M H Benzaama

A M Mokhtari

M Lachi

C Maalouf

S Menhoudj

Sunspot analysis under varying conditions climate: distributed radiation on cooling floor and its effect on dynamic thermal behaviour

The dynamic thermal simulation of buildings is a real challenge, in terms of regulations and labelling but also of decisions (implementation, materials choice, architectural design, rehabilitation ...). Today, we lack reference models of the dynamic thermal behaviour of the cooling floor under solar radiation effect.

In fact, the simulation models developed in literature are represented in a very simplified method and cannot be used for a detailed analysis of thermal comfort. The present study aims to reduce the knowledge gap and resolve the limitations such as (i) studying the effect of sunspot for a real weather conditions, (ii) visualize the dynamic thermal behaviour of indoor air and surface cooling floor relative to the sunspot shifting and (iii) predict different sunspot shape as a function of geographic location. A 3D model is presented in this paper to evaluate the sunspot impact on cooling floor coupled to underground tank under climatic conditions in Algeria. The sunspot is calculated using a coupled TRNSYS-FLUENT dynamic simulation. Simulations are run for different periods and weather conditions. The results have shown that the developed model can provide a real simulation of thermal performance of the cooling floor taking into account the sunspot shifting. The incident solar heat flux on cooling floor reaches a maximum of 300 W/m 2 for Bechar city and 120 W/m 2 for Oran city. A wide surface temperature ranges of 13°C between the umbrageous and illuminated areas. For Oran weather conditions, the indoor air temperature in the

2

umbrageous area is around 24 °C, while that of the illuminated area is 28 °C which can cause a temperature heterogeneity in the room.

S etrn

The top of the atmosphere direct normal solar irradiance.

𝐸 𝑑𝑛

Direct normal irradiation at the earth's surface on a clear day ε Tilt angle of the surface from the horizontal plane ρ g

Ground reflectivity Introduction

The reduction of fossil-based energy use continues to be the primary concern in all areas of research. For high-performance buildings, low-temperature heating is one of the practical solutions to reduce energy use and cooling energy needs. For this purpose, and in order to reduce the considerable building sector's energy consumption, Algeria is initiating a green energy dynamic by launching an ambitious development of renewable energies and energy efficiency program [START_REF] Sahnoune | Analysis and impact of the measures to mitigate climate change in Algeria[END_REF]. In this context, several renewable energy technologies for cooling can be considered, one such approach is the geothermal systems. These systems are used to transfer thermal energy stored in the ground, with the aim of reducing the energy demand of buildings' cooling. Two different types of geothermal systems for cooling are used in the Algerian context: blowing fresh air and cooling floor coupled to the geothermal systems. Several studies have been made for the Algerian climate on geothermal cooling systems by blowing fresh air (air earth-to-air heat exchangers) such as Nasreddine Sakhri et al., [START_REF] Lekhal | Effect of geoclimatic conditions and pipe material on heating performance of earth-air heat exchangers[END_REF][START_REF] Benzaama | Investigation of the thermal behavior of a combined geothermal system for cooling with regards to Algeria's climate[END_REF][START_REF] Menhoudj | Study of the energy performance of an Earth-Air heat exchanger for refreshing buildings in Algeria[END_REF][START_REF] Lekhal | Thermal performance of a residential house equipped with a combined system: A direct solar floor and an earth-air heat exchanger[END_REF][START_REF] Sakhri | Chamkha, Heating Capacity of an Earth to Air Heat Exchanger in Arid Regions -Experimental Investigation[END_REF][START_REF] Sakhri | Experimental study of an earth-to-air heat exchanger coupled to the solar chimney for heating and cooling applications in arid regions[END_REF][START_REF] Sakhri | Experimental investigation of the performance of earth-to-air heat exchangers in arid environments[END_REF][START_REF] Sakhri | Effect of the pipe material and burying depthon the thermal efficiency of earth-to-air heat exchangers[END_REF][START_REF] Sakhri | Experimental Study of Thermal and Hygrometric Behavior of Earth to Air Heat Exchanger with Two Working Regimes in Arid Region[END_REF]. Furthermore, M. H. Benzaama el al., [START_REF] Benzaama | Experimental and numerical analysis of the energy performance of a water/ soil exchanger coupled to a cooling floor for North Africa[END_REF][START_REF] Benzaama | Investigation of the thermal behavior of a combined geothermal systemfor cooling with regards to Algeria's climate[END_REF] have studied the energy efficiency of seasonal storage coupled with a cooling floor. The studies were devoted solely to the efficiency of the geothermal system, without a thorough analysis of the cooling floor.

heat distribution in the occupied area. In cooling, several studies indicate two major problems. The first is the risk of condensation and the second is overheating. For the condensation problem, the temperature of the cooling floor surface must be higher than dew temperature. In this purpose, several researchers have been interested in modelling the surface temperature of a cooling floor such as Xiaozhou Wu et al., [START_REF] Wu | A new simplified model to calculate surface temperature and heat transfer of radiant floor heating and cooling systems[END_REF]. A parametric study was carried out on the influence of the average water temperature, the spacing step and the thickness of each layer of the cooling floor on the surface temperature. The results show that to decrease the surface temperature, the spacing step and the average water temperature must be reduced.

