The built environment plays a crucial role in global energy consumption, with buildings accounting for a large share of energy use worldwide. Therefore, addressing energy efficiency in this sector is essential for reducing overall energy demand and mitigating environmental impacts. In Algeria, the building sector is the largest energy consumer, accounting for more than 41% of the overall energy consumption, surpassing the agriculture (33%), energy (19%), and industry and transport (7%) sectors. The Algerian National Agency for the Promotion and Rationalization of Energy Use (APRUE) aims to reduce energy consumption in residential and tertiary sectors by 10% to 15% by 2030. This goal presents several challenges, encompassing political, economic, social, cultural, and geographical issues [1,2].

Addressing this crisis requires aligning the architectural and energy strategies of housing. Recent data shows that natural gas and electricity dominate energy consumption, accounting for 53.61% and 33.7%, respectively, while liquefied petroleum gas and biomass represent just 12.46% and 0.01% of global consumption [3]. However, statistics indicate that useful energy is primarily consumed for heating, air conditioning, and domestic hot water production, and it is also essential for food cold storage (refrigerators and freezers), cooking, and lighting [4]. To tackle these challenges, the strategy must focus on finding more suitable solutions, exploring energy alternatives, and harnessing various potentials for energy use to develop applications beneficial to this energy-intensive sector. The overarching goal of this effort is to achieve more efficient and rational energy management. Actions and procedures will concentrate on enhancing thermal comfort and improving energy efficiency [5,6].

As the demand for heating and cooling in buildings rises during colder and warmer seasons, their energy consumption has increased significantly. Consequently, phase change materials (PCM) have become the preferred choice for latent thermal storage applications in the building industry. This approach is gaining popularity in Algeria, where incorporating PCM has proven to be ideal and effective for significantly reducing energy costs in buildings, refrigeration systems, and water heaters. The importance of these contributions is directly related to quantifying the energy needs for heating and cooling. Implementing these measures can lead to more environmentally friendly solutions [7]. First, latent heat can be stored with limited storage volumes and it is possible to store six to eight times more thermal energy than sensible heat in the same volume In addition, the phenomena generated using PCM (energy storage or release) lead to a stabilization of operating temperatures [8–10]. Furthermore, incorporating phase change materials (PCM) into buildings can decrease energy dependency by utilizing latent heat storage to boost thermal inertia without significantly adding to the building’s weight [11–13]. Finally, integrating PCM into the building’s structure can enhance the thermal inertia of its envelope, which can slow down heat transfer during peak times and minimize large indoor temperature variations. This results in improved thermal comfort and reduced energy consumption [14–17].

Among the standards necessary for the thermal design of buildings, two basic standards must be considered, user comfort and efficient energy management, which can lead to contradictory recommendations. In the analysis of these two aspects, the humidity content of the air can have significant impacts. However, the majority of building energy simulation codes neglect air humidity or represent it in a very simplified manner. Often humidity is simply transported by the air, whereas in the majority of real cases, its interactions with hygroscopic materials cannot be neglected. In the design of an efficient building (in the energy efficiency sense), in addition to the need to offer more efficient and less energy-consuming equipment, it is essential to control thermal exchanges through the envelope.

The energy balance results from a balance between thermal gains and losses, between the envelope and its environments (interior and exterior). The design of envelopes, capable of exploiting free energy gains while limiting losses, must contribute to reducing energy needs without harming interior comfort. The envelope then becomes a real heat exchanger that can be managed and adapted to indoor and outdoor environments [18].

Bioclimatic design has developed significantly since the 1970s and has given rise to numerous research which has made it possible to produce bioclimatic design tools, for architects, design offices, and engineers. Through this work, we want to achieve a reliable and comprehensive tool. The desired completeness is achieved by considering all the physical phenomena necessary for a complete representation of reality. We are also interested in the study of certain parameters that can be decisive for indoor comfort, in particular relative humidity, temperatures, and incoming mass flow rates. In current buildings, it is preferred to reduce the thickness of the walls to reduce costs while respecting standards to limit thermal losses. However, such structures do not provide sufficient thermal inertia capable of dampening fluctuations in the external temperature. One of the ways to reduce the energy needs of a building is therefore the design of an energy-efficient envelope, limiting losses and recovering passive contributions as much as possible. To achieve these objectives, a certain number of basic principles need to be considered and the most important ones are insulation and thermal inertia as well as the use of solar gain.

This paper addresses the pressing issue of energy consumption in the building sector in Algeria, which accounts for a significant portion of the nation’s energy usage. Despite the dominance of natural gas and electricity in energy consumption, the focus remains on heating, air conditioning, domestic hot water production, and other essential services. To tackle these challenges, a comprehensive strategy is necessary, one that integrates energy-efficient solutions and harnesses available resources effectively. The utilization of PCM allows for the storage of latent heat, leading to stabilized operating temperatures and improved energy efficiency. Moreover, the paper highlights the significance of considering air humidity in building energy simulations, as it plays a crucial role in indoor comfort and energy management.

