Saving energy and thermal comfort are becoming a matter of extreme concern regarding the objective of increasing the energy efficiency in buildings. The high glazed buildings are popular nowadays and are used even for living and office buildings. The occupant of highly glazed buildings, however, could experience thermal discomfort during several seasons, specifically when a floor system provides the heating.

In that situation, radiant Floor Heating Systems (FHS) are largely used to avoid radiant temperature asymmetry and ensure thermal comfort [1]. The energy performance of FHS hugely depends on the thermal inertia of the building structure since they are integrated. Thus, thermal inertia plays a substantial role when the issue is concerning the design of FHS, since thermal discomfort may occur specifically when the spaces are suddenly crowded or exposed to direct solar radiation.

There are different types of FHS, mainly lightweight or embedded systems, and they operate differently because of the thermal inertia of the materials. In contrast with the lightweight systems, embedded systems are concrete or anhydrite slabs. They are less performant regarding their thermal response, specifically for discontinuously occupied rooms [2].

Furthermore, they are not reactive when the weather conditions are unstable and unpredictable such as variable direct sun radiation. Thus, they may generate overheating for persistent sun radiation exposure. A performant radiant system satisfies the requirements of occupants’ thermal comfort in transient climatic conditions or when some spaces of the building are subject to unpredictable occupation scenarios.

Few investigations dealing with exposed radiant systems and building envelope to sun patch have been performed. Very few experimental analyses have been previously conducted to discuss the interaction between the heating slab and the sunbeam exposure and its effect on the thermal comfort of the occupants. Indeed, outcomes of radiant cooling systems used in the summer period are by far further studied in the literature than radiant heating slab, which harshly impacts the performance of the air conditioning systems [3–5].

The research works on the impact of direct solar radiation on the heated radiant slabs are few. de Almeida Rocha et al. [6] have estimated the amount of heat dissipated by the sun patch and its exact location utilizing the pixel counting technique. They studied the impact of the sun patch position on the exposed surface temperature and, thus, on the local thermal comfort. Earlier, Rodler et al. [7] validated a three-dimensional heat transfer model that considers the sun patch applied on an internal surface of the building envelope by applying a short time sample. Benzaama et al. [8] have modeled the sun patch and its location on a radiant heat slab. They observed a significant impact on both indoor air and surface temperature. They suggested better designing the glazing area to avoid overheating when the floor heating system is still in use. More recently, Beji et al. [2], Li et al. [9], Merabtine et al. [10,11] addressed the topic of estimating the thermal dynamic of heated radiant slabs utilizing various numerical and experimental approaches. They highlighted a ratio that could be used to estimate the overheating period over the heating period.

Most of the works mentioned above were mainly conducted in theoretical ways or by keeping the sunspot in the same location (no consideration to the dynamic sun path). Thus, the main issue is how the indoor environment of large glazed spaces interacts with the heating floor system when a direct solar gain occurs over a long period in mid-season. To fill this research gap, this study aims to verify and experimentally analyze the thermal response of the radiant slab when a dynamic solar patch appears; and to calibrate a former developed validated numerical model to predict the average surface temperature of the heated slab and the air temperature of the glazed space. The adopted methodology, depicted in Fig. 1, requires both experimental measurements and numerical modeling, which was formerly developed in Merabtine et al. [10,11] in the case no sun patch is applied. The model is amended and extended to integrate solar radiation as a time-dependent thermal load. Once validated, the model was used to evaluate the sun patch effect upon the dynamic behavior of the FHS’s main operation parameters, such as the indoor air temperature and the surface and depth temperatures of the radiant slab.

To make easier the numerical modeling, the real configuration of the radiant heated slab’s real configuration is arranged to establish a 2D way modeling by assuming a heated floor with a straight line pipe. Hence, the heat flux vector is in the normal direction related to the slab surface. In this 2D model, x-axis represents the horizontal direction. In our former studies [10,11], we demonstrated that this assumption may be acceptable when the distance between piped is relatively small to diffuse heat in two main directions.

A central difference explicit scheme is adopted for discretization purposes. The first time and the second space derivatives are discretized following this scheme for the internal nodes. A local energy balance was used for the boundary nodes.

