Thermal performance of cascaded thermal storage with phase-change materials (PCMs). Part I: Steady cases

•Entropy generation rate and heat transfer rate are combined for optimization.•Optimal solution with entropy theory for steady cascaded thermal storage is obtained.•Optimization result of entropy theory is compared with that of entransy theory.•Temperature with entropy exhibits geometric distribution, while that with entransy is linear.•For steady case, entransy and entropy are suitable for heat-transfer and heat-work conversion, respectively. Cascaded latent thermal storage is an efficient technique for balancing the gap between demand and supply in renewable energy utilization. In this work, the steady cascaded thermal storage system with multiple phase-change materials (PCMs) of different phase-change temperatures is theoretically optimized from the viewpoint of thermodynamics. Analytical solutions for optimal temperatures of heat transfer fluid (HTF) and PCMs are obtained based on entropy and entransy concepts. The corresponding qualifications for optimization solutions are also discussed. With an increase in stage number or that in NTU, both thermal and exergy efficiencies increase. Compared with single-stage thermal storage, the cascaded thermal storage with multiple PCMs can not only improve the thermal performance, but also extend the application scope of thermal energy with multi-grade thermal energies provided. The temperature distribution for HTF and PCMs with entransy optimization is linear, while that with entropy optimization is geometric progression. The application situations of entropy and entransy in thermal energy utilization are identified by comparing optimal result based on entropy with that based on entransy. This optimization can not only be used to establish the steady cascaded thermal storage system, but also guide the filtration of PCMs used in such systems.