Thermal and Energetic Contributions of PCM Plaster According to its Location and Type of Masonry—Experimental and Numerical Studies in a City With a Temperate Mediterranean Climate

The integration of phase change materials (PCMs) in the construction sector is very promising for the improvement of the thermal and energy performance of buildings. This multi-variable study aims to reveal the contribution of PCM plaster according to the type of masonry (single cement bricks or double clay bricks), the type of plaster (PCM or cement plaster) and its location (interior or exterior) to reduce indoor temperature fluctuations and energy consumption levels. Small-scale experimentation and dwelling dynamic modelling of several types of rooms have revealed that compared to cement plaster, PCM plaster on the interior surface of exposed walls reduces the indoor temperature fluctuation range by up to 2.5°C on winter days and by up to 2.6°C on summer days if it is applied on the exterior surface of the single-partition walls. In the case of double-partition walls, the reduction in the indoor temperature fluctuation range reaches 1°C on winter days and 1.3°C on summer days. Interior PCM plaster reduces the heating energy demand in winter by up to 25% for single partitions and 21% for double partitions. In summer, the reduction in cooling energy demand with exterior PCM plaster is up to 36% for single walls and 44% for double walls. Compared to cement plaster, although the thermal and energy reduction percentages of PCM plaster are greater for single-partition walls, the temperature fluctuations and energy consumption are lower for double-partition walls. Determination of the optimum melting temperature and thickness of PCM plaster would improve the performance obtained.

INDEX TERMS Building, materials, phase change materials, cement plaster, modelling, thermal comfort, cooling, heating, energy.

COP Coefficient of performance. Cp
Specific heat capacity of the material (kJ/kg K). i Node being modelled. i+1 Adjacent node towards the inner side. i-1 Adjacent node towards the outer side. j Previous time step. j+1 Simulation time step.
The associate editor coordinating the review of this manuscript and approving it for publication was Javed Iqbal . k E Thermal conductivity between nodes i and i-1 (W/m.K). k W Thermal conductivity between nodes i and i+1 (W/m.K). PCM Phase change material. Layer thickness (m). ρ Density (kg/m 3 ).

I. INTRODUCTION
Satisfying the population energy demand is a goal that every country wants to achieve because it is the key to ensure technological advancement and economic development [1].
To meet the global demand for energy, which is growing every year, we have to determine the best way to produce and store more energy [2]. The unrelenting depletion of fossil energy resources and the alarming scenario of global warming have forced countries to try to reduce their carbon footprint. To reduce the carbon footprint, countries have started to develop the use of sustainable energy resources integrating various thermal energy storage systems [3].
The building sector accounts for the largest share of the world's final energy consumption of approximately 36% and generates 39% of the global CO2 emissions [4].
Many studies have demonstrated that the use of phase change materials (PCMs) improves the building thermal performance [5]- [8]. The use of PCMs as a storage element to improve heating, air ventilation and air conditioning is an effective energy efficiency measure [9], [10], and it reduces the building energy consumption due to the high latent heat of PCMs at low temperatures [11]. In building applications we can use PCMs in two ways: by using them in separate heat and storage devices or by incorporating them into building materials such as plaster, mortar or concrete [12], [13].
To integrate PCMs in building materials, we can adopt several ways such as impregnation of porous building materials, macro-encapsulation, shape-stabilized PCMs in separate storage devices and micro-encapsulation [14]. The most common methods described in the literature for micro-encapsulation are interfacial polymerization, emulsion polymerization, in situ polymerization, suspension polymerization, coacervation, and spray drying.
The use of gypsum plaster with micro-encapsulated PCM is becoming increasingly common [15].
It has been found that the melting temperature of the PCM to be integrated in gypsum wallboard depends on the average ambient temperature, which varies from one building to another and from one season to another. For external walls, it also depends on the external temperature and the thermal resistance of the walls [16].
Omari et al. [17] studied the thermal behaviour of a micro-PCM composite material dispersed in an insulating polymer matrix subjected to cyclic harmonic thermal excitation by varying the panel thickness and PCM percentage.
