## 3 Results and Discussion
### System Operating Map  
The previous analyses were focused on the performance of the system itself, and results obtained with the detailed CFD model were used, where one of the boundary conditions was the surface temperature of the slab in contact with the air chamber, assumed to be 310 K. In this section, the thermal performance of the system coupled to the building is analyzed in a simplified way, with the objective of setting system operation conditions depending on the space to be conditioned. Thus, the boundary condition here is the temperature of the space to be conditioned below the slab: the previous assumption of the surface temperature of the slab necessary for the resolution of the CFD model is removed, and an assumption of the temperature of the space below the slab is made instead. An outline of the analytical model used for this purpose is shown in Figure 13. The boundary conditions of this model are the inlet air temperature and mass flow rate and the temperature of the space below the slab. Then, the model obtains the heat flux evacuated from the space. In order to set an operation map of the system, the heat flux was calculated for different values of the above-mentioned boundary conditions. In particular, three different inlet air velocity values (mass flow rate) were used: 0.5, 1.0, and 1.5 m/s; five different inlet air temperature values: 18, 20, 22, 24, and 26 \({}^{\circ}\)C; and ten different values of the indoor air temperature: from 18 to 27 \({}^{\circ}\)C in steps of 1 \({}^{\circ}\)C.  
Figure 11: Variation of thermal efficiency and THPF with airflow rate. Figure 12: Variation of heat flux and ventilation power with airflow rate. The heat flux \(\dot{Q}\) is calculated using Equations (1), (2) and (5) as follows:  
\[\dot{Q}=1-e^{\left(-\frac{bA}{C_{Pair}\dot{m}_{air}}\right)}C_{Pair}\dot{m}_{air} (T_{slab}-T_{inlet}) \tag{8}\]  
On the other hand, a steady-state energy balance can be applied on the slab surface (Equation (9)), which implies that the heat flux by convection from Equation (8) is equal to that by conduction through the slab and by convection and radiation to the indoor space environment. \[\dot{Q}=\frac{T_{sp}-T_{slab}}{R_{cr}-R_{slab}} \tag{9}\]  
In Equation (9), \(T_{sp}\) is the indoor space temperature, \(R_{cr}\) is the indoor convective-radiant thermal resistance, and \(R_{slab}\) is the thermal resistance of the slab. In Equations (8) and (9), Tinlet, mair, and Tsp are known. Then, the model obtains Tslab and the heat flux. The convective heat transfer coefficient h of Equation (8) is assumed here to be equal to the numerically calculated value from the CFD model for a certain inlet air mass flow rate (mair) as follows: In Equation (8), the heat flux is set to be equal to the value obtained from the CFD for the corresponding mass flow rate with an air inlet temperature T inletCFD of 300 K and a slab temperature TslabCFD of 310 K. Thus, the convective heat transfer coefficient h can be calculated as follows:  
\[h=-\frac{C_{Pair}\dot{m}_{air}}{A}ln\left(1-\frac{QCFC}{C_{Pair}\dot{m}_{air}( T_{slabCFD}-T_{inletCFD})}\right) \tag{10}\]  
According to Table 3.8 and Table E.1 of the CIBSE guidelines [35], the value of \(R_{cr}\) of Equation (9) can be assumed to be 0.17 m\({}^{2}\) K/W for an indoor ceiling with a downward heat flux. The results for the best performance case for the different space temperatures and air inlet temperatures and mass flow rates are shown in Figure 14. The figure shows the heat removed from the space on the ordinate axis and the air temperature of the interior space to be conditioned on the abscissa axis for the five different inlet air temperatures and the three air velocities considered. As can be seen in the figure, for a given temperature of the space to be conditioned, the greater the heat removed, the higher the mass flow rate and the lower the inlet air temperature. The usefulness of this analysis and this figure is that it can be interpreted as an operating map of the system.