## 2 Materials and Methods
### PCM Selection for Experimental Tests  
The following criteria must be considered to select the right PCM for a given application:  
* Operating temperature range;
* Availability of the material;
* Handling of the material;
* Environmental compatibility of the material. In our case, we need a PCM with a melting temperature slightly over 0 \({}^{\circ}\)C, a small melting range (which is beneficial for applications requiring precise temperature control),  
Figure 1: Specific stored heat vs. temperature behavior. PCM is compared to sensitive materials, where \(\Delta\)Q PCM is significantly higher than \(\Delta\)Q sensitive in the melting range [21]. and as large a phase transition enthalpy as possible. Mixtures of various PCMs with different melting points could be used to adjust the melting point. However, PCM mixtures usually have lower phase transition enthalpies and a broader melting range [21]. Table 1 displays the material parameters of possibly suitable PCMs from Rubitherm. These PCMs have transition temperatures of 5 \({}^{\circ}\)C and 17 \({}^{\circ}\)C, respectively. Equation (1) can be used to compute the quantity of heat (\(Q\)) \"contained\" in a given RT5 HC PCM sample. In this equation, \"\(m\)\" (kg) stands for the mass of the sample and \"\(Cp\)\" is the heat storage capacity (kJ/kg) of the sample in the relevant temperature range (\(-2\)\({}^{\circ}\)C to 13 \({}^{\circ}\)C). The paraffin-based RT5 HC PCM actually comes with a heat storage capacity of 250 kJ/kg between \(-2\)\({}^{\circ}\)C and 13 \({}^{\circ}\)C. It also has a smaller melting range than the PCM SP15_gel. Furthermore, organic PCMs are easier to handle and test. They are also less expensive than inorganic PCMs and easier to store [23]. \[Q=m\ Cp \tag{1}\]  
To confirm the data provided in Table 1, we heated a 250 mL sample of PCM RT5 HC to 20 \({}^{\circ}\)C before cooling it down to \(-10\)\({}^{\circ}\)C. The cooling curve shows how the sensible heat dissipates over a period of around 30 min until the sample reaches the solidification temperature of 6 \({}^{\circ}\)C. During the liquid-solid phase transition, the latent heat stabilizes the temperature for 200 min. The freezing point is reached after 300 min. Given the unique challenges associated with food processing applications, the phase transition characteristics, heat storage capacity, and thermal stability of biological PCMs including shea butter and beeswax were also evaluated. We heated several 250 mL samples of biological PCMs up to 80 \({}^{\circ}\)C (these PCMs have higher melting points) before cooling them down to \(-10\)\({}^{\circ}\)C. The measurement results are shown in Figure 2.  
Beeswax experiences a phase transition between 63 \({}^{\circ}\)C and 50 \({}^{\circ}\)C. Bringing down this temperature range by at least 40 \({}^{\circ}\)C would require specific additives, which would undermine the inherent benefits of using natural waves, such as their biodegradability, non-toxicity, and sustainability. Therefore, natural beeswax is unsuitable for our intended applications. The cooling curve of shea butter also reveals it to be unsuitable for late frost protection applications, as its cooling curve is simply too irregular. Among the various PCMs tested, paraffin RT5 HC is, therefore, the most suitable for late frost protection applications. This material meets the necessary melting temperature criteria and exhibits an adequate heat storage capacity.