## 3 Results
### Evolution of Temperatures During the Discharge Process of the TES Systems
Therefore, the segregation of temperature and the appearance of the thermocline confirmed the static character of the granular material in the confined bed, indicating the effective mechanical confinement of the bed. The thermocline of the confined-bed TES system illustrated in Figure 3 was found to be very thin, occupying only a small portion of the bed height. The evolution and thickness of this thermocline can be modeled by a 1D analytical heat transfer model [43; 44] to obtain proper agreement with the experimental measurements [25]. The evolution of temperature distribution during the discharge of the alumina block TES system is in Figure 3 as colormaps. In contrast to the granular material TES system, the convection heat transfer coefficient between the alumina block channel walls and the HTF was low at around 60 W/m\({}^{2}\)K [45]. Thus, the temperature of air and alumina differed during the discharge of the solid block TES system. Therefore, two sets of colormaps of the solid block TES system during the discharge process are included in Figure 3, one of which was constructed using the temperature distribution of the air measured in the central channel, and the other considering the temperature distribution of the alumina measured at the wall of the central channel. In this case, the measurements registered by the eight thermocouples used for the air and the eight thermocouples used for the alumina were used to build the colormaps, following a similar procedure to that applied for the granular material TES system, i.e., considering the local temperature measured for both air and alumina as representative of the temperature of that medium in the whole cross-section and interpolating the values registered by each thermocouple to obtain smooth colormaps. The colormaps of the temperature distribution of the air and alumina in the solid block TES system show a similar evolution; however, the alumina temperature was always locally higher than that of the air at specific time instances, since heat was transferred from the alumina to the air during the discharge process. The discharge process of the solid block TES system occurred with temperature segregation along the system height, with higher temperatures in the top blocks and lower temperatures in those located at the bottom, similar to the discharge of the confined-bed TES system. Nonetheless, the separation of high and low temperatures in the TES system was not so clear for the solid blocks as for the confined bed, in which a narrow thermocline appeared. In the case of the discharge of the alumina block TES system, the zone of temperature variation was much more diffuse, obtaining a gradient of temperature along the height of the TES system during the discharge process. This wider temperature distribution in the alumina block TES system is characteristic of the discharge of thermal energy storage systems based on large solids [46; 47]. The granular material and the alumina block TES systems were also compared in terms of the time evolution of the air temperature at different locations during the discharge process. In particular, the temperatures of air measured by the thermocouple closest to the outlet of the TES systems, corresponding to 95% of the total height for both thermal energy storage systems, and by the thermocouple located at 60% of the system height are compared in Figure 4. The homogenous temperature of the fluidized-bed TES system was confirmed by the superposition of the time evolution of the temperature measured at 60 and 95% of the total height on the same curve. As expected, the temperature of the fluidized-bed TES system evolved as an inverse exponential from the initial temperature to room temperature as the discharge process progressed [24; 26]. In contrast, the discharge of the confined-bed TES system with temperature segregation resulted in a very different time evolution of the temperature.