Furthermore, Lun Zhang et al., [START_REF] Zhang | Simplified calculation for cooling/heating capacity, surface temperature distribution of radiant floor[END_REF] have shown that the thickness of each layer of the cooling floor has no effect on the surface temperature and heat transfer. Moreover, Xing Jin et al. [START_REF] Jin | Numerical simulation of radiant floor cooling system: The effects of thermal resistance of pipe and water velocity on the performance[END_REF] have shown that a thermal conductivity of the hydraulic circuit has an effect on the performance of the cooling floor.

However, the effect of water speed does not have a significant effect on the cooling system.

Cooling floor Overheating due to solar gains have been the subject of several studies focusing on analyzing their effect on thermal comfort. K. Zhao et al., [START_REF] Zhao | Yi Jiang Cooling capacity prediction of radiant floors in large spaces of an airpor[END_REF] studied the effect of solar radiation on the cooling capacity of the cooling floor. A calculation method has been proposed to study the effect of the different emissivity values of the wall surface on the cooling capacity. They reported that the cooling capacity of the cooling floor increased significantly when exposed to a solar beam of 40-100 Wm -2 .

Tian et al., [START_REF] Tian | Establishment and experimental validation of a dynamic heat transfer model for concrete radiant cooling slab based on reaction coefficient method[END_REF] et Feng et al., [START_REF] Jingjuan (dove) Feng | New method for the design of radiant floor cooling systems with solar radiation[END_REF] have established a new model to calculate the cooling capacity as a function of solar radiation transmitted by the window. However, the models developed impose that the heat solar flux is uniform on cooling floor. Moreover, Michel de carli et al., [START_REF] De | Effect of modelling solar radiation on the cooling performance of radiant floors[END_REF] have shown that we can't have a precise simulations using a simplified model. In this context, there are several simplified models in literature for the study of solar radiation effect on cooling floor such as RC-network model, software simulation programs as TRNSYS and heat conduction transfer function. However, for real conditions, solar heat flux is only received on part of the cooling floor called sunspot. Some studies have been conducted concerning the sunspot simulation such as K. Kontoleon [START_REF] Kontoleon | Glazing solar heat gain analysis and optimization at varying orientations and placements in aspect of distributed radiation at the interior surfaces[END_REF]. As drawbacks, the proposed model does not allow to evaluate the dynamic thermal behaviour of indoor air depending on the sunspot localization. Furthermore, for Tunisian climate conditions, Boukhris et al., [START_REF] Boukhris | Coupling the building simulation tool ZAER with a sunspot model[END_REF] proposed for a passive building, a sunspot calculation method using ZAER tool. The inconvenience of this method that is able to evaluate only parallelepiped-shape rooms due to the rectangular characteristic of the mesh.

For Algerian climate conditions, S. Saadi et al., [START_REF] Saadi | Study of two new configurations of the Barra-Costantini system with sunspot modelling[END_REF] developed a thermal models taking into consideration the sunspot area on the internal walls. This model can't predict the real location of the sunspot on the floor for example. Nevertheless, we can't visualize in 3D, the sunspot movement and the dynamic thermal behavior of the indoor air relative to the sunspot localization.

An experimental study was made by C. Beji, et al., [START_REF] Beji | Experimental study on the effects of direct sun radiation on the dynamic thermal behavior of a floor-heating system[END_REF] on the effect of the sunspot on the heating floor.

As drawbacks, the solar patch was experimentally simulated by an electric heating film with a modulated power. The solar intensity was kept constant with a rectangular constant shape

The study of the effect of the sunspot was made on passive buildings and buildings equipped with a heating floor. To our best knowledge, there is just one research on the effect of the sunspot on the cooling floor. Haida Tang et al., [START_REF] Tang | Novel method for the design of radiant floor cooling systems through homogenizing spatial solar radiation distribution[END_REF] developed a 3D model to simulate the sunspot thermal behaviour on cooling floor. The authors found the difficulty to track the localization and the movement of the sunspot. In addition, indoor air temperature is assumed uniform despite the existence of the sunspot, and the distribution of entering solar heat flux on the floor was imposed. On other hand, few researchers took an interest in the absorbed solar heat flux. Athienitis and Stylianou [START_REF] Athienitis | Method and global relationship for estimation of transmitted solar energy distribution in passive solar rooms[END_REF] and Cucumo et al [START_REF] Cucumo | Estimating effective solar absorptances in rooms[END_REF], showed an approach to evaluate the solar absorbance of a room, based on the radio-irradiation method (RIM) algorithm developed by Sparrow and Cess [START_REF] Sparrow | Radiation Heat Transfer[END_REF]. Absorbed solar radiation is presented in relation to the number of elements that the surface of the wall is divided. For the sunspot models presented in the literature, the solar power absorbed and reflected at the sunspot location has not been developed.

