## 2 Simulation Models
### Experimental Validation of the Radiant Floor Model  
The radiant floor model developed was experimentally validated by using data from a laboratory trial conducted at Applus laboratories, in Barcelona, further to a request by Uponor Hispania, S.A.U., a specialist in radiant-floor-based HVAC systems. The trial, the details of which were furnished by Uponor, aimed, among other objectives, to experimentally measure the time taken to reach a comfortable temperature in a wood-covered radiant floor heating system. The temperatures recorded in the trials were used to validate the radiant floor model applied here. The 90-millimetre-thick radiant floor heating system (Figure 3) comprised 19-millimetre-thick varnished oakwood planks secured with adhesives, a 30 mm anhydrite-based mortar slab with a 16 mm diameter embedded cross-linked polyethylene piping, and a smooth 25 mm enhancing-agent-modified EPS self-secured panel. The pipes were spaced at 150 mm in a 2 m \(\times\) 2 m sample floor. The trial was conducted in a 4.0 m \(\times\) 4.0 m \(\times\) 3.0 m chamber built to the specifications laid down in European standard EN 442-2 [64] for radiators and connectors, i.e., with five water-cooled sides and one insulated side fitted with the emitter. Beginning at a temperature of 1 \({}^{\circ}\)C for both flooring and chamber, the trials consisted of pumping a given water flow, at a specified temperature, through the piping and determining the surface temperatures on the flooring and in the chamber until the latter reached 20 \({}^{\circ}\)C, measured at a reference point in the centre of the chamber 0.75 m above the flooring. Eight thermocouples were positioned on the wood covering to record the surface temperatures. The three stages of flooring construction depicted in the photographs in Figure 4 show the positions of the piping in the mortar and of the thermocouples on the wood covering. The trials were conducted at inflow water temperatures of 35 \({}^{\circ}\)C, 40 \({}^{\circ}\)C, and 45 \({}^{\circ}\)C, and a flow rate of 200 L/h, in line with European standard EN 1264 [64]. The accuracy of the transient thermal model for radiant flooring developed for this study was validated at inflow water temperatures of 35 \({}^{\circ}\)C, 40 \({}^{\circ}\)C, and 45 \({}^{\circ}\)C. The boundary conditions for each were defined by the parameters of inflowing water temperature, water  
Figure 4: Trial flooring set-up. (**a**) Piping layout; (**b**) mortar layer; (**c**) floor covering and positions of surface-temperature sensors. Figure 3: Cross-section of radiant flooring used in the model validation trials. flow rate, and the experimentally measured air and wall temperatures of the chamber (\(T_{cr}^{exp}\)). The model output consisted of the flooring surface temperatures. For the purposes of validation, the flooring was thermally coupled to the chamber environment and the water. The water-side convective heat transfer coefficient was found with the Gnielinski correlation [65] for inner flow in smooth pipes. The convective-radiative heat transfer coefficient at the covering surface (\(h_{cr}\)) was found from the mean experimental covering temperature (\(T_{s}^{exp}\)) and the chamber temperature, along with the surface heat flux, (\(\hat{q}_{s}\)), calculated as laid down in the aforementioned standard EN 1264 [64]. For any given time, then, the convective-radiative coefficient was calculated as \(h_{cr}=\hat{q}_{s}/\left(T_{s}^{exp}-T_{cr}^{exp}\right)\). For each inflow water temperature, the model-predicted surface temperature was compared to the mean surface temperature on the flooring recorded during the trials (Figure 5). The root mean square (RMS) error was then calculated between the model and experimental values for each water inflow temperature. The use of a single average temperature could have been a limitation of the model, since the tube arrangement in the experiment was serpentine, which could have led to the presentation of a less uniform temperature distribution on the surface compared to a spiral arrangement.