The Impact of Arid Climate on the Indoor Thermal Comfort in the South-East of Morocco

The main objective of this work is to study the heat transfer through an administrative building’s envelope in Errachidia City in Morocco. A numerical simulation based on the finite element method was made to describe the effect of introducing several thermal insulators (air, hemp wool, glass wool, rock wool, and extruded polystyrene) of different thicknesses (5 cm, 10 cm, and 15 cm) on the heat transfer through the building’s envelope under different climatic conditions. For the stationary regime, the summer period was chosen on August 7, 2019, at 17 h, while the winter period was opted on January 1, 2020, at 7 h. Otherwise, for the transitional regime, the summer period was chosen from August 1 to 8, 2019, and the winter period from January first to 8, 2020. The physical model analyzes the temperature variation at the different layers of the wall. It depends on the indoor temperature, the instantaneous climatic conditions of the outdoor air, solar radiations, and the thermal properties of the building’s envelope. The results show that the air gap is a good thermal insulator; it acts as a damper of temperature and heat flux.


Introduction
The thermal comfort's guarantee inside the building and the reduction of energy needs require the implementation of walls combining various functions and characteristics (insulation, accumulation/restitution of solar gains). The building's envelope presents the seat of heat transfer; it is the physical interface between the external environment and the indoor air, which is desired to be maintained on a stable temperature range. Thus, to ensure a good level of comfort for the occupants, the heat stored in summer must be evacuated by an air conditioning system. While in winter, the heat loss must be compensated by a heating system which leads to waste a huge amount of energy in most buildings. Therefore, to guarantee the lowest energy consumption and the high quality of indoor comfort, it is essential to develop a high-performance envelope. For this reason, sev-eral studies have been done to enhance the thermal performance of a building's envelope such as using advanced materials [1][2][3][4], employing insulation layers [5][6][7], and varying its thickness [8].
In the literature, several researchers have focused on the impact of thermal insulations and its characteristics on the heat transfer through the building's envelope. Asan [9] presented a study about the influence of thermophysical characteristics of a building's wall on time lag and decrement factor taking into account the convection boundary conditions; he has proven by computations applied for different building materials that those characteristics have a significant impact on the time lag and decrement factor. Boukendil et al. [2] examined a 2-D steady-state model to study the coupled conductive, convective, and radiative heat transfer through a honeycomb wall with a medium of air gap. The results show that the total heat flux through this wall varies almost linearly despite the difference between the indoor and the outdoors's temperature. They also concluded the overall heat exchange coefficients for the thermal behavior prediction of this wall system. In addition to this, other researchers proved that the use of air gap gives optimal results. Jamal et al. [10] studied the coupled heat transfer mode by conduction, natural convection, and radiation in a double solid wall with a medium of air gap. The result shows that the use of air gap as insulation would highly help in reducing the energy consumption of buildings.
The geometric configuration of a multilayer building's envelope is illustrated in Figure 1. The left side of the wall is exposed to the ambient air, while its temperature T i is maintained constant. A convective heat transfer occurred between the interior facade and ambient air. The right facade of the wall is opened to a periodic outdoor ambient air temperature TðtÞ and towards the solar radiations φðtÞ. Convective and radiative conditions are established inside and outside the wall, and it is translated by global coefficients he and hi.
For the summer and winter periods with a wind speed v < 5 m/s, the convective heat transfer coefficients he [21] and hi [22] are given by h e = 5:7 + 3:8v, where v is the average wind speed m/s, T air is the indoor ambient temperature, T si is the outdoor average temperature, and H is the wall's height.