They concluded that the reduction in temperature fluctuations achieved in summer required an optimal choice of the PCM thickness and percentage, melting temperature and thermal properties of the matrix, considering the climatic conditions and thermal loads to avoid a poor winter result.
Childs and Stovall [18] studied a building with cellulose walls integrating PCM by treating the impact of different elements of interest such as the PCM dosage, PCM location in walls, outside temperature and wall orientation and showed that the installation of PCM at the inner face of the walls allowed to obtain a major energy gain.
An experimental study was conducted by Yang et al. [19] on walls impregnated with rectangular encapsulated hydrated salt under a temperature mode corresponding to transition seasons characterized by unstable temperatures.
The experiment showed that the amplitude of the indoor air temperature was reduced by more than 32% when PCM was placed near the inner face of the wall over the temperature amplitude of the indoor air temperature when PCM was placed on the outer face.
Scalat et al. [20] concluded, in a large-scale experimental study, that wall panels impregnated with PCM could attain charging and discharging times of approximately 7 hours, which enables energy storage in the heating mode but also in the cooling mode, and they pointed out that the rate of heat loss varied according to the temperature difference, construction method, room size, occupancy characteristics, and heat losses and gains.
Olivier [21] studied gypsum board with 45% PCM and concluded that under the same test conditions, it stored 5 times more energy per unit mass than a thermal brick wall, 9.5 times more energy than a brick wall, and almost 3 times more energy per unit mass than a common gypsum board.
Athienitis et al. [22] investigated the thermal performance of PCM gypsum panels used in a passive solar building. They found that the room temperature could be reduced by approximately 4 • C during the day, and the heating load could be reduced by 15%. Other experimental studies revealed that the integration of PCM in gypsum panels could reduce indoor air temperature fluctuations by 4 • C, especially in summer [23], [24].
Kuznik et al. [25] experimented on a full-scale test room with a wallboard composed of 60% micro-encapsulated PCM, of which the melting temperature was 22 • C. They concluded that 5-mm PCM wall panels improved the thermal inertia of the building room. The energy storage was twice as high as that of a concrete layer of approximately 8 cm.
Kuznik and Virgone [26] applied two identical test cells to investigate the effects of PCM wallboards; a heating/cooling step with a sinusoidal evolution was tested. The PCM wallboards caused a time lag between the indoor and outdoor temperature evolutions and reduced the external temperature amplitude.
The same conclusion was drawn by Shilei et al. [27] when combining gypsum panels with PCMs in winter in the northeast of China.
In a study on concrete walls containing PCMs in San Francisco and Los Angeles, Thiele et al. [28] found that the cooling load that could be reduced in summer was greater than the heating load in winter.
Kuznik et al. [29] installed plasterboard containing PCM on the sidewalls and ceiling of an office in a building under renovation, and compared to another office not containing PCM, they found a reduction in the operating temperature of up to 3 • C.
Considering the advantages offered by PCMs cited in the scientific literature, through this study, we wanted to provide a clear answer on the impact of PCM plaster on the thermal comfort and energy consumption necessary for cooling and heating if used as interior and/or exterior wall cladding instead of the cement plaster widely used in the Mediterranean countries.
The major contributions of this study are: • To address the point not sufficiently covered by the literature, namely, the thermal and energy contributions of PCM plaster through a multi-variable study considering the type of masonry (single cement brick partition or double clay brick partition), the type of rendering (PCM rendering or cement plaster) and its location (interior and/or exterior).
• To verify and quantify the thermal and energy contributions of PCM plaster and compare them to those of cement plaster. The subject is addressed in the context of a temperate Mediterranean climate where the outside temperatures are neither very high in summer nor very low in winter.

II. METHODOLOGY
The study consisted of: • A small-scale experiment aimed at observing the thermal performance of eight cells of identical dimensions whose sidewalls exhibit several configurations, namely, the walls are either single-partition cement bricks or double-partition clay bricks, and on the internal and external faces of these sidewalls, either a cement plaster widely used in construction in Morocco is applied as external or internal plaster or a plaster containing micro-encapsulated PCM.
