## 6 Comparison with the State-of- the-Art  
The combination of heat pumps with LTES is gaining interest, due to the possibility of better managing the operation of the heat pump, especially when driven by renewables. A vast review of the possible couplings between heat pumps and LTES is discussed in [31]. However, in the majority of research studies, the integration of the PCM and the heat pump cycle is not direct, but is rather achieved through the use of an external tank. In [32], the use of ice as a PCM for direct embedding in the evaporator of a heat pump is investigated numerically, but no details on the possible layout of the storage are given and the results are reported in terms of exergy analysis and power consumption for the heat pump; showing that a reduction in the electricity consumption of the heat pump cycle is not a significant effect.  
Figure 8: Discharge power for different HTF flow rates for four layers and an HTF inlet at 12 \({}^{\circ}\)C.  
Figure 9: Average PCM temperature for different numbers of stacked PCM layers during discharge. HTF flow rate 0.5 kg/s, HTF inlet 12 \({}^{\circ}\)C.  
pump is possible. In [33], the experimental evaluation of a PCM (RT42, with melting temperature of 42 \({}^{\circ}\)C) for integration in the condenser of a heat pump is discussed. In this case, the optimization of the melting temperature of the paraffin is achieved by switching from air-source to solar-assisted operation. The solar-assisted operation guaranteed lower melting/solidification times, due to the higher temperature difference that was possible. In [34], a three-sleeve HEX design for integration in the heat pump cycle for heating and cooling purposes is discussed. Compared to the design presented in the current paper, the passages for the PCM, refrigerant, and water are concentric annuli. Interestingly, the profiles for the temperature and pressure in the storage are similar to those described for the present design. In particular, similarities include some fluctuations in the evaporator power of the heat pump, due to fluctuations in the temperature of the refrigerant, as well as the general initial rapid decrease in PCM temperature (during charging) or increase (during discharge), followed by a change in the slope of temperature once the melting range is reached, and a slow variation of temperature afterwards. However, compared to the three-sleeve design, the configuration presented here has some advantages, such as the higher storage density, due to the higher packing factor of the HEX, and the easier scalability to larger scales, due to the array-like configuration. A peculiarity of the current configuration, which also simplifies the design and analysis of the HEX, is the thermal conduction dominating the heat transfer mechanism, since, due to the arrangement of channels and their dimensions, convection does not occur. Despite having found that convection can boost the melting process of PCMs [18; 35], it was, however, found that, at HEX level, it is still more convenient to use heat transfer enhancement techniques, e.g., through fins or other methods, to increase the heat exchange area rather than exploiting natural convection in the paraffin [36]. This is due to the low thermal conductivity of the paraffin, which causes a slow onset of natural convection during melting, thus increasing the time needed for charging, which is not desirable for applications in heat pumps.  
Such a literature overview further reinforces the advancements presented in the current configuration, while showing that the evaluation of systems is still mostly based on experimental measurements; whereas, a more organic design requires suitable tools, such as the one presented here.