## 1 Introduction
In other words, defining an ideal benchmark heater for operative temperature control is non-trivial, and needs to be addressed for better comparison between different heat emitter systems. To this aim, in the present paper, we consider an average-sized enclosure provided by the CEN technical committee TC130 working group WG13, with a user sitting in the middle (Figure 2). We investigate how the operative temperature sensed by this user changes with the typology and size of emitter, and whether there exist optimal configurations corresponding to the highest \(t_{op}\). We address panel radiators (10- and 21-type), underfloor (UFH) square, UFH strip and ceiling heater. A 10-type radiator has only one panel and no convector fins, while the 21-type has two panels with one set of fins in between, bas illustrated in Figure 3. They are placed on the cold wall, with centrelines aligned, as in Figure 4.  
Figure 1: Ideal point heater (**left**) and real heat emitter (**right**). bWe adopt a combined numerical-analytical model that follows the ISO Standard [25], coupled with a simple interpolation method which was introduced in [27] when assessing domestic hot water consumption. We first obtain the surface temperatures of the enclosure numerically, with IDA ICE, for each heat emitter type and for different sizes; these temperatures are then used as boundary conditions for an analytical calculation of the according operative temperature. The resulting \(t_{op}\) is finally studied as a function of the emitters' dimensions to identify general trends, comparing the different devices and finding optimal configurations. Concerning panel radiators, by keeping the heat output constant we determine analytical \(t_{op}\) curves in function of their panel dimensions, finding an optimal width range of both the 10- and 21-type. We prove that the thermal comfort performance of radiators is more sensitive to the height than to the width, and that the convector and 21-type provide the lowest operative temperatures. On the other hand, the 10-type can provide a \(t_{op}\) as high as the air temperature, and accordingly it can be identified as our \"ideal\" emitter. For the case at hand, we also list a series of analytical formulas for calculating \(t_{op}\) for radiators of 10- or 21-type, with panel size in the range considered and excluding back wall losses (Adiabatic internal surfaces are used in the model; namely, no additional heat is transferred from the ceiling heater and UFH to the colder rooms above and below. This additional heat loss is also omitted for the radiators, to guarantee an accurate comparison.). The UFH and ceiling heater provide in general higher operative temperatures, approaching, and often exceeding, the air temperature. We find, both analytically and numerically, a maximum \(t_{op}\) for sizes smaller than the whole width of the room: the analytical solution allows to locate them precisely, up to three digits. Remarkably, if one considers typical radiator sizes with height 0.6 m, when compared to a 10-type the UFH provides a \(t_{op}\) that is higher by 0.25 K-0.3 K, and by 0.35 K in the case of a 21-type (In theory one might conclude that the UFH is our ideal heater, but in practical cases the embedded emission losses are relevant [8].). Figure 3: 10-type and 21-type panel radiators. Figure 2: Room setup. The present paper is organized as follows: in Section 2 we describe the test chamber, the simulation setup and the different methods for computing the operative temperature. In Section 3 we report our results for each single case, some general discussion then appears in Section 4 and finally, Section 5 contains a summary of our findings and concluding remarks. In Appendix A we include considerations about the view factors, a comparison between our analytical and numerical methods and the analytical formulas to determine the operative temperature for any radiator size discussed in the study.