The present study emphasizes the importance of bioclimatic design principles and the development of reliable tools to optimize building performance. By considering all relevant physical phenomena and parameters such as relative humidity and temperature, the research aims to provide a comprehensive understanding of indoor comfort factors. Additionally, the paper underscores the importance of energy-efficient envelopes in reducing thermal losses and passive contributions. The research methodology involves simulating the thermo-aeraulic behavior of a multi-zone home in Ghardaïa, Algeria, using a coupled mathematical model. Furthermore, a wall model incorporating PCM is implemented, considering the region’s climatic conditions. The melting temperature of the PCM material used is specified at 22.6°C [19–21].

The majority of building energy simulation codes neglect air humidity or represent it in a very simplified manner. In this study, the proposed model focuses on the description of thermo-aeraulic transfers in this construction.

The proposed construction is made up of several glass rooms, walls, doors, and windows. The division of the habitat into thermal zones induces the creation of temperature nodes by zone. A certain number of information fields are connected to a node, reflecting for example the assignment of a node in an area or the topology of the overall electrical network associated with the house. In addition, a type was assigned to each node. Indeed, compared to the equations, the nodes are concerned with different phenomena.

For example, a node that represents a wall will concern heat conduction terms. This same node, depending on its situation, can also involve convection processes. On the external face of the envelope wall, the surface node is affected by external radiation and convective exchanges. We should note that the size of this structure can quickly become large as this building is divided into multiple areas and each area has multiple glass walls and windows. The size of this structure is linked to the dimensions of the systems to be solved and the notion of calculation time must not be neglected.

The present study was carried out on a habitat in the Ghardaïa region (Southern Algeria) where the exterior envelope promotes the development of a comfortable indoor environment by controlling the exchange of energy between the interior space and the environment. The house has a living area of 71.3 m² and the height of the walls is 2.8 m, while the other dimensions are shown in detail in Fig. 2. Windows and doors contribute significantly to the energy balance. Their contributions depend on several parameters such as climate, orientation, setting, and local relative surface (window-ground). The apartment has an area of 95.74 m² with a living space of 71.3 m².

A certain amount of information is connected to a typical node, reflecting for example the assignment of this node in an area or the topology of the associated global electrical network. Indeed, compared to the equations, the nodes are concerned with different phenomena. Then, it appears necessary to assign a type to each node. For a given building, when the node structure is established, it is easy to fill in each element of the mathematical model. Indeed, all that has to be done is to scan the node structure and assign the relevant terms.

For this house, the exterior wall envelope is made up of a heavy stone structure (40 cm thick) surrounded by two layers with a thickness of 1.5 cm of mortar cement. The internal face is covered with a layer of plaster 1 cm thick. The internal walls (or dividing walls) are considered heavy stone structures 15 cm wide, surrounded by two layers of cement mortar 1.5 cm thick and two layers of plaster 1 cm thick. The windows are single glazing, clear with a thermal transmission coefficient equal to U = 5.91 W m⁻² K⁻¹. The doors are made of wood with a thickness of 2 cm and the following parameters: λ = 0.14 W m⁻¹ K⁻¹, ρ = 500 kg m⁻³, and Cp = 2500 J kg⁻¹ K⁻¹.

Fig. 3 shows the instantaneous evolution of the solar illumination incident on the facades. The curves plotted in Figs. 4 and 5 describe the behavior of outdoor ambient air temperatures and wind speed, respectively. All results were calculated using data from 25–30 August, 2013.

Figs. 6 and 7 show the variations in temperatures and specific humidity of rooms in the home. It can be seen that the two parameters vary with the same scenario. Upon closer examination, it becomes evident that the fluctuations in temperatures follow a consistent pattern across different scenarios. Specifically, the variation between the minimum and maximum temperatures for the same profile falls within the range of 1.2°C to 1.7°C. This narrow range of temperature fluctuations can be attributed to the thermal characteristics of the building envelope, primarily composed of stone. Stone possesses significant energy storage capacity, which enables it to absorb and release heat gradually, thereby regulating indoor temperatures and minimizing temperature variations.

Furthermore, the variations in specific humidity exhibit a proportional relationship with temperatures. As temperatures rise or fall, specific humidity levels also adjust accordingly. This correlation between temperature and specific humidity underscores the dynamic interplay between thermal conditions and moisture content within the indoor environment.

The mass flow of the incoming air also influences the interior temperatures and humidity of the rooms of the home, which is reflected respectively in Figs. 8 and 9. The increase in the incoming mass flow reduces the thermal inertia of the envelope. By definition, a material with high thermal inertia causes a significant phase shift and stabilization of temperatures. The variation in specific humidity is proportional to indoor temperatures and follows the same scenario.

The influence of relative humidity is not considerable given that the phenomenon of propagation of specific humidity is long. However, the influence is significant on specific humidity as shown in Fig. 10. Figs. 11 and 12 show the model simulation results for different incoming air temperatures. The change in the temperature of the incoming air has a direct effect on the values obtained from the simulation. Moreover, this change does not affect the degree of thermal inertia of the home.

