## 3 Passive Systems for the Stadium's Envelope--Heating and Cooling Loads
### Heating and Cooling Loads Calculation  
The heating and cooling loads calculation for the Stadium's indoor space was executed following the fundamental methodology describing the thermal losses and the solar gains through the buildings' envelope [54]. As mentioned previously, the overall process was implemented with TRNSYS. The relevant simulation model and the Stadium's profile are presented in Figure 6.  
The involved thermophysical parameters were defined by either the Greek Directive on Buildings' Energy Performance [53] or the ASHRAE Fundamentals [52]. Specifically:  
* the U-values of the envelope's opaque and transparent surfaces are mentioned above for the existing envelope's conditions;
* the U-values for the new windows, with the specifications presented in the previous section, were provided by a globally acknowledged, certified manufacturer with officially submitted quotations, between 1.3 and 1.9 W/m\({}^{2}\)K;* the solar gain factors of the transparent surfaces are assumed equal to 0.62 and 0.39 for the existing and the new glazing, respectively [52];
* the thermal transition coefficients \(\mathrm{h_{i}}\) and \(\mathrm{h_{o}}\), regarding heat transfer with convection and radiation from the Stadium's envelope to indoor non-conditioned and outdoor space, respectively, were assumed equal to:
* \(\mathrm{h_{i}}\) = 10 W/m\({}^{2}\)K and \(\mathrm{h_{o}}\) = 25 W/m\({}^{2}\)K for air flow over horizontal surfaces and for average wind speed of 5 m/s [52; 54];
* \(\mathrm{h_{i}}\) = 7.7 W/m\({}^{2}\)K and \(\mathrm{h_{o}}\) = 25 W/m\({}^{2}\)K for air flow next to vertical surfaces and for average wind speed of 5 m/s [52; 54].
* the natural ventilation, expressed in Air Changes per Hour (ACH), which describes the air flow penetration through the openings' frame, is calculated by the following relationship [52]: \[\mathrm{ACH}=\mathrm{K_{1}}+\mathrm{K_{2}}(\mathrm{T_{zone}}-\mathrm{T_{amb}})+ \mathrm{K_{3}}\cdot\mathrm{u_{w}},\] (3) where \(\mathrm{u_{w}}\) is the average wind velocity, \(\mathrm{T_{zone}}\) and \(\mathrm{T_{amb}}\) are the indoor space and the ambient environment temperature and the parameters \(\mathrm{K_{1}}\), \(\mathrm{K_{2}}\) and \(\mathrm{K_{3}}\) are set equal to (0.100, 0.023, 0.070) for the existing, inadequate sealing condition and equal to (0.100, 0.011, 0.034) for the proposed openings [52];
* the following indoor space thermal comfort conditions are adopted, as defined in the Greek Directive: temperature 22 \({}^{\circ}\)C-18 \({}^{\circ}\)C in winter and 26 \({}^{\circ}\)C-25 \({}^{\circ}\)C in summer for offices and changing rooms-sports halls respectively, relative humidity 50% [53];
* the ventilation requirements, the internal heat gains from occupants, devices, etc., are retrieved from the Greek Directive on Buildings' Energy Performance [53];
* the daily usage schedule and the number of users for the existing facilities in the Stadium were provided by the Stadium's Management.  
The heating and cooling loads annual calculation is executed on hourly average steps, based on the available time series presented in Section 2.2 for the available incident solar radiation, the wind velocity and the ambient temperature. In this way, annual heating and cooling loads time series with average hourly values are calculated. For a more comprehensive and conceivable presentation, the heating and cooling loads annual time series are monthly summarized and presented in Tables 1 and 2 for the existing and the proposed envelope's condition, respectively.