# Analytical Investigation of a Novel System for Combined Dew Point Cooling and Water Recovery
## 3 Results  
### Performance Indicators  
Several different indicators were used to describe DPC-WR system performance. The cooling effectiveness of the DPC-WR system is described with COP (coefficient of performance), defined as an amount of the cooling capacity divided by the electric power input (Equation (21)).  
\[\text{COP}=\frac{\dot{Q}_{4}^{S}}{W_{net}} \tag{21}\]  
The driving force behind the DPC-WR system is the renewable psychometric energy related to the latent heat of water evaporation. This renewable energy is delivered to the DPC-WR system with ambient air, which is also a necessary medium in the dew point cooling process. Therefore, the only external energy supplied to the DPC-WR system is the electric power input to the fan to transport the air through the following stages of the system. For the same reason, the cooling capacity in Equation (21) applies only to the 2 nd stage of the DPC-WR system. The air in the 1 st stage is also cooled and its temperature after leaving the 1 st stage is lower than at the inlet to the system. However, the heat transfer associated with the cooling in the 1 st stage is also the driving force of the entire process. For this reason, only the cooling capacity of the 2 nd stage is used in the calculations, which is to simplify the understanding of the COP, also in relation to other indicators.  
The electric power input to the fan is described with Equation (22), where \(\Delta p\) is the pressure drop defined with the Darcy-Weisbach coefficient of airflow friction losses (Equation (23)). The coefficient of fluid friction losses related to the laminar flow in rectangular channels where the width/height ratio is high is described with Equation (24) [24].  
\[\dot{W}_{net}=\frac{\Delta p\dot{V}}{\eta},\text{ kW} \tag{22}\]  
\[\Delta p=f\frac{L}{4R_{h}}\frac{\rho_{a}u^{2}}{2},\text{ Pa} \tag{23}\]  
Figure 3: Validation of the mathematical model of the DPC-WR system: (**a**) Validation of the exhaust air temperature; (**b**) Validation of the exhaust air relative humidity.  
\[f=\frac{96}{\text{Re}}=\frac{96\
u}{4R_{h}u} \tag{24}\]  
The water recovery effectiveness of the DPC-WR system is described by the GOR (gained input ratio), defined as the heat released during condensation divided by the electric power input (Equation (25)). It describes the effectiveness of the use of electric energy supplied to the DPC-WR system in the process of water recovery via condensation.  
\[\text{GOR}=\frac{\dot{\dot{Q}}_{4}^{L}}{\dot{W}_{net}} \tag{25}\]  
The overall effectiveness of the DPC-WR system is described by the EUF (energy utilization factor) (Equation (26)). This indicator includes both electric power input and renewable energy delivered with air. EUF describes the effectiveness of the utilization of energy supplied to the DPC-WR system for combined cooling and water recovery purposes.  
\[\text{EUF}=\frac{Q_{4}^{S}+Q_{4}^{L}}{Q_{1}^{T}+W_{net}} \tag{26}\]  
The rest of the indicators relate to water recovery. The specific energy consumption (SEC) is defined as the amount of energy needed to recover 1 m\({}^{3}\) of water (Equation (27)). The recovered water is the water condensed in the primary channels in the 2 nd stage. It should be noted that the proposed system is modular; therefore, any water capacity can be recovered by multiplying modules as needed. Due to this fact, the daily water recovery for one unit of the DPC-WR system is not considered a very informative indicator, so another indicator is introduced, which is the specific daily water production (SDWP). SDWP is defined as the daily amount of recovered water related to 1 kg/s of air delivered to the DPC-WR system (Equation (28)).  
\[\text{SEC}=\frac{N_{net}}{\Delta x_{4}V_{4}}\frac{1}{3600^{7}},\text{ kWh/m}^{3} \tag{27}\]  
\[\text{SDWP}=\frac{24\cdot 1000\cdot 3600\cdot\Delta x_{4}V_{4}}{G_{1}},\text{ liter/day/(kg/s)} \tag{28}\]