## 1 Introduction  
The latest report of the Intergovernmental Panel on Climate Change (IPCC) paints a very damning picture. In the most optimistic scenario, the experts predict a temperature rise of more than 1.5 \({}^{\circ}\)C as early as 2030, against a warming of more than 4 \({}^{\circ}\)C according to the most pessimistic scenario [1]. It is clear that the ambitious objective set by the COP21 and the Paris Agreement to limit global warming to 1.5 \({}^{\circ}\)C will not be met. This increase in temperature is responsible for the frequent heat waves and temperature records recently observed in several regions of the world. Faced with this situation, it is essential to take actions to limit greenhouse gas emissions in order to achieve a zero carbon footprint. The building sector, which accounts for 40% of greenhouse gas emissions, remains one of the first sectors of action to reduce energy consumption and thus limit greenhouse gas emissions [2]. To reduce this energy consumption, mainly used for heating and cooling, it is essential to improve the energy efficiency of buildings by insulation and by taking advantage of renewable energies, such as solar energy. Thermal energy storage is an effective solution to achieve these objectives through its many advantages:  
* the correction of the phase shift between demand and off-peak periods during which prices are more favorable,
* the time shift between production and consumption which allows the reduction of the dependence on fossil fuels by using renewable energies and the limitation of heat losses through storage. The basic principle of thermal energy storage is the same regardless of the application. A thermal energy storage cycle is divided into three parts: charging, storage and discharging. During the production period, energy is used to charge the storage system. The stored energy can later be returned to the environment as a supplement or substitute for the heating or cooling system, thus reducing energy consumption. The different thermal energy storage techniques are classified according to the scale, the method used and the duration of the storage. Depending on the duration of the storage, we distinguish short-term and long-term (seasonal) storage. Short-term storage is used on the scale of a few hours, whereas long-term storage is used for longer periods (weeks and months). In addition, short-term storage is used to correct daily (diurnal) or hourly temperature variations, while long-term storage is used to smooth out seasonal temperature fluctuations. Thermal energy storage can also be classified according to the storage mechanism. Thermal storage can be done in essentially three ways: sensible heat storage, latent heat storage, and thermochemical storage. The difference between these three methods lies in the material used, the operating temperature and many other parameters. Historically, sensible heat energy storage is the most used in buildings [3; 4; 5; 6]. However, it requires large volumes of materials due to the low energy density. The use of phase change materials (PCMs) overcomes this constraint through the contribution of latent heat of phase change, which allows the design of more compact systems [7]. Due to the latent heat involved in the phase change processes, PCMs offer high thermal capacity, and more energy can be stored in the building envelope compared to traditional sensible materials. The main advantages of latent heat storage over sensible heat are higher energy density (up to 14 times higher), nearly constant storage temperature and the wide variety of materials available. However, PCMs are subjected to many problems due to their low thermal conductivity, supercooling, phase segregation, etc. [7]. Numerous experimental and numerical studies have shown that the integration of PCMs into building envelopes can improve thermal comfort (maintaining the temperature inside a building room between 15 and 35 \({}^{\circ}\)C) by reducing peaks and fluctuations in indoor temperature [6; 7; 8; 9; 10; 11].