In the present study, the effect of sunspot on the thermal behaviour of a cooling floor coupled with a geothermal system is presented. According to the state of the art, the sunspot effect has been addressed by few researchers. Just one study has been devoted to the effect of sunspot on cooling floor [START_REF] Tang | Novel method for the design of radiant floor cooling systems through homogenizing spatial solar radiation distribution[END_REF]. Moreover, the published numerical sunspot models do not represent the reality. This models don't provide a realistic explanation of the thermal behaviour of cooling floor. Several limitations can be summarized under the following issues:

1. The solar power received on the cooling floor is imposed. The real climatic conditions are not taken into account; The paper is organized as follows: Section 2 describes the methodology of the study. Then, the experimental device and the numerical model are presented in section 3 and 4. The sections 5, 6, and 7

are dedicated to the analysis of the results and their discussion, followed by recommendations and conclusions.

2.

Climate description

The thermal behavior of a building depends on external conditions such as the outdoor temperature, outdoor humidity, and solar radiation with its environment. [START_REF] Rahmouni | Prospects of hydrogen production potential from renewable resources in Algeria[END_REF] for further information about the location and climatic conditions of Oran and Bechar cities.

Methodology

Using a static coupling method between TRNSYS and FLUENT, the thermal behaviour of the sunspot and indoor air were accurately predicted. As shown in Figure 1, the methodology implemented in this paper followed a coupled approach involving CFD simulation and transient systems simulation program (TRNSYS).

Figure 1: Conceptual framework for the study methodology

We first modelled the cooling floor coupled to the underground tank (UNT) using TRNSYS software.

Secondly, we used the results obtained by TRNSYS tool, as inputs in FLUENT to predict the sunspot on cooling floor exchanging appropriate boundary conditions as shown on figure 2. The benefits provided by one tool are missing in the other tool, such that an 'optimum' model would be the complement of both tools, requiring a coupling strategy [START_REF] Gowreesunker | Coupled TRNSYS-CFD simulations evaluating the performance of PCM plate heat exchangers in an airport terminal building displacement conditioning system[END_REF]. Indeed, FLUENT requires surface temperature and heat flux coefficients to describe the dynamic thermal behaviour of experimental cell, but these values are unknown 10 before realization. Moreover, we can get these parameters using TRNSYS which are more realistic and depend on the climatic conditions, the thermal properties of cell materials and the cooling source. geographic site and sunshine factor (figure 3). The solar ray tracing algorithm lets calculate the solar heat flux using a source term in the energy equation [32]. The solar load model's ray tracing algorithm can be used to predict the direct illumination energy source that results from incident solar radiation. It takes a beam that is modelled using the sun position vector [32]. -Outdoor temperature measured using a mini weather station (OREGON type).

Table 1 shows the characteristics of the measurement sensors used. The condition of the experimental cell construction is considered to be highly isolated and the thermal properties of the exterior walls, partition, ceiling and floor are specified in Table 2.

UNT coupled to cooling floor model

The UNT system is modelled by associating type 38 with type 711 (Figure 6). The association between these components allows modelling the thermal behavior of a water storage tank buried in the ground. )]

(1

)
Where 𝑍 is the soil depth (m), 𝑡 is the time (hour), 𝑡 0 is the time of year with minimum soil surface temperature (hour), 𝑇 𝑚 is the mean surface temperature (°C), 𝐴 𝑠 is the amplitude of soil surface temperature throughout the year (K), and 𝛼 𝑠𝑜𝑖𝑙 is the soil thermal diffusivity (m 2 /s).

The energy balance on a water node takes into account storage losses from the tank and conduction between segments, and this is written as follows:

𝜌 𝑤 𝐶 𝑝,𝑤 𝑉 𝑖 𝑑𝑇 𝑖 𝑑𝑡 = -(𝑈𝐴) 𝑖 (𝑇 𝑖 -𝑇 𝑒𝑛𝑣 ) + (𝑘𝐴) 𝑖-1 (𝑇 𝑖-1 -𝑇 𝑖 ) ∆ℎ 𝑖-1 -(𝑘𝐴) 𝑖 (𝑇 𝑖 -𝑇 𝑖+1 ) ∆ℎ 𝑖+1 (2)
where 𝜌 𝑤 is the water density (kg/m 3 ), 𝐶 𝑝,𝑤 is the heat capacity of water (J/kg K), 𝑈𝐴 is the overall loss coefficient (W/k), 𝑇 𝑒𝑛𝑣 is the environmental temperature and ∆ℎ is the separation between centers of segments.

The total loss from the tank is written as follows:

𝑄 ̇𝑒𝑛𝑣 = ∑ (𝑈𝐴) 𝑖 𝑁 𝑖=1 (𝑇 𝑖 -𝑇 𝑒𝑛𝑣 ) (3)
The energy input to the tank due to the cold inlet flow is given as follow:

𝑄 ̇𝑖𝑛 = 𝑚̇𝐶 𝑝,𝑤 (𝑇 𝑖𝑛𝑙 -𝑇 𝑜𝑢𝑡𝑙 ) (4)
The two illumination parameters used to describe the intensity of the solar load consist of two irradiation terms, direct solar irradiation and diffuse solar irradiation. The direct solar irradiation uses a two-band spectral model and accounts for material properties in IR-and visible bands. The diffuse solar irradiation uses a single-band hemispherical averaged spectral model only present in actual sun light [START_REF] Jonsson | Including solar load in CFD analysus of temperature distribution in a car passenger compartment[END_REF].

