## 3 Identification of Boundary Conditions
### Available Waste Heat from Engine  
The waste heat needed to drive the sorption system should come from the main engine. In particular, depending on the working pair for the sorption system and the layout chosen, heat at different temperatures might be needed. Two main heat sources can, indeed, be employed: waste heat from the exhaust gases, which should be recovered through an economizer, or the cooling water for the engine, which can be recovered thanks to a heat exchanger. Whereas the temperature of the exhaust gases is strongly dependent on the part load ratio (PLR) of the main engine, the temperature of the cooling water is usually constant, between 85 \({}^{\circ}\)C and 90 \({}^{\circ}\)C [20]. The available waste heat from the exhaust was  
Figure 4: Share of cooling demand for cold room and fish refrigeration in the Mediterranean Sea, for different fishing vessels from A to D (see Table 1).  
Figure 3: Cooling demand for different fishing vessels, from A to D (see Table 1), and seawater temperatures.  
calculated using the equations reported in [20]. Similarly, the waste heat available from the cooling water was fitted with an equation, on the basis of the data reported in [32]. The fitting equations are:  
\[\dot{m}_{exhust}\bigg{[}\frac{\text{kg}}{h\text{ kW}_{p}}\bigg{]}=6.1943\cdot PLR+0.7051; \tag{4}\]  
\[T_{exhust}[^{\circ}\text{C}]=-443.21\;PLR^{2}+745.94\;PLR+117.27; \tag{5}\]  
\[Q_{cooling\;water}\bigg{[}\frac{\text{kWh}}{\text{ kW}_{p}}\bigg{]}=0.1374\;PLR+0.0281. \tag{6}\]  
The profile for the route during various days was simplified to the one shown in Figure 5, which reports the calculated exhaust gas temperature and flow rate for the exhaust gases. Compared to the case reported in [33], the simplified route eliminates spikes in the \(PLR\), thus maintaining a safety factor. Starting from such a profile, the waste heat available was calculated, under the following assumptions:  
The heat from the exhaust gases is brought at \(T_{target}=200\;^{\circ}\text{C}\);  
The heat from the coolant circuit is at \(90\;^{\circ}\text{C}\);  
The \(PLR\) of the engine, and therefore recoverable waste heat, are constant for each time step of one hour considered in the route profile.  
The waste heat recovered from exhausts was calculated as:  
\[Q_{exhust}=\dot{m}_{exhust}c_{p_{exhust}}\big{(}T_{exhust}-T_{target}\big{)}t _{step}. \tag{7}\]  
Instead, the waste heat from cooling water can be calculated directly from the fitting Equation (6), considering the actual size of the engine on each of the four vessels considered in the analysis.  
It needs to be stated that the profiles reported in Figures 5 and 6 are quite regular, with the exceptions of the first and last days at sea. Consequently, as already done in [20], the profile was adjusted to consider the different days of navigation of the fishing vessels, according to what is reported in Table 1.  
The waste heat available for all the cases is shown in Figure 6. As can be noted, only less than 25% of heat was the cooling water of the main engine, whereas a higher contribution was given by the exhaust gases. Clearly, the higher amount of waste heat in case C and B was due to the higher size of the engine.  
Figure 5: Exhaust temperature and flow rate for a typical route.