## 7 Results and Discussion
The last column of the table shows the average oversizing of the power of the heaters, calculated as the ratio between the effective power and the one needed at steady-state condition (design point). A clear difference can be seen between the power of 2 kW and small differences between 3 and 4 kW. Using a heater power of 2 kW, the time that it took to achieve the comfort conditions was about five hours (see Figure 23); for this reason, it would be interesting to have smart, remote, or mobile control of the building. Looking at the thermal power supply of 3 and 4 kW, the duration of the transient was about 1 h in both cases, and the increase of the power of the heaters, from 2.3 to 3.1 times the minimum necessary, did not make a significant decrease in the delay that was needed to get comfortable conditions. If one considers the time of peoples' adaption in a new environment and can accept short delays, it is possible to conclude that both cases lead to comfortable conditions in a short time, of the order of a quarter of an hour, even if users switch on the heating, with no advance, only when they go into the house. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Suggested Comfort Temperature**} & \multirow{2}{*}{**Average**} \\ \cline{3-4}  & & **19**\({}^{\circ}\)C & **20**\({}^{\circ}\)C & **21**\({}^{\circ}\)C & \\ \hline \multirow{3}{*}{**average**} & 2000 & 164\% & 153\% & 144\% & 150\% \\  & 3000 & 247\% & 230\% & 216\% & 230\% \\ \cline{1-1}  & 4000 & 329\% & 307\% & 288\% & 310\% \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Oversizing of the heaters power. Figure 22: Time needed to reach the internal comfort temperature. Figure 23 shows the profile of temperature, in time, after switching on the heater with a \"cold house\" at 6 \({}^{\circ}\)C. The three different curves describe the transient of the internal air, which is the most important parameter. Another parameter, which has a lower but not negligible impact on the thermal comfort of people, is the mean radiant temperature (MRT). This depends on the temperature of the surfaces of the room, and it is defined as a weighted mean, on the area, of the surface temperature of bodies, to which people are exposed. The temperature of the heater has a strong impact on the calculation of the MRT, because it has a small area but it has a high temperature. To emphasize the effect of the heater and to show the effect of the walls on someone that \"does not see the heater\", the third curve reports the room MRT calculated on all the surfaces apart from the heater one. It is possible to see that the transient of the MRT was substantially like the one of the inlet air. Nevertheless, if we look at the MRT, calculated on the not-heated surfaces only, it is possible to see that the temperature was lower than the internal one and that MRT took about twice as long to reach comfortable values. For this reason, it is important to evaluate this parameter in building simulations. Figure 24 displays the variation of temperature, for different heater power levels, with different outdoor temperatures. As the total power, required from this building at steady-state, was only 1300 W, it can be clearly seen, in Figure 24, that a heater power of 2000 W would need the help of a building management system and remote control to reach a comfortable condition in time. On the other hand, looking at the green line with 4000 W, it is possible to notice that it did not cause any relevant reduction of the delay with respect to the case whereby only heaters with 3000 W were installed. Figure 23: Transient profile of temperatures with a 2-kW heater.