## 1 Introduction  
Radiant systems are being used for heating and cooling purposes for a long time [1; 2]. Radiant ceilings are increasingly used, especially for commercial applications, but the most common type of radiant system is still the radiant floor. The sizing of radiant systems has been debated in the past and standardized methods are today available [3]. Even though the systems are used and studied since several years, there are questions which are frequently asked by designers and practitioners which are still open and under discussion. The questions are related to the thermal inertia of the systems and which control strategies should be better in buildings during the heating period. In particular in new and retrofitted buildings, where the envelope presents high levels of insulation, it is argued if it is better to have low or high inertia radiant systems for controlling the indoor operative temperature and avoid overheating especially in mid seasons when outdoor temperature is mild and solar radiation is high. There are, hence, mainly two aspects to take simultaneously into account: the building envelope and the radiant systems. Looking at building envelope, the thermal inertia of the building structure has been under debate for a long time. One of the first works looking at the different models to be used in the calculation of thermal behaviour of structures is the one of [PERSON] and [PERSON] [4], where several simplified methods were already criticized while dynamic simulations were predicted as most suitable methods. More recently thermal inertia of buildings structures has been debated, mainly in cooling conditions, e.g., [5; 6]. Looking at results dealing with heating purposes, several papers have been published in the last years. [PERSON] et al. [7] examined external wall systems with the same U-value but different dynamic properties in order to evaluate the associated achievable energy savings. They found that the difference in the heating demand with a low inertia wall compared to a high inertia one may reach about10%. A similar saving has been evaluated by [PERSON] et al. [8], who found a difference in heating conditions of about 15% among the different solutions of retrofit in both continuous and intermittent operation by combining both thermal insulation and thermal mass techniques in Mediterranean climates. These percentages seem to be the maximum difference which can be found in literature when dealing with heating demand in well-insulated buildings. As an example in [9] a parametric simulation study has been performed based on different climatic conditions and with different heaviness of the structures in Mediterranean climates. Regarding heating demand there was no sensible difference in the same location with massive or light structures. This is also in agreement with the most extensive and recent review on the thermal inertia of buildings [10]. The reported impact of thermal inertia on energy demand found in this work is relatively small. For residential buildings the energy savings reported are often in the order of magnitude of a few percent, which is far less pronounced than the impact of other energy saving measures such as increasing thermal insulation of the building envelope. As for the radiant systems, in the past the works have been carried out especially under steady-state conditions. The most important steady-state parameters which describe the performance of radiant systems are heating/cooling capacity and thermal resistance [3; 11; 12]; however, steady-state analysis is not sufficient to describe the performance of radiant systems involving an important amount of thermal mass, like embedded surface systems and thermo-active building systems (TABS). Since the 1990s dynamic simulations have been carried out especially for the TABS which is a type of radiant system based on the thermal inertia of the structural slab [13].