• A dynamic modelling experiment of a dwelling with rooms of different sizes and exposures with the same walls and plaster configurations as the small-scale experiment. The indoor temperatures in winter and summer as well as the energy required for cooling and heating of the different rooms were observed and compared. The cooling and heating energy demands are then evaluated considering an on/off wall-mounted split heating and cooling system with a coefficient of performance of 2.5.

III. SMALL-SCALE EXPERIMENTATION A. EXPERIMENTATION SET UP
Eight cells of identical internal dimensions (50 cm × 50 cm × 60 cm) are made. Figure 1 shows a photo of the used experimental cells.
The walls of the cells are either single or double partitioned: • The single-partition walls are made of cement bricks, which offer a high wall strength, easy installation and suitable price, but their thermal insulation is poor (T k = 0.84 W/m.K).
• The double-partition walls are made of clay bricks, which are lighter and more fragile, but they are more expensive, and their installation is more complicated than the cement bricks since the exterior walls contain a cavity allowing for the possible insertion of thermal insulation. However, this allows for a greater thermal insulation than cement bricks (T k = 0.35 W/m.K). The interior and exterior faces of these walls are then lined with either PCM or cement plaster. Table 1 summarizes the different configurations of the walls and plaster materials of the cells studied. Figure 2 shows the walls composition of cells S1, S2, S3 and S4 made from cement bricks. These cells have a single 15-cm thick cement brick partition wall. On the inner surface of these sidewalls, either plaster containing micro-encapsulated PCM (INERTEK 23; latent heat: 180 J/g;  melting temperature = 23 • C) with a thickness of 15 mm is applied or cement plaster with the same thickness. On the outside of these walls, either 12 mm of the same PCM plaster is applied or cement plaster, followed by a 3-mm layer of exterior paint plaster. The floor and slab are made of 70-mm thick concrete.  configurations on the inner and outer surfaces as the S1, S2, S3 and S4 cells (PCM plaster or cement plaster). The floor and slab are also made of concrete and are 70 mm thick. Table 2 lists the material characteristics of the different layers of the cell walls. Calibrated thermocouples are installed at the cell centres to simultaneously measure the internal temperatures. They are connected to a data acquisition device that measures and records the temperature every 15 minutes. The outdoor temperature is monitored and recorded by a small weather station. Figure 4 gives a scheme of the experimental set up. B. RESULTS Figure 5 shows the results of the outdoor and indoor temperatures measured for single-partition cells S1 to S4 over 2 days with the outdoor temperatures ranging from 3 • C to 15 • C. For cell S4 with cement plaster on the interior and exterior faces, the indoor temperature ranges from 8.6 • C to 23.7 • C within a fluctuation range ( T For cell S1, with its interior and exterior faces covered with PCM plaster, the indoor temperature ranges from 6.6 • C to 16.2 • C within a fluctuation range of 9.6 • C. Cell S2 with interior PCM plaster and exterior cement plaster has an indoor temperature ranging from 7.5 • C to 16.6 • C and a fluctuation range of 9.1 • C. Cell S3 with interior cement plaster and exterior PCM plaster exhibits a fluctuation range of 12.9 • C since the indoor temperature ranges from 6.8 • C to 19.7 • C.   Figure 6 shows the measured outside and inside temperatures for double-walled cells D1 to D4 over 2 days under the same conditions as those of cells S1 to S4. For cell D4 with both interior and exterior cement plaster, the indoor temperature varies between 9.4 • C and 21.8 • C within a fluctuation range of 12.4 • C. For cell D1 with interior and exterior PCM plaster, the indoor temperature ranges from 7 • C to 15.1 • C within a range of 8.1 • C. Cell D2 with interior PCM plaster and exterior cement plaster has an indoor temperature ranging from 8.3 • C to 20.6 • C and a fluctuation range of 12.3 • C. For cell D3 with interior cement plaster and exterior PCM plaster, the indoor temperature ranges from 7.6 • C to 16.2 • C within a fluctuation range of 8.6 • C.
