# Energy-Based Thermo-Hydraulic Performance of Roughened Absorber in Solar Air Heater Duct
## 4 Result and Discussions
### The Effect of Relative Pitch  
The exergy efficiency of ribs with conical protrusions is plotted against the temperature increase parameter for different relative rib pitches but for a fixed relative rib height of \(e/D=0.289\) and constant solar insolation of 1000 W/m\({}^{2}\), as shown in Figure 9. Over a range of increasing temperature increase parameter, the exergy efficiency increases at first, then achieves a maximum value and lastly decreases. The exergy efficiency maximum occurs for different temperature increase parameters, which depends on the relative rib pitch. Table 4 reports the values of relative rib pitches relative to the temperature increase parameter at which the maximum exergy efficiency is achieved. A smooth SAH achieves the highest exergy efficiency if the temperature increase parameter is smaller than 0.0076 K\(\cdot\)m\({}^{2}\)/W. For temperature increase parameters exceeding 0.0076 K\(\cdot\)m\({}^{2}\)/W, the relative rib height parameter takes precedence. A relative rib pitch value of \(p/e=12\) achieves the highest exegetic efficiency in the range of temperature increase parameter between 0.0076 K\(\cdot\)m\({}^{2}\)/W and 0.0092 K\(\cdot\)m\({}^{2}\)/W. When the temperature increase parameter is larger than 0.0092 K\(\cdot\)m\({}^{2}\)/W, the highest exergy efficiency is achieved by a relative rib pitch value of \(p/e=10\). At a solar insolation of 1000 W/m\({}^{2}\), Figure 10 shows how the exergy efficiency changes with the Reynolds number if the relative rib height is constant at \(e/D=0.00289\). The exergy efficiency increases with the Reynolds number and, after achieving a maximum, decreases with a further increase in the Reynolds number. Table 4 reports the optimal values of rib pitches for achieving maximum exergy efficiency with respect to the Reynolds number range. When the Reynolds number is smaller than 8570, conical protrusion ribs with a relative rib pitch of \(p/e=10\) exhibit the optimum exergy efficiency. When the SAH works in the range of Reynolds number 8570-10870, the relative rib pitch of \(p/e=12\) achieves maximum exergy efficiency. When compared to the SAH with protrusion ribs, the smooth-duct SAH delivers the highest exergy efficiency for a Reynolds number larger than 10870. In addition, the plots show that relative rib pitches of \(p/e=6\) and 8 do not have a major impact on the SAH performance. Table 5 depicts the enhancement factor in the exergy efficiency owing to conical protrusion ribs at different values of relative rib pitches.  
Figure 8: Exergy efficiency as function of Re.  
Figure 10: Exergy efficiency as function of Re.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**\(I\) = 1000 W/m\({}^{2}\) and \(e\)/D = 0.0289**} \\ \hline
**Parameter** & **Optimum Value** & \(\Delta T/I\) & \(Re\) \\ \hline \multirow{2}{*}{\(p/e\)} & Smooth & \(\Delta T/I<0.0076\) & \(Re>10870\) \\  & \(p/e=12\) & \(0.0076<\Delta T/I<0.0092\) & \(8570<Re<10870\) \\  & \(p/e=10\) & \(0.0092<\Delta T/I\) & \(Re<8570\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: The optimum rib pitch.  
Figure 9: Exergy efficiency as function of \(\Delta T/I\).