## 4 Results and Discussion
This means that, since the coolant state stays on the saturation line, the coolant temperature drops very slightly in the course of phase change even if the coolant enthalpy increases, as mentioned earlier in Section 3.3. The temperature drop of the oxygen coolant is shown in a zoom-in view in Figure 10.  
Figure 10 also shows that, for methane and propane, temperature rises are much greater and the pressure drops are much smaller compared to those of oxygen. These facts are also represented in Table 2. The ultimate reason for these changes is that the oxidizer mass flow rate is greater than the fuel mass flow rate for both cases, which is also presented in Table 2. Even if oxygen has the lowest specific heat out of the three propellants as shown in Figure 10, the pressure drops are much higher than the cooling temperature drops. Figure 10: Pressure versus temperature evolution of the considered coolants as they change phase along the thrust chamber cooling channels. Figure 9: Change of the properties of the oxygen coolant throughout the LOX/LC3H8 engine cooling channels. in Figure 11, heat capacity, which is the mass flow rate multiplied by the specific heat, is the highest in the oxygen flow for both engines. Figure 12 shows the heat capacity of all coolants along the cooling channels throughout the thrust chamber for both engines cooled with both propellants. The oxygen heat capacity has the highest values for both cases along the entire region. A higher heat capacity enables the coolant to store thermal energy with a lower temperature increase at the outlet, as shown in Table 2, which, in turn, results in a lower wall temperature overall. Figure 12 also indicates that, in the phase change region, the heat capacities of all coolants rise sharply, due to the contribution of latent heat to heat capacity. The spiky behavior of the specific heats is exhibited in Figure 11. The figure presents the change of the specific heats in the temperature range from 100 to 600 K at a constant pressure of 35 bar, which is roughly the working pressure in this analysis. The data are obtained from the NIST database at 20 K intervals, which is roughly the data interval used in the analysis. The propellants change their phase at significantly different temperatures, where the respective specific heats spike at corresponding phase change temperatures. Another significant factor determining the engine wall temperatures is how efficiently heat flows from the cooling channel wall to coolant, i.e., the heat transfer coefficient in the cooling channels. Coolant convective heat transfer coefficients corrected for the fin effect for all coolants are presented in Figure 13. As the results suggest, oxygen cooling provides the highest values for both cases. The primary reason for this is the higher oxidizer mass flow rate as well. According to Equation (8), the heat transfer coefficient is proportional to the mass flow rate through the Reynolds number. A higher heat transfer coefficient results in a lower wall temperature overall, as in the case of oxygen cooling. \begin{table}
\begin{tabular}{l c c c} \hline
**Coolant** & \(\mathbf{T_{out}}\) & \(\mathbf{P_{out}}\) & \(\hat{m_{e}}\) \\ \hline LOX (LOX/LCH4) & 340.8 K & 31.2 bar & 4.41 kg/s \\ \hline LCH4 (LOX/LCH4) & 571.3 K & 35.1 bar & 1.10 kg/s \\ \hline LOX (LOX/LC3H8) & 310.1 K & 31.8 bar & 4.54 kg/s \\ \hline LC3H8 (LOX/LC3H8) & 594.4 K & 36.4 bar & 1.16 kg/s \\ \hline \end{tabular}
\end{table} 
Table 2: Resulting coolant parameters. Figure 11: Specific heat values of oxygen, methane, and propane at the constant pressure of 35 bar.