## 3 Results and Discussion
### Self-Heating by Joule's Effect  
Figure 7 shows the results of the self-heating test. First, Figure 7a shows \(\Delta\mathrm{T_{max}}\) and \(\Delta\mathrm{T_{av}}\) reached by [PERSON]'s heating of the 3D printed circuits as a function of the number of printed layers. Here, an increase in both the maximum and the average temperatures with the number of printed layers can be observed, which can be explained by the previously mentioned expression for the electrical conductivity (1). Here, the higher cross-sectional area (Figure 5d) and the higher electrical conductivity when increasing the number of printed layers (Figure 6a) are related to the lower electrical resistance of the printed circuits. Furthermore, according to [PERSON]'s law (2), a decrease in the electrical resistance is related to an increase in the intensity, \(I\), for the same applied voltage, \(V\), and, according to [PERSON]'s heating law (3), the heat generated during [PERSON]'s heating test, \(Q\), is related to the square of the intensity. \[V=I\cdot R \tag{2}\]  
\[Q=I^{2}\cdot R\cdot t \tag{3}\]  
In this regard, the higher amount of printed material the circuit presents, the higher temperature it reaches by [PERSON]'s heating. Furthermore, by increasing the number of layers,  
Figure 7: Self-heating tests by [PERSON]’s heating. (**a**) Average and maximum temperature increment with respect to room temperature (left axis), and printed circuit volume (right axis) as a function of the number of printed layers, (**b**) IR images at different heating times during self-heating tests as a function of the number of printed layers and (**c**) self-heating test of a 4-layer circuit showing average and maximum temperature increments of the circuit as a function of time. the specific area of the printed circuit decreases (Figure 5d), thus minimizing heat losses. On the other hand, the difference observed between \(\Delta\mathrm{T}_{\mathrm{max}}\) and \(\Delta\mathrm{T}_{\mathrm{av}}\) values is explained because of the non-heated substrate. The standard deviation between different measurements can be caused by homogeneity issues in the printed circuits. Nevertheless, the self-heating tests showed great results in terms of heating capability with the relatively low applied voltage in comparison with previous studies performed with thermally cured resins and much higher carbon nanoparticle contents [24; 38]. In this context, the four-layer circuit would be suitable for deicing purposes even in \(-30\)\({}^{\circ}\)C conditions since it is capable of reaching an average temperature increment with respect to room temperature above \(30\)\({}^{\circ}\)C [39]. On the other hand, the IR images shown in Figure 7b demonstrate the fast and homogeneous heating achieved by the printed circuits. Here, the slight temperature differences along the circuit can be caused by local heterogeneities of the nanocomposite, such as CNT aggregates, that could lead to the presence of high and low electrically conductive areas. Moreover, Figure 7c shows an example of the \(\Delta\mathrm{T}_{\mathrm{max}}\) and \(\Delta\mathrm{T}_{\mathrm{av}}\) as a function of time during a self-heating test carried out for a four-layer circuit. Here, the fast heating of the circuit can be noticed since it was able to reach a temperature increment with regard to room temperature of around \(30\)\({}^{\circ}\)C within \(1\) min. Figure 8a shows a cyclic self-heating test. Here, a great repeatability in the temperature reached by [PERSON]'s heating can be observed among the five cycles of heating and cooling, since the deviation in the temperature reached was below \(3\%\). Moreover, the self-heating test carried out for \(2\) h of continuous heating (Figure 8b) showed an ever-increasing temperature with time due to the ever-higher electron mobility promoted by the temperature increase.