## 3 Identification of Boundary Conditions
### Calculation of Cooling Demand  
The cooling demand of a refrigeration system on-board a fishing vessel mainly consists of two contributions: the cooling demand to counterweight the cold room heat losses towards the adjacent rooms and the load for cooling the fish down to a temperature that allows its preservation. The cooling load due to the cold room heat losses can be calculated as:  
\[\dot{Q}_{heat\ losses}=UA(T_{sur}-T_{internal}), \tag{2}\]  
where \(U\) is the overall heat transfer coefficient of the cold room, considered equal to 0.4 W/m\({}^{2}\)K, according to the TRNSYS analysis done in [20]; \(A\) is the heat exchange area (external area of the cold room); \(T_{sur}\) is the temperature of the surroundings of the cold room, considered equal to \(T_{sur}=T_{senwater}\) + 5 \({}^{\circ}\)C in summer and \(T_{sur}=T_{senwater}-5\)\({}^{\circ}\)C in winter [31]; \(T_{internal}\) is the temperature of the cold room, considered equal to \(-\)21 \({}^{\circ}\)C. The cold room in all the fishing vessels examined was below the deck and therefore not directly exposed to the external ambient. However, considering that the surroundings of the cold room are rooms that are not conditioned, the assumption of \(T_{sur}=T_{senwater}\pm 5\)\({}^{\circ}\)C can be considered reasonable. The cooling demand due to the energy needed to freeze the fish in a defined time, \(t_{ref. }\) is due to three contributions: the sensible heat of the fish to bring it from insertion temperature to the freezing temperature, the latent heat due to the freezing of the fish, and the sensible heat from the freezing point to the temperature of the cold room:  
\[\dot{Q}_{fish}=M_{fish}\frac{c_{p1}\big{(}T_{senwater}-T_{freezing}\big{)}+ \lambda_{freezing}+c_{p2}\big{(}T_{freezing}-T_{cold\ room}\big{)}}{t_{ref}}, \tag{3}\]  
where \(c_{p1}\) is equal to 3.7 kJ/(kgK), \(c_{p2}\) is equal to 2.2 kJ/(kgK), the freezing point \(T_{freezing}\) is equal to -2.2 \({}^{\circ}\)C, and the latent heat released during freezing \(\lambda_{freezing}\) is equal to 270 kJ/kg [32], the time needed to freeze the fish, \(t_{ref}\), was fixed as 4 h according to [20]. The results, in terms of overall cooling demand for the different fishing vessels typologies (A to D) and operating temperatures, i.e., the four seas/occans in two seasons, summer and winter, are reported in Figure 3. It can be noted that the cooling demand is specific for each type of vessel rather than the ambient temperature. Indeed, a refrigeration system should be sized for a capacity of about 16 kW in cases A and D, 33 kW in case B, 42 kW in case C. Such values are due to the higher capacity required in the summer but, as previously stated, there is not a relevant difference between the various seasons in the two oceans and the difference in the Mediterranean and North Sea can be considered still within the capacity of regulation of the system. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Mediterranean Sea** & **North Sea** & **Atlantic Ocean** & **Indian Ocean** \\ \hline
**Summer** & 26 \({}^{\circ}\)C & 18 \({}^{\circ}\)C & 28 \({}^{\circ}\)C & 29 \({}^{\circ}\)C \\ \hline
**Winter** & 14 \({}^{\circ}\)C & 5 \({}^{\circ}\)C & 25 \({}^{\circ}\)C & 25 \({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Seawater temperatures selected for calculations. In order to better understand how the various contributions affect the overall cooling demand, the share of power needed for the cold room and for fish refrigeration is shown in Figure 4 for the Mediterranean sea. The contribution of the cold room goes from 1.4 kW for the smaller fishing vessel (case D) to 4.3 kW for case C. During winter, the demand is around 45% lower, going from 1.1 kW to 2.8 kW. The contribution due to the fish caught is the prevalent one, going from 15.4 kW to 37 kW during summer and from 13.6 to 32.6 kW during winter. This indicates that only 10 to 15% of the overall cooling demand is due to the cold room.