# Performance Analysis of the Multi-Stage Dew-Point Indirect Evaporative Air Cooler
## 3 Results and Discussion  
Until now, the analysis of indirect evaporative dew-point exchangers allowed for a good understanding of their operation characteristics for various operational parameters. Generally regenerative counter-flow evaporative heat exchangers achieve higher dew-point efficiencies, while cross-flow heat exchangers based on the Maistostsenko-cycle achieve higher cooling capacities [20]. To calculate the cooling capacity of the unit, the inlet air flow was assumed to be \(\dot{m}=1.0\) kg/s. In Figure 3a,c,e, the influence of the ratio of the working to the primary air flow in each section is presented. The counter-flow and cross-flow parts are marked as 2 and 3, respectively. The influence of the relative length of the cross-part on the outlet air temperature is presented. Based on the temperatures obtained, the cooling capacity of the device was calculated for various configurations, which are shown in Figure 3b,d,f. It can be noticed that in the case of \(W_{2}/W_{1}=0.1\), the cross-section of the proposed exchanger allows for lowering the air temperature after the exchanger. It follows from the fact that until the cross-flow section achieves 0.7, the outlet temperature decreases. The minimum air temperature at the exit of the exchanger occurs when the cross-flow section length is \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Parameter**} & **DPIEC 1 and DPIEC 2** & **DPIEC 3** \\  & **Multi-Stage Dew-Point** & **Regenerative Dew-Point** \\  & **Evaporative Cooler** & **Evaporative Cooler** \\ \hline Cooler length & 1.0 m & 1.0 m \\ Cooler width & 1.0 m & 1.0 m \\ Cooler channel height & 3.0 mm & 3.0 mm \\ Inlet velocity & 3.0 m/s & 3.0 m/s \\ NTU\({}_{1}\) & 6.38 & 6.38 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Analyzed dew-point evaporative cooler operating parameters. Figure 2: Initial conditions for the multi-stage dew-point evaporative cooler. equal to 0.7. In general, lower temperatures are observed for a higher working-to-product air-flow ratio in the cross-flow section (\(W_{3}/W_{1}\)). Nevertheless, for \(W_{3}/W_{1}\) equal to 0.5, 0.7, and 1.0, the temperature values fluctuate by 0.5 \({}^{\circ}\)C. By increasing the \(W_{2}/W_{1}\) ratio from 0.1 to 0.3 and 0.5, there is a possibility to achieve lower outlet air temperatures. For different lengths of the cross-section and \(W_{2}/W_{1}=0.1\) and \(W_{2}/W_{1}=0.3\), the outlet air temperatures are in the range 20.6-24.8 and 18.8-20.3 \({}^{\circ}\)C, respectively. According to Figure 3, for working-to-product air-flow ratio \(W_{2}/W_{1}=0.5\), the exchanger achieves the lowest values of the outlet temperatures in the range 17.9 \({}^{\circ}\)C-21.3 \({}^{\circ}\)C.  
Figure 3: _Cont._  
Figure 3: Cont. By analyzing the different relative lengths of the cross-section for the three ratios, \(W_{2}/W_{1}=0.1\), \(W_{2}/W_{1}=0.3\), and \(W_{2}/W_{1}=0.5\), the minimum outlet temperatures are obtained for different lengths of the cross-section. For example, for parameters \(W_{2}/W_{1}=0.1\) and \(W_{3}/W_{1}=1.0\), the air temperature behind the exchanger is the lowest for \(X_{cross}=0.7\); for \(W_{2}/W_{1}=0.3\) and \(W_{3}/W_{1}=1.0\), the air temperature behind the exchanger is the lowest for \(X_{cross}=0.4\); and for \(W_{3}/W_{1}=0.5\) and \(W_{3}/W_{1}=1.0\), the air temperature after the exchanger is the lowest for \(X_{cross}=0.1\). It follows that the higher the value of the air flow that is reversed to the working channel, the smaller part of the exchanger can be devoted to the cross-section. It can be seen in Figure 3b that the proposed exchanger achieves a maximum cooling power ranging from 5.6 to 8.6 kW for the ratio \(W_{2}/W_{1}=0.1\), even though the air is cooled  
Figure 3: Cooling performance of multi-stage DPIEC in the case of ambient air parameters: \(t=30\)\({}^{\circ}\)C, RH = 45%. (**a**) Outlet air temperature for \(W_{2}/W_{1}\) equal to 0.1. (**b**) Cooling capacity for \(W_{2}/W_{1}\) equal to 0.1. (**c**) Outlet air temperature for \(W_{2}/W_{1}\) equal to 0.3.