## 4 Results
### Identification of Parameters and Validation  
As previously mentioned, the model parameters have been obtained with the results of the experimental prototype of the radiant roof system. The parameters to be determined were the coefficients \(K\) and \(n\) (see Equation (5)) of the convective film coefficient in heating and cooling mode. These parameters were determined by applying least squares to a subsample of the results obtained. Figure 11 shows the total heat flux, absorbed when the cover was in cooling mode (left) and dissipated when in heating mode (right). In both cases, it was a function of the water temperature difference for various flow rates tested. The total heat flux was measured for different water flows and water temperature differences (see Figure 10). For both heating and cooling mode, as the flow through the radiant cover was reduced, the thermal jump of the water between the inlet and the outlet was higher for the same given total heat flux. As described in Equation (5), the total absorbed heat flux was broken down into convective heat flux and radiant heat flux. The radiant heat flux varied as a  
Figure 11: Total heat flux. Cooling mode vs. heating mode. Figure 10: Water flow variation—analysis of radiant and air mean temperatures and water temperatures. function of the thermal jump between the average water temperature (\(\overline{T_{W}}\)) and the average radiant temperature (\(T_{rad}\)) of the cell in which the radiant ceiling is located. Figure 12 shows the behaviour of radiant heat flux in both cooling (left) and heating (right) mode compared to \(LMTD_{rad}\). Also, it is necessary to know the emissivity of the material used. Emissivity is estimated by an identification procedure using a comparison between experimental data and estimation from the model. Starting from the premise that construction materials have an emissivity between 0.7 and 0.9. The emissivity obtained was 0.85. This linearity in the results obtained translated into a radiant transfer coefficient that was practically constant for both the cooling and heating modes. It was observed that, at the same temperature difference, the radiant heat flux obtained was higher in heating mode than in cooling mode. It implies an average \(h_{rad}\) of 4.6 \(\frac{W}{\text{m}^{2-z}\text{C}}\) for the system in cooling mode and 6.2 \(\frac{W}{\text{m}^{2-z}\text{C}}\) for heating mode. The convective heat flux obtained in the experiments carried out as a function of the \(LMTD_{cv}\) is shown in Figure 13 for heating and cooling modes. As shown in Figure 13, convective heat flux was higher in cooling than heating mode for the same difference in water temperature. This occurred because the cooling mode stimulated air movement (cold ceiling) due to a buoyancy effect. Also, the results of Figure 13 allow for an estimation of the convective heat transfer (Equation (5)). Figure 14 shows the results of the convective heat transfer evolution. Figure 12: Radiant heat flux. Cooling mode vs. heating mode. Figure 13: Convective heat flux. Cooling mode (**left**) vs. heating mode (**right**). It was possible to adjust the expression (see Equation (5)) using data from Figure 14. Experimental data were divided into two groups: group 1 identified the coefficients (40% of the experimental data) and group 2 validated the expressions (60% of the data). Coefficients for Equation (5) were different for heating and cooling modes. Equation (12) shows the result for cooling mode and Equation (13) for heating mode. \[h_{cv1}=\mathrm{e}^{1.8127}\cdot LMTD_{cv}{}^{0.4596} \tag{12}\]  
\[h_{cv2}=\mathrm{e}^{0.83}\cdot LMTD_{cv}{}^{0.2975} \tag{13}\]  
The validation of the proposed model in cooling mode is given by executing the model with the input data (air temperature, temperature of surrounding surfaces, water flow, and water inlet temperature). There were two results that needed to be validated: total heat flux and water outlet temperature. Figure 15 compares the estimated and measured values of total heat flux (left) and water outlet temperature (right).