# Techno-Economic Analysis of Waste Heat Recovery in Automotive Manufacturing Plants
## 4 Results and Discussion
### Thermodynamic Analysis of the Proposed Carnot Battery
This highlights that an increase in the ambient air temperature reduces the efficiency of ORC, especially when the temperature difference between the waste heat and the air is narrower. Therefore, the P2P is low. Figure 2: The parameter assessment map of the proposed Carnot battery in \(T_{\text{wh,out}}-T_{\text{air}}\) diagram for (**a**) the COP of the heat pump, (**b**) the efficiency of the ORC, (**c**) the net output power of the ORC, and (**d**) the P2P of the Carnot battery. This study also presents a comparison of the thermodynamic assessment of the ORC system, both with and without a recuperator. The analysis focuses on the efficiency differences between the ORC system and their impact on the P2P of the Carnot battery, as shown in Figure 3. The results show that the ORC with a recuperator achieves higher efficiency compared to the system without one. This improvement is due to the recuperator recovering some of the heat of the working fluid after the expansion process, which is used to raise the temperature of the working fluid after the pump. As a result, the ORC requires less heat input, leading to an increase in overall efficiency. A literature study [40] also reported a theoretical analysis of the ORC with a recuperator using various organic working fluids, which improved efficiency. When the waste heat outlet temperature is assumed to be around 60 \({}^{\circ}\)C and the air temperature is 25 \({}^{\circ}\)C, the efficiency of the ORC without a recuperator is lower than with a recuperator, with a difference of 0.0080. Similarly, under the same conditions, the P2P of the Carnot battery for the ORC without a recuperator is also lower compared to the system with a recuperator, with a difference of 0.0230. In this study, a PCM mixture consisting of 53% KNO\({}_{3}\), 40% NaNO\({}_{2}\), and 7% NaNO\({}_{3}\) was selected for its optimal thermal properties in the TES system. The results show that incorporating a recuperator in the ORC significantly influences the TES  
Figure 3: The comparison of the proposed system with and without a recuperator in (**a**) the efficiency of the ORC and (**b**) the P2P of the Carnot battery. Specifically, when a recuperator is included, the \(\zeta\) ratio ranges from 5.86 to 6.16. In contrast, without a recuperator, the \(\zeta\) ratio increases to a range of 6.15 to 6.54. This suggests that using a recuperator can reduce the PCM mass requirement for TES, thereby improving cost effectiveness. The mean squared error (MSE) was used to determine the average of the squared difference between the efficiency of the ORC both with and without a recuperator, as well as the P2P of the Carnot battery and \(\zeta\) ratio for TES. The square root of MSE or RMSE was also used in this assessment. Both MSE and RMSE can be calculated using Equations (14) and (15), where \(\hat{y}\) is the data of the system with a recuperator, \(\hat{y}\) is the data of the system without a recuperator, and \(N\) is the total number of the data points. The results of the MSE and RMSE are really low, which can be seen in Table 5.  
\[MSE=\frac{1}{N}\sum_{i=1}^{N}(\hat{y}_{i}-\hat{y})^{2} \tag{14}\]  
\[RMSE=\sqrt{MSE} \tag{15}\]