On winter days, as the S1, S2, D1 and D2 cells have internal surfaces covered in PCM plaster, this enables them to attain a small temperature fluctuation and low sensitivity to outdoor temperature variation. Simulation of the thermal behaviour in winter and summer seasons will allow the determination of the behaviour under other conditions of outside temperatures and the corresponding energy based on the different wall configurations and the use of either PCM or cement plaster.

IV. MODELLING A. CASES STUDIED
To investigate the impact of the degree of exposure to outdoor weather on the effect of PCM utilization on the indoor temperature, a residential dwelling with exterior walls exhibiting different surfaces and orientations was modelled (Figure 7). Different configurations of the external walls were simulated in the small-scale experiment. Thus, these external walls were either single-or double-partitioned walls with their internal and external faces coated with either PCM or cement plaster. Exterior paint plaster was applied on top of the exterior PCM plaster layer to avoid its deterioration due to the outdoor weather conditions (rain, UV rays, etc.).
As shown in Figure 8, room 2 has a south orientation and receives solar radiation on two of its walls throughout the day. Room 1 also faces south. Rooms 3 and 4 are oriented north and east, respectively, which allows them to receive solar radiation only in the morning, while room 5 has little exposure. Table 3 summarizes the areas and orientations of the walls and windows of the different rooms.
The simulations were performed in DesignBuilder software, which uses the EnergyPlus calculation engine and allows the modelling of multi-layer walls and thermal properties of PCMs using the finite difference method for the spatio-temporal discretization of the thermal equation and boundary conditions.
The heat transfer equation is written as [30]: The thermal conductivities (k W and k E ) are written as: The heat capacity of the PCM also varies with each time step and its value is expressed as a function of the specific VOLUME 8, 2020  enthalpy (kJ/kg) and temperature according to the following equation:  Figures 9 and 10 show the evolution of the indoor temperature for well-exposed room 2 on typical winter and summer days when the walls are under the single partition. On a typical winter day, compared to cement plaster (S4), the PCM plaster on the interior surfaces (S1 and S2) reduces the fluctuation range of the indoor temperature. The fluctuation range is only 3.4 • C if PCM is applied on the interior  surface and is 5.4 • C if it is applied on the exterior surface, and if both the interior and exterior surfaces are coated in cement plaster, the range is 6.2 • C. This reduction in the indoor temperature fluctuation with interior PCM plaster occurs because the low indoor temperature is nearer the melting temperature of the PCM (T M = 23 • C) on a winter day, in the proximity of which phase change occurs, thus allowing heat storage and transfer. When PCM is applied to the exterior surfaces of the walls (S3), the contribution of PCM plaster is reduced because the outdoor temperatures to which it is subjected are low and far from its melting temperature.
On a summer day, the amplitude of the indoor temperature is 2 • C if PCM plaster is applied to the exterior surfaces (S1 and S3) and is 4.1 • C if it is applied to the interior surfaces, while the amplitude of the indoor temperature is 4.7 • C if both the interior and exterior surfaces are coated in cement plaster.
This reduction in the indoor temperature fluctuation with exterior PCM plaster occurs because on a summer day, the PCM placed on the exterior surfaces (S1 and S3) is close to the heat source (solar radiation), thus subjecting it to outdoor temperatures ranging from 21 • C to 30.5 • C near its melting temperature (T M = 23 • C), which allows the PCM to melt and solidify and thus store and transfer heat, respectively. When PCM plaster is applied only on the interior surface (S2) where the indoor temperature is above the melting temperature, the PCM effect is reduced. In this case, the contribution to the indoor temperature is not much different from that obtained with cement plaster (S4).   Figures 11 and 12 shows the evolution of the indoor temperature for well-exposed room 2 on typical winter and summer days when the walls are under the double-partition mode.
On a typical winter day, compared to cement plaster (D4), the PCM plaster on the interior surface of the walls (D1 and D2) reduces the indoor temperature fluctuation. The fluctuation range is 3.1 • C if PCM is applied to the interior surface and is 3.9 • C if it is applied on the exterior surface. It is 4 • C in the case of cement plaster on both the interior and exterior surfaces.
