## 7 Results and Discussion
Figure 19: Inlet air temperature variation. Figure 20: Internal air temperature with different input powers: (**a**) 2000 W; (**b**) 3000 W; and (**c**) 4000 W.  
Figure 20 shows that in case of outdoor temperature equal to 0 \({}^{\circ}\)C, the internal temperature reached 21 \({}^{\circ}\)C, in about 350 min. The time needed to get to thermal comfort decreased to 280 min if the outdoor temperature increased from 0 to 20 \({}^{\circ}\)C. In graph (b), the power was 3000 W and the time significantly decreased to 90 min, for an external temperature equal to 0 \({}^{\circ}\)C. Moreover, graph (c) shows that the delay dropped to 50 min for a power equal to 4000W. Figure 21 shows the energy consumption in the building in order to achieve the temperature of 21 \({}^{\circ}\)C, with variable input power and external temperature. If we think about a domestic plant, which is remotely controlled (activated), in advance, to guarantee the thermal comfort conditions at a predefined time, the lower the power of the heater is, the longer the plant must be turned on in advance. For this reason, the higher energy consumption was obtained with the heater power of 2000 W, about 11.3 kWh, because the heating period, which leads to the comfort condition, was longer. The power consumption for the other input powers considered were 4.5 and 3.2 kWh, respectively. It is worth noting that, if one thinks of switching on the plant in advance to achieve thermal comfort when one arrives, the larger the heater power is, the less they consume. The fluctuation on the graphs after reaching the comfort temperature were due to the on/off control. Figure 22 shows the amount of time that was needed to reach the final comfort state, for many different conditions. The different colors of the bars represent the different powers of the heating system. On the other hand, the numbers on the bar are the internal temperature set-points that were investigated (19, 20, and 21 \({}^{\circ}\)C). The big blue bars on the right side represent the time that would be needed if the size of the heating system was exactly equal to the required amount for steady-state condition. In the case whereby the heater power was exactly equal to the one required at steady-state, the duration of the transient would be unacceptably long, and this would make it impossible to appreciate the differences between other bars, if they are plotted together. For this reason, to make it clearer, the results for 2.0, 3.0, and 4.0 kW were separately reported, in Table 10.  
Figure 21: Energy consumption with different input powers: (**a**) 2000 W; (**b**) 3000 W; and (**c**) 4000 W.  
Today, a wide range of cheap and non-invasive devices, which enable remote control of heating systems, are available on the market. Even the cheapest of these devices can switch on the heating via mobile phone, tablet, or by means of a web interface, and they can also be used in old buildings, which would be difficult and expensive to turn into smart buildings. Bearing in mind the transient conditions, corresponding to what happens when one goes into a cold and unused house, it is possible to imagine that such buildings are placed far from the main city in the countryside or the mountains, and it is possible to switch on the heating before traveling there. In this case, a delay of some hours could be a proper period, for people travelling, to get a thermally-comfortable house. Within this new context, transient analyses are useful tools to evaluate, from a different point of view, the proper power size of the heaters and the percentage of oversizing of heater power in comparison with the one calculated for the steady-state. Table 10 reports a set of scenarios that were evaluated using the model. In all of these cases, the power of the heaters strongly exceeded the heat flow rate at steady-state. In Table 10, percent oversizing of heaters power is represented, considering different powers of the heating system and different comfort temperatures.