2.2.
Method. The external wall under study is assumed to be only in the x direction and time dependent. The one-dimensional, transient heat conduction equation for this problem is as follows: where λ is the thermal conductivity, ρ is the density, and Cp is the specific heat of the wall material.    International Journal of Photoenergy (iv) At the interior side of the wall, the boundary condition is where hi is the interior convective heat transfer coefficients, T x=0 is the wall interior side's temperature, and T i is the indoor temperature (v) At the exterior side of the wall, the boundary condition is where he is the exterior convective heat transfer coefficients, T x=L is the wall exterior side's temperature, T e is the outdoor temperature, and φðtÞ is the solar radiation flux in which the solar absorption coefficient of the brick is α = 0:6 [23] Transitional regime T i = 20°C Figure 2 T i = 25°C    Table 2 presents the characteristics of the studied wall (thickness (e), length (L), internal surface resistance (R si ), external surface resistance (R se ), and the initial conditions for stationary and transitional regimes during winter and summer periods 2.4. Climatic Data. The climate data conditions for the two studied periods (from 1 st to 8 th August 2019 and from 1 st to 8 th January 2020) were provided by Moulay Ali Cherif airport station. Indoors, the air temperature during the winter period is 20°C, and during the summer period, it is 25°C. Figures 2 and 3 show the instantaneous measured values of the outdoor air temperature for the two periods. The climate of Errachidia City is semidesert, and it is characterized by a very hot summer season with a very high diurnal temperature range. Indeed, maximum temperatures reach 41°C during the day, with a diurnal amplitude of around 15°C, and it is very cold in winter with minimum temperatures which can reach 0°C. Solar radiation reaches up to 900 W/m 2 in summer and 500 W/m 2 in winter (Figures 4 and 5). These climatic conditions support the discomfort of the inhabitants.  Figure 6) at different points of the wall; it is a typical situation that occurs when the air temperature inside is warmer 20°C than the outdoor temperature 0°C. Heat flux in the direction from the warm inside toward the colder outside portion of the wall. The inside of the building gets cold because of this, and a heater is needed to keep thermal comfort inside the building, which leads us to choose the appropriate thermal insulator to minimize the energy consumption of heating. Figure 7 shows the temperature profiles at different thicknesses (5 cm, 10 cm, and 15 cm) for different thermal insulations (air gap, glass wool, hemp wool, rock wool, and polystyrene) during the winter period. The profiles are similar and varied in the same manner for all thermal insulators.

Results and Discussion
We note that the increase of the insulators' thickness provokes an increase in the thermal resistance of the walls.
The impact of each thermal insulation for every chosen thickness is illustrated in Figure 8. We note that using air gap as an insulator reduces heat transfer through the studied wall with the three different thicknesses. The air gap blocks heat from exiting to the outside. The obtained results are similar to the results of Lairgi et al. [1]. Figure 9 shows the lines of the total heat flux at different points of the wall on August 5 th , 2019, at 14 h. The inside ambient air's temperature equals 25°C, which is colder than the outdoor temperature (40°C). Consequently, the heat flux's direction is from the outside toward the inside portion of the wall. By observing the evolution of the heat flux ( Figure 9) at any point of the wall, we note that the thermal insulation slows this heat transfer. Figure 10 shows the temperature profiles for various thicknesses (5 cm, 10 cm, and 15 cm) of different thermal insulators during the summer period. We note that the profiles are similar and vary in the same manner for all thermal insulations. Moreover, the increase of thermal insulators' thicknesses leads to a significant thermal resistance of the walls. These results are similar to the results obtained by Perumal et al. [24]. Figure 11 shows the effect of each thermal insulation for every chosen thickness during the summer period. We conclude that for the three thicknesses, thermal insulation by air gap is highly desirable; it gives the best results in terms of slowing heat transfer through the wall and reducing the costs.

Transitional
Regime. According to the previous results, we have chosen a thickness of 5 cm of each thermal insulator for the transitional regime. To analyze the effect of different insulators on the heat transfer through the building's envelope, we have recorded the different temperatures, T 1 at the interior side, T 2 at the interior side of the insulator, T 3 at the exterior side of the insulator, and T 4 at the exterior side of the wall (Figure 12).    Air gap 15cm Glass wool 15cm Hemp wool 15cm Rock wool 15cm Poly 15cm Air gap 15cm Glass wool 15cm Hemp wool 15cm      Figure 13 presents the temperature's variation from January 1 st to 8 th , 2020, at the midheight of the envelope, which is presented by a double-layered hollow clay brick and different thermal insulators (Figure 13).
The results show the layer's temperature waves in the same manner as the external side's one T 4 . Moreover, we found that the temperature profile at the external facade of the wall T 4 and the external side of the insulation T 3 is almost identical, which reveals a high capacity of hollow clay bricks to store heat during the day and to diffuse it at night. The five insulations were studied acting as a thermal barrier that blocks heat to exit. Indeed, the temperature of the internal side of the insulation (glass wool, rock wool, hemp wool, and polystyrene) T 2 varies from a minimum of 18°C and a maximum of 19°C while its external side T 3 varies from 7°C to 18°C which disclose a heat block rate of 64%. While for the air gap insulation, T 2 varies from 18.5°C to 19 and T 3 waves from 6 to 19°C (Table 3). Thus, using air gap as insulation blocks heat to exit with a rate of 68%. Consequently, the thermal insulation by air gap leads to an optimal result compared to the other thermal insulators under study.       International Journal of Photoenergy These results have previously been highlighted by other recent researches [1,6,10]. Figure 14 shows the heat flux as a function of the thickness four times per day (7 h, 12 h, 19 h, and 23 h) for the different insulators used.
The recorded flux for the five insulators (air gap, glass wool, hemp wool, rock wool, and polystyrene) is maximal at 12 h and minimal at 7 h, and it varies approximatively from 20 W/m 2 to 30 W/m 2 between 19 h and 23 h.
We note that the heat flux has a linear curve at the external layer of the wall, but with different values depending on the different moments during the day. At 12 h, the heat flux is higher compared to another time, and it reaches a value of 55 W/m 2 at the external side of the wall, and it decreased to 30 W/m 2 at 23 h; then, it gradually diminished towards the inside with a value of 2.5 W/m 2 for the air gap and approximatively 4 W/m 2 for the other insulators. Figure 15 shows the heat flux as a function of the thickness and insulators at t = 12 h. We note that there is no difference between the profiles of the four insulators at the external layer of brick. However, at the two other layers, the heat flux profile is almost constant and reaches a value of 5 W/m 2 for the glass wool, hemp wool, rock wool, and polystyrene while it is twice lower for the air gap with a value of 2.5 W/m 2 . Figure 16 presents the temperature's variation for the summer period from August first to 8 th , 2019, at the midheight of the envelope, which is consisting a double-layered hollow clay brick and different thermal insulators.