Similar to the single-partition case, PCM plaster on the interior surface results in a small indoor temperature fluctuation because on a winter day, the indoor temperature is closer to the PCM melting temperature where phase change occurs. Whereas if PCM is applied to the exterior surface of the walls (D3), the contribution of PCM plaster is reduced because the outdoor temperature is farther removed from its melting temperature.
On a typical summer day, the indoor temperature fluctuation range is 2.6 • C with interior PCM plaster and is 2.9 • C with cement plaster whereas for exterior PCM plaster, the fluctuation range is reduced to 1.6 • C. This reduction occurs because the PCM placed on the exterior surfaces (D1 and D3) receives solar radiation, which subjects it to a temperature near its melting point, thus allowing heat storage and transfer. When PCM plaster is applied only on the interior surface (D2), the indoor temperature is higher than the PCM melting temperature, which reduces its contribution. The observed indoor temperature is therefore not very different from that obtained with cement plaster (D4).  Table 4 summarizes the results of the PCM plaster contributions obtained for room 2: in the case of single-partition walls, on a typical winter day and with interior PCM plaster, the indoor temperature varies between 12.4 • C and 15.8 • C, i.e., a fluctuation range of 2.8 • C, which is smaller than that obtained with cement plaster. In the case of double-partition walls, the indoor temperature varies between 13.9 • C and 17 • C, i.e., a range of 0.9 • C, which is smaller than that obtained with cement plaster. Although the gain in fluctuation reduction due to the double partition is less notable than that due to the single partition (0.9 • C instead of 2.8 • C), the fluctuation range is less important (3.1 • C instead of 3.4 • C) and the temperatures are slightly higher and therefore closer to the thermal comfort level.
On a typical summer day, with exterior PCM plaster, the indoor temperature varies between 27.2 • C and 29.2 • C, i.e., a fluctuation range that is 2.7 • C smaller than that obtained with cement plaster. In the case of double-partition walls, the indoor temperature varies between 28.4 • C and 31 • C, i.e., a range that is 1.2 • C smaller than that obtained with cement plaster. The gain in fluctuation range reduction due to the double partition is less notable than that due to the single partition (1.2 • C instead of 2.7 • C), but the fluctuation is less important (1.6 • C instead of 2 • C).  Table 5 lists the daily fluctuation ranges of the indoor temperature for the five rooms with single-partition walls on a winter day:

2) INDOOR TEMPERATURE FLUCTUATION RANGE a: SINGLE-PARTITION WALLS
As previously observed for room 2, compared to cement plaster, interior PCM plaster reduces the indoor temperature fluctuation for the other rooms: the values of T • S1 and T • S2 are lower than the values of T • S3 and T • S4 , respectively. The room indoor temperature fluctuation ranges are the largest in the case of interior and exterior cement plaster: T • S4 ranges from 2.5 • C for room 4 to 10.1 • C for room 1. Exterior PCM plaster does not drastically improve the fluctuation range of T • S3 : it ranges from 2.3 • C for room 4 up to 9.5 • C for room 1. PCM plaster is rather interesting as interior plaster because the indoor temperature is closer to its melting temperature, thus allowing the exploitation of its heat storage and transfer capacities. Thus, the temperature fluctuation interval T • S2 ranges from 1.8 • C for room 4 to 8.5 • C for room 1 in the case of PCM plaster only on the interior surface. As in the case of room 2, applying PCM plaster to the outside of a wall with interior PCM plaster will only slightly improve the fluctuation ( T • S1 : from 1.8 • C for room 4 to 8.2 • C for room 2). The indoor temperature fluctuation range obtained with PCM plaster is compared to that obtained with cement plaster: it is observed that the reduction in indoor temperature fluctuation range T • S4 − T • S1 varies between 0.7 • C and 2.8 • C with both interior and exterior PCM plaster. With interior PCM plaster, the reduction, i.e., T • S4 − T • S2 , ranges from 0.7 • C to 2.5 • C. Moreover, the contribution to T • S4 − T • S3 is smaller in the case of exterior PCM plaster: it ranges from 0.2 • C to 0.9 • C. As indicated in table 6, on a summer day, compared to cement plaster, PCM plaster on the exterior surface reduces the room indoor temperature fluctuation ranges of rooms 1 to 5: the values of T • S1 and T • S3 are lower than the values of T • S2 and T • S4 , respectively. The fluctuation is the largest in the case of both