## 2 Method  
In this study, we consider an enclosure with thermal layer properties and dimensions 4 m \(\times\) 4 m \(\times\) 3 m specified by the CEN TC130 European Committee, shown in Figure 2. The external wall has U-value 0.25 W/m\({}^{2}\) K, and heat recovery ventilation in the room provided an air change rate of 1 ACH with temperature efficiency 0.8. Vertical temperature gradients are mainly influenced by the amount of air circulation within an enclosure. As it was shown in [8], gradients measured for radiators and UFH were approximately 0 K/m for ventilated rooms. The ventilation flow rates and room geometry (mainly the height of the room) within the referenced study are similar to the room considered in this paper. We accordingly neglect the possible effects of a vertical temperature gradient, assuming indoor air mixing and lack of stratification to be similar. This approximation is therefore true at least for radiators and UFH, however no information exists for ceiling heater. We do note that including a vertical gradient would yield marginally different surface (and thus operative) temperatures, since the temperature differences for convection calculation purposes would change between the room air and enclosing surfaces only slightly. A more detailed study on this phenomenon would certainly be interesting, however it would require extensive measurements to accurately assess the variation in the gradient values, as the size of the emitters changes within a broad range. We locate the calculation point, namely the centre of mass of an average sitting user, at 0.6 m above the floor in the room centre (i.e., at 2 m distance from each wall) [25]. The most performing heater configuration will then be the one providing the highest operative temperature, with the same heater nominal output. The steady-state boundary conditions are the following: Indoor air temperature \(T_{int}=20\)\({}^{\circ}\)C, external air temperature \(T_{ext}=-15\)\({}^{\circ}\)C. Both direct normal and diffuse horizontal irradiance are set to zero. 134 W of power are required to heat up the room under these predefined conditions (the heat outputs throughout the simulations were within \(\pm\)0.5 W of this value). IDA ICE calculates the heat emission from any hydronic heating device as follows. The characteristic equation used to determine and model the device's heat output comes in the form of an empirical power law [21],  
\[P=kldT^{n}\,, \tag{1}\]  
Figure 4: Radiators placement. where \(k\) and \(n\) are coefficients determined individually for each emitter type, with \(l\) its length and \(dT\) the logarithmic mean temperature difference between heating water and indoor air. This governing equation therefore holds true for radiators, ceiling panels and UFH. The detailed version of the model, containing the heat balance equations used in the IDA ICE software for e.g., the calculation of relevant flow and surface temperatures, can be found in [28]. For underfloor heating, the pipe installation depth and the fluid-to-slab heat transfer coefficient are provided by the user along with the nominal heat output \(P_{nom}\) at a given temperature drop \(\Delta T_{nom}\) for the underfloor heating system. The maximal mass flow \(G_{max}\) through the underfloor piping is then calculated as  
\[G_{max}=\frac{P_{nom}}{\Delta T_{nom}c_{p}}\,, \tag{2}\]  
where \(c_{p}\) is the specific heat capacity of water at constant pressure. The exact heat output, return temperature and mass flow depend on the actual amount of heat required within the room. Heat transfer from the heating water to the surfaces of heating pipe and floor is modelled with an n-layered RC-network, see [28] for exact model descriptions. The piping layer is basically given by a heat exchanger, with an active plane at constant surface temperature located inside the floor slab.