## 3 Validation of the Mathematical Model  
The model was validated against data obtained from the experiment on a laboratory-scale prototype of DPCT. The schematic of the testing station used for verification of the mathematical model is presented in Figure 6. The setup utilizes a counter-flow recuperator with half of the channels wetted with water (distributed through spray nozzles), allowing for the transfer of the pre-cooled air from dry channels to wet channels in a dew-point cycle. Water is supplied from a basin equipped with an electric heater, simulating the operational temperature of the water, which is cooled by the DPCT. A fan is used to force the air to flow through the cooling tower. Measurements were taken using Sensirion SHT85 air temperature and humidity sensors (Sensirion AG, Stafa, Switzerland) (accuracy of 0.1 \({}^{\circ}\)C and 1.5% RH, respectively) and Sensirion SHT85 sensors in a water proof cover for the water temperature (accuracy of 0.1 \({}^{\circ}\)C). Water was supplied by a pump located in the basin. Air temperature and humidity were measured at four points in the system: at the inlet to the exchanger, directly behind the dry channel, directly before the wet channel, and at the outlet of the exchanger. Water temperature measurements were taken directly in the  
Figure 5: Outdoor air parameters during cooling season in Polish climate. (**a**) Air temperature. (**b**) Air relative humidity.  
basins: the first basin contained warm water intended for cooling, and the second basin held already cooled fluid. To maintain continuous water flow, the cold, already-cooled water was returned to the tank with hot water. Warm water was obtained by heating it with a regular electric heater (capacity: 1.5 kW). In addition, an electric heater was used to increase the temperature of the airflow to simulate summer conditions. The inlet air temperature was stabilized at 25 \({}^{\circ}\)C and 10 g/kg humidity using a laboratory air conditioning system, and the water temperature varied from 50 to 60 \({}^{\circ}\)C with a 1 \({}^{\circ}\)C interval. The steady-state conditions were achieved after approximately 15 min of 45 min of each testing interval. The airflow rate was 200 m\({}^{3}\)/h, and the water flow rate was app. 90 kg/h.  
The validation was performed by comparing the outlet water temperature obtained during the experimental tests and from the numerical model. The model was set on identical operational conditions as in the experimental set-up, including the exchanger geometry and inlet air and water parameters. The validation of the model (the correlation between simulation and experiment results) is presented in Figure 7. It can be observed that the highest difference in temperatures of the cooled water between the numerical and experimental results is 1.0 \({}^{\circ}\)C, with an average temperature difference of app. 0.5 \({}^{\circ}\)C (the average discrepancy, defined as the temperature difference between the inlet and outlet temperature obtained from the model divided by the temperature difference between the inlet and outlet temperature obtained from the experiment, was 5.35%). The correlation between the model and the experiment is 0.9934. Furthermore, the model and the experiment exhibit the same trend in the obtained water temperatures at the exchanger outlet, depending on the initial conditions. Therefore, it can be concluded that the agreement between experimental results and the mathematical model is satisfactory, and the model can be utilized for simulating the operation of the DFCT.  
Figure 6: Scheme and photograph of the measuring station. (**a**) Scheme (nomenclature: T—water temperature sensor; T, RH—air temperature and humidity sensor). (**b**) Photograph.