## 3 Results
### Thermal Exchange at the Surface  
As already mentioned in the methodological section, when analyzing the heat transmission in the surface, it is mandatory to consider that the three heat transmission mechanisms are possible. Starting with the convection process, as stated in Equation (5), the quantification of the convection heat rate requires defining a series of parameters concerning the convection cell. First of all, the reference temperature (Equation (9)) was set (by considering the average sand and ambient temperatures) at the value of 44.40 \({}^{\circ}\)C. This value constitutes the starting point to establish the properties of the air in the conditions of the experimental test. Table 3 presents the values of these properties for the reference temperature [40; 41]. \begin{table}
\begin{tabular}{c c c c} \hline \hline \(\hat{m}\) & \(T_{i}\) (\({}^{\circ}\)C) & \(T_{o}\) (\({}^{\circ}\)C) & \(\dot{Q}_{cond}\) (W) \\ \hline
38.78 & 59.14 & 58.85 & 69.30 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Determination of the heat transferred by conduction. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{4}{c}{**Average Temperatures (\({}^{\circ}\)C)**} & \multicolumn{4}{c}{**Thermal Conductivity (W/mK)**} \\ \hline
**S2** & **S3** & **S4** & **K2-3** & **K3-4** & **K2-4** \\ \hline
38.78 & 34.69 & 30.27 & 0.590 & 0.445 & 0.515 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average temperature for the sensors included in the study (during the stationary regime) and thermal conductivity of the sandy material calculated for the different sets of sensors. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\rho\) (kg/m\({}^{3}\)) & \(v\) (m\({}^{2}\)/s) & \(\mu\) (Pa\(\cdot\)s) & \(K_{a}\) (W/mK) & \(\alpha\) (m\({}^{2}\)/s) & \(Pr\) & \(Cp\) (kJ/kg\(\cdot^{\circ}\)C) \\ \hline
1.092 & 17.6 \(\times\) 10\({}^{-6}\) & 19.12 \(\times\) 10\({}^{-6}\) & 0.0265 & 24.8 \(\times\) 10\({}^{-6}\) & 0.71 & 1.014 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Properties of the air for the reference temperature of the study. Considering the information of Table 3, a \(Re\) = 5 \(\times\) 10\({}^{5}\) (for a turbulent regime) and \(u_{F}\) = 0.5 m/s (measured during the tests) are established, and \(Xc\) and \(Nu\) are then respectively calculated for obtaining the convection heat transfer coefficient \(h_{c}\) (Equations (6)-(8)). Table 4 shows the aforementioned parameters. When trying to determine the total convection heat rate in the case under study, it is important to consider the variation of the air temperature. For including this variation in the calculation, the region between the sensors under study (S2-S4) was divided into a series of rings (Figure 10). As shown in Figure 9, each ring selected in the area between sensors corresponds to one pixel of the camera. In this way, the convection heat rate is extended to all the pixels for which temperature is evaluated by the thermal chamber corresponding to all the radial rings from S2 to S4. Table 5 shows the calculation of the convection heat rate for the distances from the center to each pixel and the total heat exchanged by convection in the surface. Each value of \(\hat{q}_{\textit{\tiny{COUP}}}\) is obtained from the average sand temperature registered by the thermal infrared camera and using Equation (5). \begin{table}
\begin{tabular}{c c c} \hline \(Xc\) (m) & \(Nu\) & \(h_{c}\) (W/m\({}^{2}\cdot\)*C) \\ \hline
1.76 & 418.86 & 6.18 \\ \hline \end{tabular}
\end{table} 
Table 4: Calculation of \(Xc\), \(Nu\) and \(h_{c}\) required for the calculation of the global convection heat rate. Figure 10: Distribution of the rings considered for the global calculation of heat thermal exchange. Focusing on the radiation effect, its quantification is made following the same procedure, which considers the average temperature data per pixel from sensors S2 to S4 in the stationary regime.