## 2 Simulation Models
### Coupling the Building and Radiant Floor Thermal Models  
The building simulations were conducted with a lumped parameter or resistance-capacitance (RC-network) model. 'RC models have proven to be advantageous and are widely used in modeling of thermal dynamics' [45] due to their low computational cost, their capacity to accommodate the main physical information on buildings, and better-than-acceptable accuracy, providing they are properly characterised [46]. This work aims to plausibly simulate the thermal performance of dwellings while using a radiant floor heating system. [PERSON] et al. [47] found that the deviation in the heating peak load of a first-order model (a lumped parameter model with one thermal capacitance) with respect to a detailed model falls between +8% and \(-\)6%, and the heating needs approximately +/\(-\)5%. They concluded that both first- and second-order models 'appear to reliably calculate the overall energy needs of buildings in both heating and cooling seasons'. On these grounds, the RC-network model presented here appears to be suitable for the purposes of this research. Any number of examples of the use of RC models for thermal simulations in buildings can be found in previous research (see [48; 49; 50; 51; 52; 53; 54; 55; 56]), as well as in studies that used such models in building simulations involving radiant flooring. [PERSON] and [PERSON] [57], for instance, developed a thermal resistance and capacitance model to optimise the control of radiant floor heating and [PERSON] et al. [58] combined a detailed model for simulating a thermally activated building component system (TABS) with an RC model for the building to address an issue closely related to that discussed here. Thanks to the RC model applied to the building, which was readily coupled to the radiant floor model described in the preceding sub-section, the output for the 26,352 (Section 3.3) simulations conducted was obtained in a reasonable amount of time. The simplified thermal model for the dwelling simulation coupled to the radiant floor model is illustrated in Figure 2. The bottom surface of the radiant flooring was assumed to be bounded by an indoor space forming part of the environment-controlled dwelling on the storey below. In the figure, \(\mathrm{T}_{\mathrm{s2}}\) is the temperature of the bottom surface of the flooring and \(\mathrm{h}_{\mathrm{cr2}}\) the convective-radiative heat transfer coefficient between that surface and the indoor space below at temperature \(\mathrm{T}_{\mathrm{i}}\). The top surface, in turn, was assumed to be bounded by the apartment to be heated, consisting in outer walls and indoor partitions separating it from other dwellings. \(\mathrm{T}_{\mathrm{cr1}}\) represents the convective-radiative temperature of the space to be heated and hcr1 the convective-radiative heat transfer coefficient between the capacitance node of the space (node C) and the top surface of the flooring at temperature \(\mathrm{T}_{\mathrm{s1}}\). \(\mathrm{U}_{\mathrm{i}}\) represents the U-value of the indoor partitions between the apartment and the adjacent spaces at temperature \(\mathrm{T}_{\mathrm{i}}\). \(\mathrm{U}_{\mathrm{e}}\) represents the U-value of the outer walls, including windows, with the outdoor environment at linear air temperature, \(\mathrm{T}_{\mathrm{sa}}\), which is defined as 'the outside air temperature which, in the absence of solar radiation, would give the same temperature distribution and rate of heat transfer through a wall (or roof) as exists due to the combined effects of the actual outdoor temperature distribution plus the incident solar radiation' [59]. The internal loads and ventilation are represented as \(\dot{Q}_{cr}\) at the capacitance node, which also included the thermal loads attributable to the solar radiation entering the space through the windows. The coupling between the radiant flooring and building model is described below.