The inputs for the Solar Calculator are given below:

Global position (latitude, longitude, and time zone), starting date and time, orientation of the building, solar irradiation method and Sunshine factor.

The sunshine factor accounts for the cloud covering the sky at a given time and location under study. so it is basically percentage of cloud cover which range from 0 to 1 where 0 means completely covered with cloud and 1 means no cloud. The cloud cover basically reduces the sunlight from sun. The sunshine factor is simply a linear multiplier that allows the incident load to be reduced in order to account for cloud cover.

Once the irradiation and solar beam direction are known, they are applied as inputs to the solar ray tracing algorithm or the discrete ordinates method [34,35].

The direct normal irradiation that is calculated using NREL's Solar Position and Intensity Code (Solpos)

given in [32]:

𝐸 𝑑𝑛 = 𝑆 𝑒𝑛𝑡𝑟𝑛 . 𝑆 𝑢𝑛𝑝𝑟𝑖𝑚𝑒 (7)
Where S etrn is the direct normal of the solar irradiance.

S unprime : the correction factor used to reduce the solar load through the atmosphere.

The equation of diffuse solar irradiation for surfaces other than vertical surfaces is given by [32]:

𝐸 𝑑 = 𝐶. 𝐸 𝑑𝑛 . (1+cos ) 2 (8)
Where  : tilt angle of the surface (in degrees) from the horizontal plane.

Both absorptivity and transmissivity are defined for normal incident angle to the surfaces but are recomputed in FLUENT to represent the correct angle. Glazing of materials can also be included when using solar ray tracing [START_REF] Jonsson | Including solar load in CFD analysus of temperature distribution in a car passenger compartment[END_REF]. For this to work the transmissivity and reflectivity has to be specified in the wall boundary conditions. Table 3 and 4 represent the composition of window and the surface radiation properties of glass. when the effect of surface emissions is important. The solar ray tracing algorithm functions as the source of solar heat and the S2S radiation model takes into account the energy diffused indoors [START_REF] Jonsson | Including solar load in CFD analysus of temperature distribution in a car passenger compartment[END_REF]. The S2S radiation model is based on a calculation that takes into consideration the characteristics of the included irradiating surfaces in relation to each other [START_REF] Jonsson | Including solar load in CFD analysus of temperature distribution in a car passenger compartment[END_REF]. The combination of these models give a realistic thermal behavior of building.

The energy equation used in the S2S model is composed of directly emitted and reflected energy. The energy reflected from a surface is dependent on the energy incident on the surface and can thus be expressed as a function of the energy flux leaving all radiating surfaces [START_REF] Jonsson | Including solar load in CFD analysus of temperature distribution in a car passenger compartment[END_REF] as shown figure 7. The energy flux from surface k is described as:

𝑞 𝑜𝑢𝑡,𝑘 = ε 𝑘 + 𝜎𝑇 𝑘 4 + 𝜌 𝑘 𝑞 𝑖𝑛,𝑘 (9)
where 𝑞 𝑜𝑢𝑡,𝑘 represents the energy flux leaving the surface, 𝑞 𝑖𝑛,𝑘 the energy flux incident on the surface, 𝜌 𝑘 the reflected energy, ε 𝑘 the emissivity, 𝜎 is the Boltzmann's constant and T is the temperature.

Results and discussion

Experimental results

We present in this section the experimental data for the period of July 2014. We follow for 10 days, the inlet temperature, cooling surface temperature and outdoor air temperature as shown in figure 8. The results show that the temperature difference beteween the inlet temperature and outdoor temperature is around 12 °C. This difference in temperature can supply the heat energy required to ensure a best thermal comfort. The cooling floor surface temperature does not exceed 25 °C which corresponds to the criteria of thermal comfort [START_REF] Olesen | Radiant floor cooling systems[END_REF]. Figure 9 shows the indoor air temperature evolution at two different zones. In the study of M.

H. Benzaama et al., [START_REF] Benzaama | Experimental and numerical analysis of the energy performance of a water/ soil exchanger coupled to a cooling floor for North Africa[END_REF] the authors presented only the temperature of the shaded zone (Position 3). The area near the window which is influenced by solar radiation is neglected. The results of figure 9 show that thermal behaviour of positions 1, 2 and 3 is different. Sensors 1 and 2 are influenced by the presence of sunspot. The irradiated surface emits a heat flow that causes overheating of the air zone where sensors 1 and 2 are placed. Figure 11 shows a temperature heterogeneity between positions 1, 2 and position 3. The temperature of the indoor air is not homogeneous in the room. The indoor air temperature in the irradiated zone (Positions 1 and 2) reaches a maximum value of 28 °C. On the other hand, the indoor air temperature in the occupied zone (Position 3) takes an average of 24 °C which corresponds to the criteria of thermal comfort (Upper limit for the operative temperature in summer is 26°C [32]). A temperature difference of 4 °C between the two zones can cause a temperature heterogeneity in the room (Discomfort).