interior and exterior cement plaster: T • S4 ranges from 2.7 • C for room 3 to 7.7 • C for room 1. Interior PCM plaster does not reduce the fluctuation interval of T • S2 : it ranges from 2.5 • C for room 3 up to 7.5 • C for room 1. For room 2, exterior PCM plaster allows for a greater reduction in the indoor temperature fluctuation because under the effect of solar radiation, and the temperature oscillates around the melting point: The temperature fluctuation of T • S3 ranges from 1.8 • C for room 3 to 6.7 • C for room 1 in the case of PCM plaster only on the outside. As in the case of room 2, applying PCM plaster to the interior surfaces has no major impact on the indoor temperature fluctuation interval of T • S1 : it ranges from 1.9 • C for room 3 to 6.5 • C for room 1. The reduction in the indoor temperature fluctuation range obtained with exterior plaster is more notable than that obtained with cement plaster: T • S4 − T • S1 ranges from 0.8 • C to 2.6 • C, and T • S4 − T • S3 ranges from 0.9 • C to 2.6 • C. In contrast, the contribution to T • S4 − T • S2 is reduced in the case of interior PCM plaster: it ranges from 0.2 • C to 0.6 • C.

b: DOUBLE-PARTITION WALLS
In the case of double-partition walls and as previously observed for room 2, on a winter day and compared to cement plaster, indoor PCM plaster reduces the indoor temperature fluctuation in the other rooms: the values of T • D1 and T • D2 are lower than the values of T • D3 and T • D4 , respectively ( Table 7 ). The fluctuation is more notable in the case of both interior and exterior cement plaster: T • D4 ranges from 1.9 • C for room 4 to 8.3 • C for room 1. Exterior PCM plaster did not improve the fluctuation: the T • D3 values are almost the same as those of T • D4 . For room 2, PCM plaster is rather interesting as interior plaster because the indoor temperature is closer to the PCM melting temperature, which allows the exploitation of its heat storage and transfer capacities. The temperature fluctuation range T • D2 ranges from 1.7 • C for room 4 to 7.9 • C for room 1 in the case of PCM plaster applied only to the interior. Applying exterior PCM plaster in combination with interior PCM plaster will only slightly improve the fluctuation of the indoor temperature T • D1 : it ranges from 1.7 • C for room 4 to 7.5 • C for room 1.
As for the single partition, the reduction in fluctuation in the case of interior PCM plaster is more notable than that in the case of cement plaster ( T • D4 − T • D1 ranges from 0.2 • C to 1.4 • C, and T • D4 − T • D2 ranges from 0.2 • C to 1 • C) and is smaller than that in the case of exterior PCM plaster ( T • D4 − T • D3 ranges from −0.1 • C to 0.4 • C). As indicated in table 8, on a summer day and compared to cement plaster, exterior PCM plaster reduces the indoor temperature fluctuation in rooms 1 to 5: T • D1 and T • D3 are lower than T • D2 and T • D4 , respectively. The fluctuation is more notable in the case of both interior and exterior cement plaster: T • D4 ranges from 2.2 • C for room 3 to 6.5 • C for room 1. With interior PCM plaster, the fluctuation interval of T • D2 ranges from 2 • C for room 3 up to 6.4 • C for room 1. Exterior PCM plaster results in a larger reduction in the indoor temperature fluctuation: T • D1 ranges from 1.6 • C to 6 • C, and T • D3 ranges from 1.7 • C to 6.2 • C. For the single partition, the fluctuation reduction is more notable in the case of exterior PCM plaster than that in the case of cement plaster and is smaller than that in the case of interior PCM plaster ( The following table 9 summarizes the main results obtained and detailed above: • Compared to cement plaster for both types of partitions, temperature fluctuations are reduced in winter by interior PCM plaster and in summer by exterior PCM plaster. • Compared to cement plaster, the reduction due to PCM plaster in the case of a double partition is less notable than that in the case of a single partition. This is explained by the thermal resistance of the double-partition wall, which is much higher than that of the single-partition wall (clay bricks are more  insulating than cement bricks, and the thickness of the double-partition wall is larger): the double partition therefore offers a low sensitivity to outside temperature variations even with cement plaster. Compared to the single partition, the impact of PCM plaster on the double partition is therefore reduced, but the temperatures are closer to the thermal comfort level, and the fluctuations are slightly smaller with a double partition (they range from 1.7 • C to 7.9 • C instead of from 1.8 • C to 8.5 • C in winter and from 1.7 • C to 6.2 • C instead of from 1.8 • C to 6.7 • C in summer).

