# BEST--Building Energy-Saving Tool for Sustainable Residential Buildings
## 2 Materials and Methods
### BEST Tool Description
#### 2.1.1 Useful Energy Demand for Heating and Cooling Heat Balance
For each time step (with a maximum interval of one hour and dynamic adjustments based on thermal variations), the software determines the required state point for the supply air, calculating the necessary psychrometric transformations based on the environmental conditions. These transformations include sensible cooling, dehumidification, heating, humidification, and their combinations. Figure 2: Example of Achievable Winter and Summer Psychometric Transformations. The transformations are plotted in the psychrometric space, as shown in Figure 2 of the article, following the corresponding thermodynamic trajectories. The calculation of the thermal energy required for each transformation is performed by integrating the variations in specific enthalpy of moist air, also considering airflows and ventilation conditions (either natural or mechanical). This approach allows for accurate determination of the net thermal and cooling demands (_QH,nd_ and _QC,nd_) necessary to meet the latent and sensible loads, explicitly distinguishing between internal contributions (occupants, equipment) and external contributions (ventilation, infiltration). The approach described inherently and naturally accounts for hourly variations in environmental parameters, as well as the effects of the thermal inertia of building structures. Consequently, it does not require an approximation method for these effects, such as the utilization factor for heat gains. The heat exchange by transmission consists of the thermal transfer to the external air, the ground, and unconditioned spaces. It also includes the extra-flow caused by infrared radiation towards the sky dome, as well as the incoming solar thermal gains transmitted through opaque components. The method is directly based on the numerical solution of the general heat exchange equation using finite difference schemes. The Fourier equation is presented as a second-order differential equation:  
\[\frac{\partial^{2}\theta}{\partial x^{2}}=\frac{1}{\alpha}\frac{\partial \theta}{\partial t} \tag{3}\]  
where:  
\(\alpha=\frac{\lambda}{\rho\varsigma_{\rm P}}\) is the thermal diffusivity [m\({}^{2}\)/s], which is the ratio between the material's thermal conductivity \(\lambda\) [W/mK] and the product of its density \(\rho\) [kg/m\({}^{3}\)] and specific heat capacity \(\varsigma_{\rm p}\) [J/kgK]. The analytical solution to the equation is complex and ill-suited for a computational procedure. For this reason, the dynamic heat exchange problem through a wall is typically solved using numerical methods. The finite difference method, sometimes referred to as the \"Heat Balance\" (HB) or \"Conduction Finite Difference\" (CondFD) method, is the most accurate approach among the existing solution methods. It does not present the issues of transfer function methods, such as the \"Conduction Transfer Function Method\" (CTF or TFM), nor the problems of impulse response methods like \"Radiant Time Series\" (RTS), which are prone to inaccuracies and instability when applied to components with high mass. The CondFD method is also the most flexible and can simulate special materials, such as phase change materials (PCMs), although these are not yet incorporated into the current version of the procedure. For the solution, an explicit forward finite difference scheme was chosen, which can be schematized as shown in Figure 3.  
The spatial discretization of the wall was simplified by dividing it into three unequal parts. Two surface zones with very small thickness (approximately 3% each of the wall's thermal capacity), whose thermal capacity was aggregated with that of the internal and external spaces, and one internal zone containing the remainder of the thermal capacity. The assignment of 3% of the wall's thermal capacity to its surface zones represents a deliberate simplification aimed at reducing model complexity while preserving an acceptable level of accuracy. These surface zones correspond to the outermost layers of the wall material and possess a lower thermal mass compared to the deeper layers.