Figs. 13 to 16 highlight the benefit of incorporating PCMs within the partition walls of rooms 1 and 2, specifically positioned between two layers of plasterboard. In this setup, the PCMs are situated at the center of the partition wall, with a thickness of 4 cm, while the plasterboards on either side have a thickness of 1.5 cm each. These walls are strategically chosen for rooms oriented towards the south-facing windows, allowing for optimal utilization of solar radiation. The simulations were conducted under conditions of clear sky and utilized climatic data from Ghardaïa during 21–22 December, 2013. It is worth noting that the model parameters and equations remained consistent throughout the simulations, except for the partition wall’s conduction properties. In this case, the thermophysical parameters of the partition wall varied based on the temperature level of the PCM material.

The results depicted demonstrate the significant impact of PCM integration on thermal performance. Specifically, the PCM’s ability to absorb and release latent heat during phase transitions contributes to maintaining stable indoor temperatures, even under fluctuating external conditions. By leveraging solar radiation absorbed through the south-facing windows, the PCM-enhanced partition walls effectively regulate indoor temperatures, reducing the need for active heating or cooling systems.

Moreover, the thickness and positioning of the PCM within the partition wall play a crucial role in optimizing thermal performance. The strategic placement of the PCM at the center of the wall maximizes its heat absorption capacity while minimizing thermal bridging effects. This configuration ensures efficient utilization of the PCM’s thermal storage capabilities, resulting in improved comfort levels and energy savings.

Thanks to increasingly detailed simulations, we were able to predict the behavior of this complex system using the nodal method [22] and the Runge-Kutta numerical method of order 4. Figs. 17 and 18 represent the simulated temperatures and specific humidities of the interior air of room 1 for two cases: one assuming that the closed habitat satisfies the characteristics given in Table 1, and the other considering that the habitat satisfies the same characteristics but with the interior walls facing the open south windows (with solar gain) of rooms 1 and 2 replaced by a plaster-PCM type partition wall. These results justify that the use of PCM improves indoor comfort given that the temperatures traced can increase by 1°C in our case. In this situation, the opening represents 20% of the facade, so it can be enlarged to take greater advantage of these direct contributions.

Fig. 19 shows the temperature profiles of the interior wall composed of the layers set out in Table 2, but increasing the thickness of the stone to 25 cm. The curves obtained in Fig. 20 represent the temperatures of the inner, middle, and outer surfaces of the wall panel containing a layer of 1 cm of plaster plus 4 cm of PCM plus another similar layer of plaster.

To discuss the obtained results, emphasis is placed on the level of thermal inertia, i.e., the temperature fluctuations and the phase shift which represents the time difference between the peaks of ambient temperatures and in the middle of the wall. These aspects are more significant for a PCM partition. The PCM wall panel in this case ensures better thermal inertia.

The present research aimed to contribute to a comprehensive understanding of energy management strategies in the building sector, with a focus on improving thermal comfort and energy efficiency. Specifically, we seek to investigate the thermo-aeraulic behavior of a multi-zone home located in Ghardaïa, Algeria, utilizing a coupled mathematical model. Furthermore, it aimed to develop and implement a wall model incorporating PCM technology, tailored to the climatic conditions of the region. The obtained results have shown coherent responses in temperatures, specific humidity levels, and mass flow rates, indicating the effectiveness of PCM-integrated building envelopes in mitigating energy consumption and stabilizing indoor environments. The observed temperature differentials and phase shifts underscore the dynamic nature of PCM technology and its ability to adapt to varying environmental conditions. In addition, the simulation results revealed that to improve the thermal inertia of a built structure, it is possible to introduce PCM into solid wall materials which, thanks to their latent heat, make it possible to store or release a large quantity of energy. The incorporation of a layer of PCM makes it possible to increase the performance of a wall or partition by damping temperature fluctuations during the summer and winter seasons. The judicious integration of smart materials is an effective way to reduce energy consumption and carbon emissions linked to housing. The results obtained in this regard show the impact of PCMs on the thermal comfort of a Saharan house.

Moreover, Introducing PCMs into a wall, thanks to their latent heat, makes it possible to store/release a large quantity of energy and improve the main comfort parameters by delaying heat transfer and dampening temperature fluctuations depending on the energy content and water from the air. The situation was more affordable in November because the comfort is almost perfect. The operating regime is quasi-stationary for a relatively long time during this transition period. The results of the work also showed that significant financial savings can be made by improving the insulation of buildings. Proper use of PCMs must be done by combining them with a thermally insulating material. Among the solutions for increasing the inertia and thermal capacity of the internal walls, PCMs are a great choice. The advantage of this type of material is the weight saving and easy implementation adapted to existing products. PCMs can improve comfort and become a good alternative to heavy walls.

Finally, while the study aims to improve hygrothermal performance through PCM integration, it may overlook other important aspects of building performance, such as structural integrity, acoustic insulation, or indoor air quality. This narrow focus could limit the overall understanding of the potential benefits and drawbacks of PCM integration in multi-zone constructions.