Model validation

Firstly, we present in figure 10, the cooling needs of the experimental cell estimated by numerical simulation using TRNSYS tools for a period from May to September. It can be seen that the need is high during the summer season and especially during the month of July with a value of 379.6 kWh. For this purpose, the choice of the period of the measuring campaign corresponds to the period in which the cooling needs are important.

Figure 10: Cooling needs

We present in this section the validation of the two models TRNSYS and FLUENT. As presented in the methodology, the geothermal system and the experimental cell are modelled on TRNSYS. TRNSYS model was validated using an experimental data. Figure 11 show that the simulation results in good agreement with the experimental data, wherein the deviation between them falls within 0.5 °C. The indoor air temperature obtained by TRNSYS is compared with the temperature of the umbrageous zone. This temperature is considered uniform throughout the room, but that does not reflect reality. The models existing in the literature such as TRNSYS validates only the temperature of the occupied area (Position 3). Experimental studies usually involve unpredictable and uncertain factors that occur due to instrumental, calibration, and human measurement errors. These uncertainties may be calculated using statistical analysis through recognized formulae. For this, the error analysis of the thermal model performance of the experimental cell was calculated by comparing its results with the experimental data. In this study, the Normalized Mean Bias Error (NMBE) and the Coefficient of Variation of the Root Mean Square Error (CV(RMSE)) were calculated. They are defined as follows:

NMBE = 1 m ̅ ∑ (𝑚 𝑖 -𝑠 𝑖 ) n i=1
𝑛-𝑃 𝑋 100(%) ( 10)

CV(RMSE) = 1 m ̅ √ ∑ (𝑚 𝑖 -𝑠 𝑖 ) 2 n i=1 𝑛-𝑃 100 (%) ( 11
)
Where m ̅ giving the global difference between the real values and the predicted ones, p is the number of adjustable model parameters, which, for calibration purposes, is suggested to be zero, 𝑛 the number of measured data points, 𝑚 𝑖 is the measured variables, and 𝑠 𝑖 is the simulated variables. The (CV(RMSE) and NMBE of indoor air temperature reported in Table 6. The results obtained, corresponds to the criteria of ASHRAE Guideline 14.

Table 6: Performance of the model.

Data Type Index

ASHRAE Guideline 14 [START_REF]Guideline 14-2014, Measurement of Energy and Demand Savings; Technical Report[END_REF][START_REF]Guideline 14-2002, Measurement of Energy and Demand Savings; Technical Report[END_REF] Present study

Calibration criteria

Hourly criteria % NMBE ± 10% -2.55%

CV (RMSE) ± 30% 3.8% The total uncertainties of the indoor air were therefore mainly determined by the uncertainty of the input parameters. Supposing that each single input parameter is independently of other inputs, the uncertainty can be estimated from CV(RMSE) and NMBE. Table 7 illustrates the effect of the uncertainties of some parameters on the uncertainties of indoor air temperature.

These were found using TRNSYS simulations. The uncertainties arose due to deviations of the model geometry or due to uncertainties in the calculation heat transfer. It can be noticed that results are very sensitive to wall insulation thickness. An increase of 5% of wall insulation thickness reduces the NMBE to -0.82% and the CVRMSE to 2.51%.

Sunspot on cooling floor

The models presented in the literature cannot be generalized for all case studies since the distribution of entering solar heat flux on the cooling floor is imposed. We show in Figure 14 the sunspot position at 12 am and 13 p.m on July 07 for Oran city conditions (Mediterranean climate). Distribution of entering solar heat flux on cooling floor is around 120 W/m 2 and 110 W/m 2 at 12 a.m and 3 p.m respectively as shown in figure 14-a, c. We observe that sunspot moves from plane X = 1 at 12 a.m. to plane X = 2 at 3 p.m. causing superheating as shown figure 14-b, d. The developed model allows to plot the surface temperature and solar heat flux distribution along a line (We take Z = -0.5 along the X axis) as shown figure 15. For 120 W/m 2 of solar heat flux received on cooling floor, the effect of the sunspot shifting on the experimental cell are more remarkable for the surface temperature variation. During this period, some pics were observed. A superheating of 35°C at 12 a.m. and 33°C at 3 p.m was observed, which gives a wide temperature range of 13°C and 11°C in comparison with the umbrageous area respectively. Sunspot shifting from 12 p.m. to 3 p.m is done for a small distance, that has an effect on floor thermal inertia which causes superheating for a long period. The incident solar radiation received on the cooling floor is redistribute due to absorption / emissivity of internal surfaces. For this purpose, we present in Figure 16 the reflected IR radiation compared to the solar radiation received on the cooling floor. For the metrological conditions of Oran and at 12 am, the reflected IR radiation is of the order of 15 W/m 2 which gives 105 W/m 2 of absorbed solar radiation. An important value that could influence the indoor air temperature for a long period of time. This results allow to evaluate the solar power that influences the cooling capacity and the dynamic thermal behaviour of the indoor air. In this purpose, we present in the next section, the influence of reflected radiation of sunspot on the dynamic thermal behaviour of indoor air.