3) HEATING AND COOLING ENERGY a: SINGLE-PARTITION WALLS
As shown in Figure 13, on a typical winter day and compared to cement plaster, the use of PCM plaster as interior plaster reduces the heating energy demand. This reduction ranges from 17% for room 4 to 27% for room 2 and is comparable to the contribution of interior PCM plaster to the reduction in indoor temperature fluctuations previously observed. The use of exterior PCM plaster does not reduce the heating energy demand. Over a whole winter season. the use of PCM plaster only on the external surfaces of exposed walls (before the coating of exterior paint plaster) imposes a negative effect on the heating energy required, since it is 4 to 36% higher than that required when using cement plaster ( Figure 14). This can be explained VOLUME 8, 2020  by the fact that, in contrast to PCM plaster, cement plaster allows a higher heat flux due to solar radiation in winter and thus affords a slight increase in the interior temperature. Conversely, compared to cement plaster, interior PCM plaster reduces the heating energy demand for all of the modelled rooms. This reduction ranges from 17% for room 1 to 25% for room 2 (the heating energy with an interior PCM plaster ranges from 519 kWh for room 5 to 1230 kWh for room 1).
On a typical summer day, compared to cement plaster, the use of interior PCM plaster does not reduce the cooling energy demand for rooms 1 and 5 ( Figure 15). This is in line with what has been observed on its impact on temperature fluctuations, namely, the use of exterior PCM plaster imposes a major impact. It allows reducing the cooling energy demand for all rooms from 13% for room 5 to 29% for room 3.
During the summer season, compared to cement plaster, interior PCM plaster does not reduce the cooling energy  demand for rooms 1, 3, 4 and 5 ( Figure 16). The reduction is 22% for room 2. Compared to cement plaster, the contribution of exterior PCM plaster applied to the exposed external surfaces of the rooms is more notable since it allows a reduction in the cooling energy demand for all the rooms. This reduction ranges from 12% for room 5 to 36% for room 1(the cooling energy with an exterior PCM plaster ranges from 11 kWh for room 2 to 941 kWh for room 5).

b: DOUBLE-PARTITION WALLS
As for single-partition walls, on a typical winter day and compared to cement plaster, the use of PCM plaster as interior plaster on double-partition walls reduces the heating energy demand ( Figure 17). This reduction ranges from 14% for rooms 1 and 4 to 24% for rooms 2 and 3. The heating energy demand for the rooms with PCM on the external surfaces is higher than that for rooms 1, 2 and 3 in the case of cement plaster.  In the winter season, the use of PCM plaster only on the external surfaces of the exposed double-partition walls imposes a negative effect on the heating energy required, and it is 7 to 51% higher than that required when cement plaster is used for the same reason cited in the case of the single-partition wall ( Figure 18). The use of interior PCM plaster reduces the heating energy demand for all the rooms from 4% for room 1 to 21% for room 3 (the heating energy with an interior PCM plaster ranges from 385 kWh for room 2 to 1104 kWh for room 1).