Summer Period.
The temperature at the external side of the wall T 4 reaches 58°C during the summer period considering the solar radiation. The thermal resistance is particularly low if glass wool, rock wool, polystyrene, and hemp wool are used as insulators compared to the air gap. Indeed, the temperature at the external side of the glass wool, hemp wool, rock wool, and polystyrene T 3 balances between 29°C and 51°C, and at its internal sides, T 2 varies between 27°C and 30°C (Table 4) which shows a heat reduction of 41.18%, while the temperature at the external side of the air gap T 3 waves from 30°C to 52°C and its internal side T 2 varies from 26°C to 28°C. Thus, the use of air gap in summer helps to reduce heat with a rate of 46.16% and reaches particularly a constant value T 1 of 25°C on the inside of the wall. Figure 17 shows the heat flux as a function of the wall thickness of the different thermal insulations used (air gap, glass wool, hemp wool, rock wool, and polystyrene) at four moments per day (7 h, 12 h, 19 h, and 23 h).
The recorded flux is maximal at 12 h and reaches a value of 115 W/m 2 at the external side of the wall, minimal at 7 h, while at 23 h, it reaches a value of 65 W/m 2 for the wall containing the air gap and a value of 60 W/m 2 for the other insulators. Then, the flux decreases slightly towards the interior of the wall with a value of 3 W/m 2 for the air gap and 5 W/m 2 for the other thermal insulators.
At 19 h, the heat flux has the same profile as at 23 h with a gap of 3 W/m 2 . Moreover, the heat flux decreases linearly in the external layer of the brick but with different values depending on the four moments of the day. At 7 h, the heat flux is becoming almost constant with a value of 2 W/m 2 . Figure 18 represents the heat flux as a function of wall thickness and thermal insulation's type at t = 12 h. We note that the profiles of the five insulators are similar at the external layer of brick; then, it decreases to the wall's internal side with different values, 2.5 W/m 2 for the air gap and 5 W/m 2 for the other insulators.     Air gap  25  26  26  28  30  52  28  58  Glass wool  26  27  27  30  29  51  28  58  Hemp wool  26  27  27  30  29  51  28  58  Rock wool  26  27  27  30  29  51  28  58  Polystyrene  26  27  27  30  29  51  28

Conclusions
In this study, we have studied the effect of thermal insulation by air gap, hemp wool, glass wool, rock wool, and extruded polystyrene, plus the impact of their thicknesses (5 cm, 10 cm, and 15 cm) on heat transfer through an administrative building's envelope located in Errachidia City, under different climatic conditions during winter and summer periods. The results show for stationary and transitional regimes, during the summer and the winter periods, in a semidesert climate of Errachidia City which is characterized by a significant sunshine. The thermal insulation by air gap is more efficient compared to the other thermal insulators under study; it acts as a heat absorber during the summer. While in winter, the air gap blocks heat towards the exit. Consequently, it ensures simultaneously the thermal comfort of the occupants and energy savings and reduces the materials' costs.

Data Availability
The datasets generated during and/or analyzed during the current study are available from the corresponding authors on reasonable request.

Conflicts of Interest
No potential conflict of interest was reported by the authors.

Rock wool t= 12h
Polystyrene t= 12h Air gap t= 12h Glass wool t= 12h Hemp wool t= 12h Figure 18: Heat flux as a function of the wall thickness and thermal insulation's type at t = 12 h during a summer period. 14 International Journal of Photoenergy