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Energies 2021, 14, 365 5 of 13 charging and discharging of the system. However, there is a lack of understanding of the impact of metallurgical issues, mainly related to non-desired reactions and issues in the ma- terials’ phase-transition behaviour (vapour pressure, undercooling, corrosion, segregation, changes in composition and microstructure) under thermal cycling at high temperatures [21]. 2.3. Equations and Correlations Regarding PCM systems, the heat transfer definition during the melting and the solidification processes is the basic problem that determines the system efficiency [27]. One of the particularities in the sizing is the definition of its latent heat storage capacity (QLHS), which is used to size the PCM mass (mPCM) in the system according to Equation (1): mPCM = QLHS (1) H f usion being the ratio of the QLHS and the latent heat of fusion of the selected PCM (Hf usion). The PCM-TES size is determined by considering the heat demand covered only by latent heat (QLHS) and by assuming that the system operates within the phase-transition range. Then, the volume of the PCM needed is calculated (VPCM) considering the status phase (solid or liquid) with the lowest density. The charging (tCH) and the discharging (tDCH) timing are calculated using Equations (2) and (3), respectively: tCH = QLHS (2) QCH tDCH = QLHS (3) QDCH considering the storage capacity of the system (QLHS) and the heat generated by the heat source during charging (QCH) or the heat demand for air preheating application during discharging (QDCH). The charge period is considered while the temperature of hot flue gases is greater than the PCM phase-change temperature until the maximum storage capacity is achieved. The discharge period is maintained while the expected outlet temperature is reached. However, this calculation is theoretical, hence, to adapt it to the real performance and the system outputs, correction factors are needed to include the influence of the system efficiency and the heat transference of the particular PCM-TES design and configuration used. The core algorithm is based on the outputs obtained from detailed simulation studies performed under a variety of working operation conditions at high temperatures and using different PCM materials for storing the wasted heat in several EII. The obtained results were analysed and used to feed the tool core and find representative correlations between the PCM-TES performance parameters. For more information, a detailed example of the simulation methodology and results can be found in Royo, et al. [28]. In this line, and in order to obtain the system outputs, different factor combinations were applied for the PCM-TES configuration, namely: • Sizing of the PCM-TES (mass and volume) • Number of concentric tubes inside the shell • PCM alternatives as storage material • Waste heat conditions (composition, temperature, and mass flow of flue gases) • Working operation conditions (temperature and mass flow of combustion air) • EII sectors with processes in the range from 500 to 1500 ◦C (ceramic and steel) Consequently, the most relevant parameters (MRP) of operation are identified and analysed under those conditions. To do so, a parametric analysis and a sensitivity analysis were conducted. As a result, thermal conductivity, volume, and storage capacity of the PCMPDF Image | Latent Heat Storage for Waste Heat Recovery in the Energy Industry
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