## Appendix A Development of the Simulation Models
### Detailed Radiant Floor Thermal Model  
As described in Section 2.1, radiant floor heating was modelled using the response factor method to calculate the heat fluxes across the three surfaces. In this method, the actual excitation of an element is represented as the superposition of triangular pulses spaced at the time-step interval used in the simulation, adopting as the size the real surface temperature at the respective time step. Given that the problem is linear, the superposition principle can also be applied and the real responses on each surface can be determined with simple algebraic equations (Equation (A1)). The outcome is the delivery of the same precision as obtained in detailed methods or high-order models with less computing time.  
The heat flux on each surface i can be calculated in a given time-step n from the following equation:  
\[\dot{q}_{s,i}(n)=\sum_{j=0}^{\infty}f_{1,i}(j)\ T_{s,1}(n-j)+\sum_{j=0}^{\infty }f_{2,i}(j)\ T_{s,2}(n-j)+\sum_{j=0}^{\infty}f_{3,i}(j)\ T_{s,3}(n-j)\] (A1)  
In Equation (A1) \(f_{1,i}\), \(f_{2,i}\), and \(f_{3,i}\) are the response factors at surface i when the unit triangular pulse excitation is applied at surfaces 1 (top), 2 (bottom), and 3 (pipe), respectively. These response factors represent the averaged heat fluxes for surface i calculated from the surface distribution of the heat flux derived by the transient 2D finite element-based model of ANSYS APDL when unit triangular temperature excitations are applied. To return these surface average values, the node heat fluxes are weighted by the amount of element surface area associated with each node. This operation is internally performed by ANSYS APDL.  
As may be inferred from Equation (A1), calculating the heat flux in a given time step calls for a large number of response factors, since the summation must be carried back in time for a period long enough to ensure accurate results. Nonetheless, after a certain number k of response factors, the ratio between the response factor on the surface i when excitation is applied on surface \(\times\) in a given time step, Ci(k) = f\(\times\)i(k)/f\(\times\)i(k - 1), and the immediately preceding factoris practically equal: Ci(k) \(\approx\) Ci(k - 1). C is known as the common ratio. It therefore suffices to determine a certain number of response factors to calculate the rest from the common ratio. The summations in Equation (A1) canconsequently be simplified by using the common ratio, as exemplified by Equation (A2) for the top surface (1), where the summation is limited to k terms.  
\[\begin{split}&\dot{q}_{s,1}(n)=\\ & f_{11}(0)\ T_{s,1}(n)+\sum\limits_{j=1}^{k}\ T_{s,1}(n-j)[f_{11} (j)-C_{1}\!\cdot\!f_{11}(j-1)\ ]+C_{1}\!\cdot\!\dot{q}_{1,1}(n-1)+\\ & f_{21}(0)\ T_{s,2}(n)+\sum\limits_{j=1}^{k}\ T_{s,2}(n-j)[f_{21} (j)-C_{1}\!\cdot\!f_{21}(j-1)\ ]+C_{1}\!\cdot\!\dot{q}_{2,1}(n-1)+\\ & f_{31}(0)\ T_{s,3}(n)+\sum\limits_{j=1}^{k}\ T_{s,3}(n-j)[f_{31} (j)-C_{1}\!\cdot\!f_{31}(j-1)\ ]+C_{1}\!\cdot\!\dot{q}_{3,1}(n-1)\end{split}\] (A2)  
To simplify further, the terms referring to time steps prior to the present step can be grouped, yielding:  
\[\dot{q}_{s,1}(n)=f_{11}(0)\ T_{s,1}(n)+f_{21}(0)\ T_{s,2}(n)+f_{31}(0)\ T_{s,3} (n)+h_{1}\] (A3)  
where \(h_{1}\) groups all the terms in Equation (A2) referring to time step n \(-\) 1.  
Analogously, the heat fluxes across the bottom (2) and pipe (3) surfaces can be calculated as follows:  
\[\dot{q}_{s,2}(n)=f_{12}(0)\ T_{s,1}(n)+f_{22}(0)\ T_{s,2}(n)+f_{32}(0)\ T_{s,3} (n)+h_{2}\] (A4)  
\[\dot{q}_{s,3}(n)=f_{13}(0)\ T_{s,1}(n)+f_{23}(0)\ T_{s,2}(n)+f_{33}(0)\ T_{s,3} (n)+h_{3}\] (A5)