## 4 Modeling of the System Components
### Evaporator and Condenser
#### 4.3.2 Thermal Modeling  
The moving boundary method was used in this work for spatial modeling of the PHEs. In the case of a general flow in a HE, both streams may change the phase, and consequently five zones can exist as shown in Figure 18.  
Figure 17: The calculated and measured pressure drop of the evaporator (**left**) and pressure resolution in different heat transfer zones in the evaporator (**right**). Figure 18: The possible distribution of heat transfer zones in a heat exchanger when both streams change the phase. Regarding the PHEs in this work, only the refrigerant stream changes the phase, and the hot stream in the evaporator and the cold stream in the condenser are in the single-phase liquid, so three zones are presented. Hence, the area of the plate is divided into three zones, which were determined using the liquid and gas saturation enthalpies of the refrigerant. The calculated thermal load of the refrigerant stream is assumed to be fully transferred to the other stream in both the evaporator and the condenser, thus establishing zone boundaries. The next step was calculating the convective heat transfer coefficients (CHTCs) in the hot and cold streams using the relevant correlations for each heat transfer zone to obtain the overall CHTC of the zone. The pressure drop in each zone was preliminarily calculated before running the thermal solver using the method and the correlation elaborated in the previous subsection. Several geometry-independent, single-phase, boiling, and condensation CHTC correlations were tested to find the best combination that could predict the experimental data of the evaporator and the condenser of the ORC unit. The four single-phase correlations are the Ditteus-Boettler correlation [24], its modified correlation suggested by [PERSON] and [PERSON] [25] considering the variations of the viscosity of the fluid due to the difference between the wall temperature and the bulk temperature, the Bogaert-Bolcs [21] correlation, and the correlation suggested by [PERSON] and [PERSON] [26]. Except for the Bogaert-Bolcs model, which was suggested for mineral oil in a PHE and is the accepted correlation among Swedish manufacturers [27], all correlations were obtained for turbulent flows in tubes. These correlations are reported in Appendix C.  
To fit the models with the experimental data of the evaporator and the condenser, some effective coefficients were tuned by minimization of the objective function using the genetic algorithm optimization method. The objective function is the calculated area of the PHE needed to obtain the same thermal performance as the experimental data. More precisely, the sum of the calculated areas of the three zones must be equal to the total heat transfer area of the plate. Therefore, the objective function is defined as the following:  
\[f=\sum_{i=1}^{n}\biggl{(}\frac{A_{cal,i}-A}{A}\biggr{)}^{2} \tag{34}\]  
where \(n\) is the number of experimental points (84 points), \(A\) is the heat transfer area of the plate taken from the manufacturer datasheet, and \(A_{cal,i}\) is the calculated area of the plate:  
\[A_{cal}=A_{L}+A_{tp}+A_{V} \tag{35}\]  
The results of the optimization are presented in the following for the evaporator and the condenser of the ORC unit using R134a as the working fluid, diathermic oil (H22) as the hot fluid, and water as the cooling medium. * Condenser: The four considered single-phase CHTC correlations in this work were combined with the two condensation CHTC correlations: the Claesson [28] and Kuo [29] models. The best results are obtained using [PERSON] and Crawford single-phase and Claesson condensation correlations. One coefficient was found for water stream correlation, two for liquid and gas single-phase R134a, and one for the condensation correlation (four in total).