## 3 Results  
### Analysis of the Measured Data  
In Figure 7 we present a plot of the measured temperature profiles (temperatures in the flat panel and at the different depths of the soil), measured during 24 h on 21 July 2015, a sunny winter day in Campinas. Observing this plot we notice that, as expected, there is an inversion of the temperature profiles from day to night. The graph starts at noon (0 min is 12:00 a.m.), and during the day the temperature in the aluminium panel is much higher than in the soil (reaching 48 \({}^{\circ}\)C). At around 17:00 h (\(\approx\) minute 300) the temperature of the panel begins to go below the soil temperature, and stays below the soil  
Figure 6: Prototype of the TEG solar flat panel with buried heat sink. temperature until around 6:30 h in the next day (\(\approx\) minute 1110), when the panel's temperature rises again and goes above the soil's temperature. However, simply by looking at the plot of Figure 7, it is impossible to conclude, taking into account both the \"forward\" (when \(T_{plate}>T_{depth}\)) and \"reverse\" (\(T_{plate}<T_{depth}\)) directions, which depth provides the highest accumulated temperature difference. Thus, we decided to calculate a parameter which gives a clear indication of which depth can result in more energy being harvested: the daily integral with respect to time of the temperature difference between the aluminium plate and the measured points in the soil (\(T_{plate}-T_{depth}\)):  
\[\int_{t_{0}}^{t_{1}}\left(T_{plate}-T_{depth}\right)dt \tag{3}\]  
where \(t_{0}\) and \(t_{1}\) are respectively the initial and final time of the temperature measurements, in hours. These integrals, that for more clarity we computed as divided in two parts, for the period when \(T_{plate}>T_{depth}\) and for the period when \(T_{plate}<T_{depth}\), are shown in Figure 8. Data represented in Figure 8 was measured during 205 consecutive days in Mataro (from 23 June 2015 to 13 January 2016) at the depths of 5 cm and 40 cm. Concerning the plot in Figure 8, for the positive integrals we can observe that:  
* During the first 60 days in the summer (approximately day No. 0 to day No. 60), most of the time the diurnal integrals of the 40 cm depth have higher values;
* During the winter days shown in the plot (approximately day No. 150 to the end of the plot), most of the time the daily integrals of the 5 cm depth present higher values. For the negative integrals we notice that:  
* During the summer, both 40 cm and 5 cm curves present similar values;
* For the rest of the days shown, the integral of 40 cm depth presents higher (negative) values. However, looking at the daily plot of these integrals in Figure 8, it is still difficult to conclude which is the best depth. A more conclusive analysis concerning the potential of energy harvesting with a given soil temperature profile can be made if we perform a summation of the diurnal integrals of the squared \(\Delta T^{2}\). Figure 7: Measured temperature at various depths, during one sunny day in the winter (21 July 2015) in Campinas. Since, according to Equation (1), the electric power that a TEG can deliver is proportional to \(\Delta T^{2}\), we calculated the energy harvesting potential \(EH_{pot_{i}}\) for each depth \(i\), as the value of these integrals for the whole period:  
\[EH_{pot_{i}}=\int_{t_{0}}^{t_{1}}\left(T_{plate}-T_{depth_{i}}\right)^{2}dt \tag{4}\]  
These integrals are presented, for each depth, in the form of a bar graph to offer an easy visualization of which depth leads to the best result. The first graph presented, in Figure 9, is for the \"forward\" integrals (when \(T_{plate}>T_{depth}\)), in Mataro. In this graph it becomes evident that the depth which produces the highest integral is 20 cm, although an installation at the depth of 10 cm would lead to close results. Figure 8: Daily integral of temperature difference (\(T_{plate}-T_{depth}\)) with respect to time, for depths of 5 cm and 40 cm, from 23 June 2015 to 13 January 2016 (period of 205 days).