0360 & 0.0104 \(<\Delta T\)/\(I\) \(<\) 0.0111 & 6910 \(<Re<\) 7530 \\  & \(e/D\) = 0.0440 & 0.0111 \(<\Delta T\)/\(I\) & \(Re<\) 6910 \\ \hline \end{tabular}
\end{table}
Table 2: Optimum values of rib height.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \multicolumn{2}{c}{\(\text{P/}\epsilon\) = 10, \(I\) = 1000 W/m\({}^{2}\)} & \(\Delta T\)/\(I\) = 0.005 & \(\Delta T\)/\(I\) = 0.01 & \(\Delta T\)/\(I\) = 0.015 & \(\Delta T\)/\(I\) = 0.020 & \(\Delta T\)/\(I\) = 0.025 \\ \hline Enhancement & \(e/D\) = 0.0200 & 1.14 & 1.28 & 1.39