3.2 Dynamic thermal behavior of indoor air

Figure 17 shows the indoor air temperature distribution in three different planes in July 07. At 12 a.m., heat transfer is observed from the sunspot to the cold surface of the cooling floor (Figure 17-a). The influenced area at 12 a.m. is larger than that at 3 p.m. Consequently, the influenced air volume at this plane (0 < X < 2) at 12 a.m. is greater than that at 3 p.m (Figure 17-b). The indoor air temperature in this plane is around 28°C. The thermal behavior at the second and third plan is identical at 12 a.m. and 3 p.m. The indoor air temperature in the Figure 18 shows that the plane 0 < X < 2 is influenced by the sunspot passage from 12 a.m.

(Figure 18

Effect of clouds on sunspot

Controlling solar energy therefore requires knowing the correct position of the sun (height and azimuth) as well as the intensity of radiation at any given moment, which depends on the clouds quantity. In this section, we present the effect of the clouds quantity on the sunspot (sunshine factor). The focus is on the solar heat flux received on the cooling floor and its effect on the thermal behaviour of the cooling floor and indoor air. Three case studies are presented: Case 1 with 0% cloud, case 2 with 50% of cloud, and case 3 with 80% of cloud as shown figure 19. The solar heat flux received on the cooling floor for the three case studies causes a different thermal behaviour of cooling floor. The sunshine factor is an important parameter that is neglected in the numerical sunspot models mentioned above. This factor allows to predict the exact power received and transmitted to the indoor air, which allows to quantify precisely the overheating due to the sunspot. Figure 21 shows that for the same day of July 7th at noon and for the climatic conditions of Oran, the overheating of the cooling floor due to the presence of the sunspot is different. For cloudy sky (50% and 80%) the overheating is of the order of 31 °C and 27 °C respectively. On the other hand, the surface temperature of the cooling floor for a clear day is of the order of 35 °C. A temperature difference of 8 °C between a clear sky and a cloudy sky. The temperature of the air around the irradiated area has a great effect on the thermal sensation of the human body. Figure 23 shows the cooling floor temperature, and the indoor air temperature around the irradiated area for the three cases. From figure 23, it is obvious that the surface temperature of the cooling floor in case 1 is more important than cases 2 and 3. This is due to the high solar heat flux received in the first case (See figure 20) compared to the other cases. A very high heat concentration on the cooling floor in the first case is observed compared to the cases 2 and 3. Therefore, this irradiated surface in case 1 radiates more heat (reflected IR solar radiation) to the indoor air, as shown in the figure 24. The reflected IR solar radiation, one of the most important factors that affect the air around the irradiated surface. Figure 23 shows that the thermal behaviour of the indoor air in the irradiated zone is not the same for the three cases. The indoor air temperature in a clear day (case 1) is higher than in a cloudy day (cases 2 and 3). for the same day and time (July 7th at noon), we find a different thermal behaviour of the indoor air and the cooling floor, which shows the benefit of taking into account the sunshine factor in the simulations in order to have a good dimensioning.

Study strength and limitations

In this study, we have developed a new calculation method that determines the distribution of total received solar radiation on cooling floor and it effect on indoor air in the Algerian context.

Several studies have been done on sunspot effect. In this studies, the dynamic thermal behaviour of the indoor air related to the sunspot displacement and the real absorptivity/emissivity was not developed.

The strength of the study relates to the evaluation of the indoor air temperature and velocity depending on sunspot displacement. This model allows to quantify the absorbed and reflected solar power for a good dimensioning of windows and cooling floor under different climates.

Therefore, we believe that our methodology can be used for other country than Algeria. More importantly, we believe that our methodology can provide the foundation for the development of thermal study and design for the Algerian context.

On the other hand, this study has limitations. The coupling between TRNSYS and FLUENT is done by a static method. We can't run continuous simulations for a long period of time.

Moreover, data monitoring was done only for 10 days, and the temperature sensors were only used for the indoor air temperature. The research could have benefited from a more extended monitoring period.

Implications on practice and future research

The implication of these results indicated the importance of the combination of TRNSYS and FLUENT to predict the dynamic thermal behavior of the indoor air, the received, absorbed and reflected solar radiation. We believe that building engineers can apply our findings for a good dimensioning and design of the cooling floor in the Algerian climate. We find it essential that the National Building Efficiency Standard of Algeria use our findings to improve the Algerian thermal regulation, which is under development. Hence, future works will be directed to improve this methodology taking into account a dynamic coupling for predicting a long-term effect of sunspot on existing buildings, while taking into consideration the occupant's activities.

Conclusion

The literature review indicates a knowledge gap that must be filled. Also, none of the published studies addressed the following issues:

 The effect of the sunspot in relation to the solar heat flux received on the cooling floor which depends on the sky state (cloudy or clear sky) and the climate conditions at different times;

 Evaluate the reflected IR solar heat flux by sunspot;

 Dynamic thermal behaviour of the indoor air of the whole room with the presence of the sunspot. This step can evaluate the thermal comfort at several levels in the room.

