## 1 Introduction  
A properly designed thermal energy storage system can improve the exploitation and profitability of many renewable and conventional energy sources. For instance, in solar thermal systems, thermal storage can allow to overcome the mismatch between supply and demand. In conventional natural gas-fueled cogeneration systems, thermal storage can be used to produce electricity when it is more economically convenient, namely for self-consumption or when the selling price is high, without wasting thermal energy, which is instead accumulated for a later use. As concerns the storage materials, water is the most used, mainly because water has a high specific heat, is not toxic, and has practically no cost. However, in the last years phase change materials (PCMs) used as thermal energy storage materials have attracted great attention, essentially because, in general, they are characterized by high thermal energy storage densities, and permit to store thermal energy in a narrow temperature range. Many works have addressed the use of PCMs for storing thermal energy from the solar source for various applications, ranging from solar water heating to solar cooling by absorption or adsorption refrigeration systems [1; 2; 3; 4; 5; 6]. [PERSON] et al. [7] analyzed the use of a paraffin-based PCM as thermal energy storage material in a solar air-based thermal system. [PERSON] at al. [8] investigated the effects of the presence of a paraffin wax in the bottom plate of a solar still for water desalination. [PERSON] et al. [9] performed numerical simulations to characterize the melting and solidification processes of a PCM integrated in a solar collector. [PERSON] et al. [10] developed a control strategy and implemented different models to simulate different operation modes of a solar heating system, including a PCM-based storage tank, over the entire heating season. Moreover, many applications of PCMs have considered cold thermal energy storage [11]. [PERSON] et al. [12] simulated a phase change composite consisting of a paraffin wax and expanded graphite for cold thermal energy storage in air conditioning applications. They also performed an experimental validation of numerical results. [PERSON] et al. [13] modeled and simulated a novel cold energy storage system based on PCMs. [PERSON] and [PERSON] [14] modeled and simulated a cold thermal energy storage system consisting of a packed bed with multiple PCMs. In this work, an experimental validation of numerical results is also reported. Various models have been developed for the numerical simulation of PCM-based thermal energy storage systems, most of which have been reported in reviews [15; 16; 17]. [PERSON] et al. [18] successfully applied the effective heat capacity (EHC) method for simulating 2D heat transfer with phase change. [PERSON] [19] developed a model to simulate a shell-and-tube thermal energy storage unit with the PCM on the shell side. [PERSON] et al. [20] employed the finite element method to simulate the convection-dominated melting of a PCM in a cylindrical-horizontal annulus. [PERSON] et al. [21] implemented both the effective heat capacity method and the enthalpy method to simulate the melting and solidification processes of a PCM. They also compared the numerical results, which were obtained using the FEMLAB solver, with experimental ones. [PERSON] et al. [22] implemented the enthalpy method to perform 3D simulations of a PCM in multi-tube heat exchanger units. [PERSON] et al. [23] developed and validated a computational fluid-dynamic (CFD) model for the numerical simulation of a PCM slurry in a horizontal tank. [PERSON] et al. [24] developed a numerical tool to simulate a lab-scale PCM-based shell-and-tube thermal energy storage system by employing the EHC method. [PERSON] et al. [25] proposed and validated a simplified modelling approach for the numerical simulation of PCM-based fin-and-tube heat exchangers. [PERSON] et al. [26] proposed a numerical model to simulate the heat transfer inside an open-cell metallic foam filled PCM.