The heat transfer equation allowing to calculate T_c (x, z, t) the temperature inside the concrete slab is expressed as:(1) 1αc∂Tc∂t=∂2Tc∂x2+∂2Tc∂z2

The fluid temperature Tf(x,t) obeys to the following equation:(2) (∂Tf∂t)+U(∂Tf∂x)=αf∂2Tf∂x2+hfρfCp,fD(Tc(x,0,t)−Tf)

Eqs. (1) and (2) have the following boundary conditions:(3a) (∂Tc∂x)x=0=0 (3b) (∂Tc∂x)x=L=0 (3c) (∂Tf∂z)z=0=0

On its lower surface the slab exchanges heat with the heating water, hence the boundary condition at this level is:(4a) −λc(∂Tc∂z)z=0=hf(t)(Tf(x,t)−Tc(x,0,t))

Since the heating slab exchanges heat at its upper surface by convection and by radiation, the following boundary condition is considered:(4b) −λc(∂Tc∂z)z=e=hr(t)(T(x,e,t)−Tr)+ha(t)(T(x,e,t)−Ta)+−δ.qs(t) where hf(t) , ha(t) and hr(t) are heat transfer coefficients expressed as follows:

In order to calibrate the numerical model based on Finite Difference Method (FDM), surface temperatures of the radiant slab (Fig. 4), the average surface temperature, in-depth temperatures, and air temperature of the heated room are assessed numerically and experimentally. The sunbeam equivalent heating is applied at 21 h after the monitoring starts.

Fig. 4a illustrates the good agreement between measurement data and numerical simulations. In fact, the identified difference remains in the range of ± 0.3°C (grey band). One could conclude that the model is accurate enough to estimate the surface temperature response.

In Fig. 4b, we can notice that for the indoor air temperature, an absolute error of 2.4°C is observed at the first heating step since the thermal inertia of the building envelope has roughly been taken into consideration in the numerical model. Once the steady state is reached, both measured and simulated results are similar for all of the heating periods.

Figs. 4c and 4d present the heated slab’s measured and simulated surface temperatures. Good accordance is observed between both profiles. The measured surface temperature Ts1 is a little bit higher than that recorded by the sensor Ts2. Indeed, to represent the actual heated slab surface temperature, the sensor Ts1 was positioned instinctively on the top surface of the slab above the inlet pipe, and Ts2 was localized in the center of the top surface of the slab, which is the less heated zone of the FHS. Regarding the numerical simulations, Ts1 and Ts2 are similar since the model equivalence considers only one straight inlet tube.

Moreover, it is noticed that before the activation of sunbeam equivalent heating, the temperature Ts1 shows a small difference with Ts2 (less than 1°C) and the temperature profiles have similar trends. Also, one may notice that the averaged surface temperature encompasses a physical meaning and permits the assessment of the radiant heat slab thermal performance (Fig. 4a).

Besides, the overheating due to the sunspot radiation stands near (i.e., at the vertical of) the hot water pipe (Fig. 4c). The sunbeam heating less impacts the non-exposed parts of the heating floor (Fig. 4d).

In the presented investigation, experiments carried out in the monitored bi-climatic chamber demonstrated that overheating duration due to the solar radiation gain reaches 8.5 h in our case study including the time after the sun patch disappears. The indoor air temperature records 26°C, while the slab temperature exceeds the upper limit of 29°C recommended by the standards. Beji et al. [2] found similar results.

The 2D developed finite difference model provides data that shows a good fit with the measurements, allowing the numerical model.

The present study’s findings can be generalized to all occupied highly glazed buildings suffering from overheating problems in mid-season. The considered FHS in our study is widely used, and a PID-based controlling system is nowadays commonly adopted.

The findings may be different for the a centralized controlling system for high-space buildings with many rooms/offices, and differently oriented and occupied spaces. In fact, complex thermal and aeraulic interactions may occur in the building between different heated spaces depending on the building height, glazed surface ratios, and orientations.

The case of “meeting rooms” with a high occupation rate compared to other office rooms still needs special attention. For such a situation, a decentralized control system has to be considered as a useful alternative solution to a centralized system. In fact, a centralized PID-based control system, even a hybrid floor heating cooling system, is not appropriate for such a case.

Integrating thermal comfort in the design avoids the need for an advanced control strategy, which could require additional device installations to keep continuous monitoring of the indoor environment, thus leading to additional installation and operation costs.