The present paper aims to reduce this knowledge gap and to address limitations such as (i) the study of the effect of sunspots under real meteorological conditions, (ii) the visualization of the

Key words :

 words Cooling floor, sunspot, dynamic thermal behaviour, coupling TRNSYS-FLUENT. Nomenclature Roman and greek letter symbols 𝑻 temperature (°C) 𝝆 density (kg/m 3 ) 𝑪 𝒑 heat capacity of water (J/kg.K) 𝒎 ̇ mass flow rate (kg/s)

  The minimum and maximum average temperatures and precipitation days of Oran and Bechar cities are represented in figures 2-a and 2-b. The results show that the maximum outdoor temperature can go up to 42°C for Bechar city and 35°C for Oran city. Figures2-c and 2-dshows the monthly number of sunny, partly cloudy, overcast and precipitation days. Days with less than 20% cloud cover are considered as sunny, with 20-80% cloud cover as partly cloudy and with more than 80% as overcast[29]. The results indicate that the sky in July for Oran city is partly cloudy for 22 days. On the other hand, for Bechar city, the sky is partly cloudy for only 5 days. For this purpose, we present in this study, the effect of cloud quantity on the solar power received on the cooling floor, for the city of Oran. Details about sky state and average temperature are given in[29,30].

Figure 2 :

 2 Figure 2: Co-simulation TRNSYS-FLUENT

Figure 3 :Figure 4 :

 34 Figure 3: Flowchart for sunspot model identification

Figure 5 :

 5 Figure 5: Experimental measures

Figure 7 :

 7 Figure 7: Solar radiation distributions

Figure 8 :

 8 Figure 8: Experimental measurements of the surface temperature and inlet temperature of the

Figure 9 :

 9 Figure 9: Experimental measurements of indoor air temperature for the umbrageous and

Figure 11 :Figure 12 :

 1112 Figure 11: Experimental indoor air temperature and simulation

Figure 13 illustrates

 13 Figure 13 illustrates the impact of thermocouple uncertainty on the indoor air temperature,

Figure 13 :

 13 Figure 13: Error bars analysis

Figure 14 :

 14 Figure 14: Solar heat flux (W/m 2 ) and surface temperature (K) of cooling floor

Figure 15 :

 15 Figure 15: Surface temperature and solar heat flux on cooling floor at different time.

Figure 16 :

 16 Figure 16: received and reflected solar radiation

  occupied area (X = 3) is around 26 °C and that of the umbrageous area (X = 4) is around 24°C. The temperature range can go up 4 °C which confirms the experimental results. a-At 12 a.m. b-At 3 p.m.

Figure 17 :

 17 Figure 17: Thermal behavior of indoor air with existence of sunspot at different planes (K)

  -a) to 3 p.m (Figure18-b). At this level, the dynamic behavior is not the same between 12 a.m. and 3 p.m. The air velocity varies between 0.06 and 0.1 m/s. On the other hand, the dynamic behavior at the second and third plan is almost the same at 12 a.m. and 3 p.m. The air velocity in the occupied area (X = 3) is around 0.1 m/s, and that of the umbrageous area (X = 4) is around 0.06 m/s. a-At 12 a.m. b-At 3 p.m.

Figure 18 :

 18 Figure 18: Dynamic behavior of indoor air with existence of sunspot at different planes (m/s)

Figure 19 :Figure 20 :

 1920 Figure 19: Illustration of the three case studies

Figure 21 :

 21 Figure 21: Surface temperature of the cooling floor for a cloudy and clear sky (Z= -0.5 along

Figure 22 :

 22 Figure 22: Reflected IR solar radiation for a cloudy and clear sky (Z= -0.5 along the X axis)

Figure 23 :Figure 24 :

 2324 Figure 23: Thermal behaviour of the cooling floor and the air around the irradiated surface

Figure 26 :

 26 Figure 26: Reflected solar radiation for different climate

  It depends heavily on meteorological and in situ conditions. Study of the effect of sunspot on the cooling floor is proposed in this study for Oran and

	Becher cities. The selection of cities is based on the specificity of the climate (solar deposit, temperature)
	and the type of soil. Oran is a city in the northwest of Algeria. It enjoys a Mediterranean climate (temperate
	climate) characterized by hot and dry summers and mild and humid winters. Bechar, it is an internal city
	located in the North West Sahara with a dry climate. A large solar energy potential is available [28] where
	approximately 2.5 MWh/m² of annual solar energy on the horizontal plane. It seems that the southern
	regions have significant resources. Bechar with 2.1 MWh/m². year, can be considered as a potential
	location for solar energy. Oran city receives solar energy of 1.8 MWh/m².year. Reader can refer to

Table 1 :

 1 Wireless sensor characteristics

	Measured parameter	Measuring range	Accuracy	Type of sensor	Units
		(Plage de mesure)	(Précision)
	Temperature	-40 °C < T°< 60 °C	± 1,5°C	Thermocouple	°C
	Outdoor temperature	-40 °C < T°< 60 °C	±1 °C	Weather station	°C

Temperature measurements were performed using K-type thermocouples. The experimental test is

Table 2 :

