**2.3 Storage by latent heat or phase change**

Storage by latent heat of fusion is carried out with little or no temperature variation since the phase change of a pure body is isothermal but by phase change of material. The case of alloys is different because melting takes place over a limited temperature range between Tsolidus and Tliquidus. Latent heat storage involves a firstorder phase transition (enthalpy variation ∆H). When the transition is essential, the material is called PCM (Phase Change Material). These materials are compounds that can store and release thermal energy through their change of state, most often from solid to liquid, but also from solid to solid. When heated, the material takes calories from the external environment and reaches a temperature, Ttr, transition temperature, then passing from a phase 1 to a phase 2 by heat absorption. If cooled, the reverse transition occurs at Ttr; the material passes from phase 2 to phase 1 and returns all the previously stored energy to the external environment while remaining at the temperature Ttr. The energy involved is the endothermic or exothermic enthalpy variation of the phase change ∆H [15].

Since heat is closely linked to temperature (second principle of thermodynamics), this storage method is more interesting than the first because it allows energy to be stored at a given temperature or a given temperature level. Besides, storage is carried out at a small temperature difference, and it offers the possibility of restoring the stored energy at a constant temperature, at least as long as the solid and liquid phases are in equilibrium. The amounts of stored energy are also higher than when

storing by sensible heat. It should be noted that in practice, not only the latent heat of state change but also the sensible heat of the liquid and the corresponding solid are exploited, which significantly increases the stored energy (Q ) (Eq. (3)) [16].

$$Q = m\_s \int\_{T\_{\text{Trad}}}^{T\_{\text{tr}}} \mathbf{C}\_p(T) . dT \star m . \Delta H \star m . \int\_{T\_{\text{tr}}}^{T\_{\text{rad}}} \mathbf{C}\_p(T) . dT \tag{3}$$

The phase changes required for this type of storage are first-order transitions. However, only solid-solid and solid-liquid transitions are used [17]. Indeed, the liquid-gas transition is technologically unusable since it leads to too high a variation in volume, and the liquid-liquid transition is vigorously too weak to generate any interest. The use of the solid-solid transition is interesting only in the case where the transition is relatively energetic, that is, for plastic crystal-crystal transitions [18]. The absence of any liquid helps the use of the materials.
