## 1 Introduction  
In recent decades, the significant increase in energy needs, together with a growing awareness of the urgency of limiting emissions of greenhouse gases and pollutants, has promoted considerable interest in the development of technologies aimed at energy saving and the adoption of renewable energy sources. To this aim, a key role is played by energy storage capabilities, and, among the different technologies available, thermal energy storage (TES) stands out for its versatility and economic feasibility. In the framework of this technology, particular attention has been paid to systems based on latent heat storage (LHS), where the accumulation and release of heat happen within a limited temperature range, being mainly associated with the phase change in a particular material. The materials adopted in these systems are generally referred to as phase change materials (PCMs) and the main interest in their use is represented by the ability to store a higher energy content taking advantage of the latent heat of the PCMs, instead of using sensible heat, which is limited by the available temperature variation. The widespread use of phase change materials also depends on the development of effective containment methods [1]. The nature of the substances used as phase change materials requires the adoption of containment materials characterized by specific requirements such as [2] mechanical resistance, flexibility, corrosion resistance, structural and thermal stability and easy management. The containment must act as a barrier between the PCM and the surrounding environment, preventing material leakage, ingress or escape of water, oxygen penetration and consequent oxidation; it should be able to adapt to the volume variations during the phase transitions; it should allow the generation of a sufficient surface area for heat exchange; and, of course, it should not introduce significant heat transfer resistance [3]. [PERSON] [4] describes the most relevant encapsulation methods and technologies. Among those methods, macroencapsulation is beneficial from different points of view such as easy processing, good heat transfer, high safety, and possibility of large-scale application [5; 6]. In macroencapsulation, significant quantities of material are enclosed in discrete units (capsules), from a few grams to a kilogram, with a particle size above 1000 \(\upmu\)m [7; 8] of different geometry: spheres, cylindrical tubes, annuluses, rectangular plates, and pouches [9]. Studies have been performed to analyze the influence of the geometry of the encapsulation on the speed of the discharge process [10; 11; 12; 13; 14]: in the discharge phase, cold water enters the heat exchange tank and flows over the encapsulated phase change material, which is cooled and solidified: the duration of solidification represents the time in which latent heat is released into the water. [PERSON] et al. [10] carried out both numerical and experimental investigations of a storage system in which an encapsulated paraffin wax was used as the PCM. The effects of the capsule geometry on the discharge speed were analyzed using a one-dimensional conductive model. Specifically, four different geometries were studied: sphere, cylinder, plate and tube. The diameters of the studied capsules ranged from 2 to 5 mm and given their small size, it was possible to neglect internal natural convection. The results obtained showed that spherical capsules have the best performance among the four types of capsules studied, while tubular capsules with a low degree of vacuum are not ideal for rapid releases of energy stored in the PCM. Heat release performance progressively decreased in the order spheres, cylinders, plates and tubes. [PERSON] and [PERSON] [11] studied the behavior of encapsulated hydrated salts, used as latent energy storage media in a hot water storage tank. The salt was a mixture of hydrated ammonium and magnesium nitrates with a low melting temperature (52.5 \({}^{\circ}\)C).