 2 Thermal properties of cell materials.

	Wall type and layer name (from		Conductivity	Specific heat	Density
		Thickness [m]
	inside to outside)		[W/(m.K)]	[kJ/(kg.K)]	[kg/m 3 ]
	External and partition wall
	Cement-coating	0.01	1.15	1.0	1800
	Brick	0.1	0.5	0.92	1100
	Insulation	0.04	0.03	1.45	20
	Brick	0.1	0.5	0.92	1100
	Cement-coating	0.01	1.15	1.0	1800

  The ground temperature for different burial depths of the tank is modelled using the Kusuda & Achenbach correlation. It is used to calculate temperature profiles in undisturbed soil at different depths. The model is based on the theory of thermal conduction applied to a semi-infinite homogeneous solid. The equation that provides soil temperatures at different depths is given as follows:

	𝑇(𝑍, 𝑡) = 𝑇 𝑚 -𝐴 𝑠 𝑒𝑥𝑝 (-𝑍 ( 365 𝛼 𝑠𝑜𝑖𝑙 𝜋	) 1 2 ⁄	) Cos [	2𝜋 365	((𝑡 -𝑡 𝑜 ) -	𝑍 2	( 𝜋 𝛼 𝑠𝑜𝑖𝑙 365	) 1 2 ⁄

Table 3 :

 3 Composition of window.

	Material	Conductivity, λ	Heat capacity, c p	Density, ρ
		(W/m.K) (at 20 °C)	(J/Kg.K)	(Kg/m 3 )
	Single glazed window	1,2	830	2750

Table 4 :

 4 The surface radiation properties[START_REF] Dong | Numerical and experimental study of the effect of solar radiation on thermal comfort in a radiant heating system[END_REF]

	Emissivity

Table 5 .

 5

		At 12 pm	At 3 pm
	Wall	Temperature	Heat convection	Temperature	Heat convection
		°C	coefficient	°C	coefficient
			(W/m 2 .K)		(W/m 2 .K)
	North	23.41	/	24.01	/
	Wall
	South	23.39	/	24.02	/
	Wall
	Est Wall	23.49	/	23.98	/
	West Wall	23.39	/	24.01	/
	Floor	23.16	0.2	23.45	0.2
	Ceiling	23.49	/	24.01	/
	301

Table 7 :

 7 Sensitivity of indoor air temperature to changes of important input parameters

		40
	(°C)	35
	air temperature	25 30
	Idoor	20
		15
		1 8 15	22 29 36 43	50 57 64 71	78 85 92 99 106 113 120 127 134 141 148 155 162 169 176 183 190 197 204 211 218 225 232 239 246
					Hours
			Indoor air temperature_Experimental	Indoor air temperature_Simulation
			Outdoor temperature

dynamic thermal behaviour of indoor air and surface cooling floor in relation to sunspot displacement, and (iii) the prediction of different sunspot shapes in relation to the geographical location.

Based on the results, we concluded that, presence and sunspot shifting has an effect on cooling floor temperature which causes superheating for a long period. The floor superheating can go up to 35 °C for Oran weather conditions and 38 °C for Bechar city. A wide temperature ranges of 13°C between the umbrageous and illuminated areas.

According to the ASHRAE Standing Standard Project Committee 55, spaces with passive or active systems that provide strongly non-uniform temperature and air velocity fields cause skin heat losses. The presented results show that the indoor air temperature and indoor velocity distributions are not uniform relative to the sunspot shifting that may cause discomfort. For Oran weather conditions, the indoor air temperature in the shaded area is around 24 °C, while that of the irradiated area is 28 °C for an air velocity which varies between 0.06 and 0.1 m/s.

Eq.5:

𝛼 𝑐𝑜𝑛𝑣 = 2.11 (𝑇 𝑠𝑢𝑟𝑓 -𝑇 𝑎𝑖𝑟 ) 0.31 [START_REF] Lekhal | Thermal performance of a residential house equipped with a combined system: A direct solar floor and an earth-air heat exchanger[END_REF] Figure 6: Simulation flow chart in TRNSYS space.

Sunspot model:

Where surfaces exposed to the sun, solar radiation heat transfer is considered. For solar radiation,

FLUENT software provides solar radiation calculation model using the Solar-Ray Tracing method. The resulting heat flux that is computed by the solar ray tracing algorithm is coupled to the FLUENT calculation via a source term in the energy equation [32]. The solar load model's ray traci ng algorithm can be used to predict the direct illumination energy source that results from incident solar radiation. It takes a beam that is modelled using the sun position vector [32]. This model can be used to visualize the dynamic thermal behaviour of indoor air and surface cooling floor relative to the sunspot shifting for a

given time and location. The model of turbulence used in this study is K-ε Standard for steady-state and Boussinesq approximation has been used in this case.

Sunspot evolution for Bechar city

In this section we can see the evolution of the sunspot for the climatic conditions of Bechar.

Bechar region is characterised by a Saharan arid and dry type climate. The purpose of this section is to show the ability the model to evaluate the sunspot effect based on the real solar power received from the region. In addition, we show the possibility of predicting other sunspot shapes. Figure 24 shows a comparison between the location (figure 24