# Techno-Economic Analysis of Waste Heat Recovery in Automotive Manufacturing Plants
## 3 Methodology  
### System Description  
Figure 1 shows the proposed Carnot battery system that is installed to recover the waste heat from RTO. In this figure, the process operation (indicated by the number) is also illustrated. This system consists of four key technologies, including heat pump, ORC, TES, and PVs. In this system, the RTO treats volatile organic compounds present in the exhaust air from the painting processes, with the exhaust air reaching temperatures around 150 \({}^{\circ}\)C. This waste heat is harnessed by the heat pump through the evaporator (EVAHHP), which evaporates the working fluid of the heat pump to the vapour state. The working fluid is then compressed by a compressor (CPR), increasing the pressure and the temperature. The compressor is driven by a motor (MTRHP) powered by electricity from PVs. Also, in a condenser of the heat pump (CDSHP), heat is transferred from the working fluid to a secondary fluid. As a result, the secondary fluid is heated up to around 145 \({}^{\circ}\)C, while the working fluid of the heat pump is condensed. The secondary fluid, now carrying the stored heat, can then be used to charge the TES system, effectively storing thermal energy for later use. The working fluid of the heat pump is then expanded in the throttle valve (TRV) and recirculated to the evaporator in a closed-loop system. The heat can then be stored in TES and used to generate power when needed. In this case, the thermal energy stored in the TES system can be utilised to heat and evaporate the working fluid of the ORC in the evaporator (EVA\({}_{\text{ORC}}\)). Once evaporated, the working fluid expands in an expander (denoted as EXP), converting thermal energy into mechanical energy stored in the evaporator (EVA\({}_{\text{ORC}}\)). The heat is stored in TES and used to generate power when needed. In this case, the thermal energy stored in the TES system can be utilised to heat and evaporate the working fluid of the ORC in the evaporator (EVA\({}_  
work and then generating electricity by a generator (GTRORC). After the expansion process, the fluid is cooled and condensed in the condenser (CDSORC). Following the condensation process, the pressure of the working fluid is increased by a pump (PMP), allowing it to be recirculated through the system in a continuous closed-loop process of the ORC system. It is important to note that because of the time shift between the application of heat pump and ORC units, some parts (like the motor-generator and the compressor-expander) can be one bi-functional unit [18], but usually, this solution decreases the efficiency; therefore, in this work, the two units will be completely separated. The model proposed in this study was developed using MATLAB R2024a, and the simulation utilised thermal property data obtained from REFPROP 10.0 [19]. The mathematical description of the proposed system is listed in Table 2, where \(\dot{m}\), \(\dot{Q}\), \(Q\), \(h\), \(P\), \(T\), \(\rho\), \(c\), \(V\), and \(\eta\) refer to mass flow rate, heat transfer rate, heat transfer, specific enthalpy, power, temperature, density, specific heat capacity, volume, and efficiency, respectively. In addition, the subscripts of sf, is, wh, and env refer to secondary fluid, isentropic, waste heat (exhaust air), and environment, respectively. In addition, a detailed calculation related to the heat exchanger can be seen in Equations (1) and (2). \[A=\frac{\dot{Q}}{U\Delta T_{\text{LMTD}}} \tag{1}\]  
\[\Delta T_{\text{LMTD}}=\frac{\Delta T_{\text{max}}-\Delta T_{\text{min}}}{ \ln\frac{\Delta T_{\text{max}}}{\Delta T_{\text{min}}}} \tag{2}\]  
The heat transfer surface area (\(A\)) of heat exchangers, such as the evaporator, recuperator, and condenser, can be calculated using Equation (1). In this equation, \(U\) represents the overall heat transfer coefficient, and \(\Delta T_{\text{LMTD}}\) refers to the logarithmic mean temperature difference.