As in the case of the single-partition walls, on a typical summer day and compared to cement plaster, interior PCM plaster on the double-partition walls does not reduce the cooling energy demand for rooms 1 and 5 ( Figure 19). The reduction in the energy required is 0.5% for room 4, 5% for room 3 and 17% for room 2. PCM plaster on the external surfaces imposes a major impact. The cooling energy reduction ranges from 9% for room 5 to 20% for room 3, while the cooling energy demand for room 2 is negligible.  The results obtained during the summer season are shown in the Figure 20. Compared to cement plaster, interior PCM does not reduce the heating energy demand for rooms 1, 4 and 5, which is in line with what has been observed on its impact on temperature fluctuations, namely, the contribution of PCM plaster applied to the exposed external surfaces of the rooms is beneficial as it allows a reduction in the cooling energy demand for all the rooms. This reduction ranges from 19% for room 5 to 44% for room 1(the cooling energy with an exterior PCM plaster ranges from 13 kWh for room 2 to 820 kWh for room 5).
Comparing the heating energy demands of the rooms with single-and double-partition walls, it can be observed that compared to cement plaster, the contribution of the application of PCM plaster to the interior surfaces is slightly more notable for the single-partition walls than for the double-partition walls in terms of the percentage reduction of the heating energy demand (from 17 to 25% for the single partition and from 4 to 21% for the double partition). However, the energy required for heating is lower for double-partition walls with interior PCM plaster (from 519 to 1230 kWh for the single partition and from 385 to 1104 kWh for the double partition).
In summer, the PCM plaster on the interior surfaces reduces the cooling energy by 12 to 36% for the single partition and 19 to 44% for the double partition. The cooling energy is lower for the double partition (13 to 820 kWh for the double partition and 11 to 941 kWh for the single partition).
The study was conducted on PCM plaster with a fixed thickness of 15 mm for the internal surface of walls and of 12 mm for the external surface. The thickness impact of the PCM used was not studied. On the other hand, the melting temperature of the chosen PCM is 23 • C, and PCM plasters with higher or lower melting temperatures have not been investigated. It would therefore be beneficial to study the impact of the PCM thickness as well as its melting temperature on the thermal and energetic contributions in future work. It would also be advisable to perform similar studies for other climates (other than the temperate Mediterranean climate in this study), especially those where the outside temperatures can be very high in summer and/or very low in winter.

V. CONCLUSION
Through this multi-variable study, we verified and quantified the contribution of plaster containing micro-encapsulated PCM used as wall-covering material.
Different configurations of the use of PCM plaster were therefore examined, namely, the types of walls and bricks and PCM location on either the inside or outside surfaces of walls, and the performance obtained with PCM plaster was compared to that obtained with cement plaster.
The results of the dynamic modelling of a dwelling with several types of rooms showed the following in terms of the thermal performance: • In winter, the PCM coating is more beneficial on the interior surface of the single-and double-partitions walls: it reduces the indoor temperature fluctuation range from 0.7 • C to 2.5 • C for the single partition and from 0.2 • C to 1 • C for the double partition.
• In summer, the PCM coating is more beneficial on the exterior wall surface: it reduces the indoor temperature fluctuation range from 0.9 • C to 2.6 • C for the single partition and from 0.3 • C to 1.3 • C for the double partition.
• The contribution of PCM is less notable in terms of the percentage reduction of the indoor temperature fluctuation range for the double-partition walls, but the temperature fluctuations with this type of wall are smaller, and the temperatures are closer to the thermal comfort level even with cement plaster (double-partition walls made of clay bricks attain a suitable thermal insulation) compared to the case of single-partition walls.
Regarding the energy level: • Interior PCM plaster reduces the heating energy demand by up to 25% with the single partition and by 21% with the double partition.
• Exterior PCM plaster reduces the cooling energy demand by up to 36% with the single partition and by 44% with the double partition.
• The heating and cooling energy required to maintain the thermal comfort of the double partition is reduced compared to the single partition (since it allows for less indoor temperatures fluctuations values). The results reveal a major contribution of the PCM plaster, but the performance should be optimized by considering other variables in future works such as the thickness of the PCM coating and PCM melting temperature in addition to the type of climate.