## 2 Materials and Methods
### Distribution of Main Engine Waste Heat  
The unused energy produced by a ship's main engine mainly includes heat in the flue gas, heat in the cooling water of the cylinder liner, heat in the lubricating oil and other forms of waste heat. The heat balance equation of the main engine is shown in Equation (1). \[Q_{f}=Q_{e}+Q_{s}+Q_{w}+Q_{o}+Q_{r} \tag{1}\]  
where: \(Q_{f}\) is the entire amount of heat produced by fuel combustion; \(Q_{e}\) is the that is converted into the actual output work of the host; \(Q_{s}\) is the heat taken away by the smoke exhaust from the host; \(Q_{w}\) is the heat taken away by the cooling water of the host cylinder \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Main Engine** & **Exhaust Gas Flow** & **Exhaust Gas** & & **Fuel** & **High-** \\
**Load (\%SMCR)** & **(kg/s)** & **Temperature (\({}^{\circ}\)C)** & **Power (kW)** & **Consumption** & **Temperature** \\  & & & & **Rate (g/kWh)** & **Steam Flow (kg/h)** \\ \hline
60 & 33.8 & 219 & 13,104 & 162.5 & 2050 \\
65 & 36.1 & 216 & 14,196 & 161.8 & 2020 \\
70 & 38.2 & 214 & 15,288 & 161.5 & 2050 \\
75 & 40.3 & 214 & 16,380 & 161.6 & 2120 \\
80 & 42.2 & 215 & 17,472 & 161.9 & 2250 \\
85 & 44.1 & 218 & 18,564 & 162.5 & 2450 \\
90 & 45.9 & 222 & 19,656 & 163.3 & 2730 \\
95 & 47.6 & 227 & 20,748 & 164.3 & 3090 \\
100 & 49.3 & 234 & 21,840 & 165.5 & 3520 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main engine performance parameters under different loads. liner; \(Q_{o}\) is lubricating oil cooling waste heat; are other kinds of waste heat, including pressurized air cooling waste heat, radiation heat dissipation, etc. The unused energy produced by a ship's main engine is \(Q_{f}\), as shown in Equation (2). \[Q_{f}=M_{f}\times H_{u} \tag{2}\]  
where: \(M_{f}\) is the consumption of host fuel, kg/h; \(H_{u}\) is the fuel's low calorific value, kJ/kg. \(M_{f}\) can be calculated by the following Formula (3). \[M_{f}=\frac{SMCR\times SFOC_{ME}}{10^{3}} \tag{3}\]  
where: \(SFOC_{ME}\) is the fuel consumption rate of the ship's main engine, g/kWh. The exhaust heat of the ship's main engine is \(Q_{s}\), as shown in Equation (4). \[Q_{s}=m_{s}\times C_{p,s}\times(T_{s}-T_{iso}) \tag{4}\]  
where: \(m_{s}\) is the mass flow rate of host flue gas, kg/s; \(C_{p,s}\) is The specific heat capacity under constant pressure, kJ/(kg-k); \(T_{s}\) is the flue gas temperature emitted from the host, \({}^{\circ}\)C; is the operating temperature of the main engine, \({}^{\circ}\)C.  
\(Q_{w}\) and \(Q_{o}\) are the heat taken away by cylin \(T_{iso}\) der liner cooling water and lubricating oil cooling respectively, which can be obtained by querying the CEAS database; \(Q_{e}\) is the heat converted into the output work of the main engine, which is the effective output power of the main engine of the ship, and the effective output power of the main engine under different loads can be obtained by querying the CEAS database; \(Q_{s}\) can be calculated by the above formula; thus, the quantity of various forms of heat of the main engine under different loads can be calculated and obtained, as shown in Table 2. The amount of various forms of heat produced by the main engine grows as the load on the main engine increases. The main engine's exhaust heat contributes to roughly half of the total waste heat. The temperature of the main engine's exhaust heat is high grade and easy to recycle. Typically, the ship owner has an exhaust gas boiler installed to recover and reuse the waste heat from the exhaust gas to make high-temperature steam (150-180 \({}^{\circ}\)C) for ship usage. However, the amount of water steam required for the ship to function is restricted. When the main engine is under heavy load, a considerable amount of exhaust gas is bypassed, therefore really realized recovery accounts for less than 20% of total exhaust gas heat loss. Many exhaust gas residual heat still can not be effectively recovered.