## 3 Materials and Methods
### Experimental Procedure: Electrical and Thermal Measurements  
A systematic experimental procedure is carried out to evaluate the wire-to-plane fins configuration with the prototype developed consequently the corona discharge characteristics are obtained. A high voltage power supply (Heinzinger(r) LNC high voltage laboratory 6000-5 pos model) is used to produce the positive DC discharge. A representative scheme of the experimental set-up for this investigation is shown in Figure 2B. The wire (emitter electrode) is connected to the high-voltage DC system that has a voltage between 0 and 6 kV and the convergent electrode is grounded. Corona experiments are performed to study the positive electric discharge phenomenon with this distribution which analyzed its electrostatic and thermal behavior. The characteristic C-V curve and the corona onset voltage are recorded and studied with respect to the different parameters mentioned for the electrical optimization. The applied voltage is increased in distinct steps and reduced as it approaches the saturation voltage. This procedure is repeated with different voltages in the corona device, and with different geometries. Each experimental electrostatic analysis is repeated at least 10 times to achieve a greater understanding of the corona effect, as well as to analyze repeatability average of measurements for the presented configuration.  
Regarding the tests to thermally characterize the performance of the devices, resistance is used as a heat source. The heat resistance value is 650 \(\Omega\), which is powered by \"Aim-TTi PLH 250 DC Power Supply\". While the corona refrigerator is moving air, the heat source is heating an isolated aluminum plate, where temperature is measured with a probe thermocouple (type K), see Figure 3. Heat flux is changed by modifying voltage supply in a low-voltage source. The corona device is placed on the aluminum plate, with a thermal contact. The stabilized temperature of the system in different heating powers defines the temperature increase as a function of heat flux applied (an example of this result is shown in Figure 3). This curve allows to define the term \(\mathbf{Ah}-\boldsymbol{\upxi}\) as the inverse of the slope. This procedure is repeated with different voltages in the corona device, and with different geometries. For thermal results, statistical analysis was carried out. With a sample of approximately 550 points, a normal error distribution is obtained with a standard deviation of 0.645. The interquartile range (1053) is defined and measurements with an absolute error greater than \(\pm\)1.5 are discarded. Extrapolating this analysis to the curves obtained from thermal resistance and heat transfer coefficient, a higher relative error level of 4% is obtained.  
In order to achieve a better understanding of the aerodynamics of the device, thermal images of the flow can be helpful. The mark of the thermal flow is obtained with a thermographic photography of a paper sheet situated in the middle of the corona device flow, in longitudinal direction (direction of the wires). Those images are obtained with thermographic camera TESTO 875-1i (160 \(\times\) 120 pixels, 33 Hz).