## Modeling
### Steady State Heat Transfer Model of Condenser
#### 3.2.1 Heat Transfer Model of the Refrigerant Side of Condenser  
The basic heat transfer formula is used to calculate the heat exchange of each micro-element segment, and the schematic diagram of each micro-element segment is shown in Figure 3.  
For a given micro-element segment \(j\), the heat exchange is calculated according to the following formula:  
\[Q_{rc,j}=h_{rc}A_{r}(IT_{rc,j}-T_{nc,j})=m_{r}(Ih_{r,in}-Oh_{r,out}). \tag{18}\]  
Each calculation unit needs to calculate the heat exchange coefficient and temperature of the refrigerant first. The refrigerant temperature is calculated according to the pressure and enthalpy value at the outlet of the previous micro-element section. When the refrigerant is in a different phase state, the heat exchange coefficient and pressure calculation method are different.  
According to the phase state of the refrigerant in the condenser, it can be divided into a superheated steam area, two-phase area and super-cooled liquid area. After judging the phase state of the refrigerant in the \(j\)th unit, the correlations between different heat transfer coefficients and pressure drop are used for calculation.  
(1) The-single phase area.  
The heat transfer coefficient of a single-phase region is calculated by the correlation formula proposed by [PERSON] and [PERSON] [32]. The corrugation angle and area expansion coefficient are considered synthetically. The formula is as follows:  
\[\begin{split} Nu_{f}=(0.2668-0.006967\beta+7.244\times 10^{-5} \beta^{2})(20.78-50.94\varphi+41.16\varphi^{2}-10.5\varphi^{3})\\ \times\text{Re}^{\prime 0.728+0.0543\sin{(\left[\pi/45 \right]+0.07]}}\text{Pr}^{1/3}(\frac{\mu_{f}}{\mu_{w}})^{0.14}\end{split} \tag{19}\]  
Figure 3: Schematic diagram of calculation micro-element segment.  
The pressure drop of refrigerant in the CDU plate condenser includes friction resistance, angle hole pressure drop and gravity pressure drop. The calculation formula of the single-phase friction pressure drop is as follows:  
\[\Delta P_{r}=\Delta P_{f}+\Delta P_{g} \tag{20}\]  
\[\Delta P_{f}=2f\frac{L}{d_{e}}\rho a^{2}(\frac{\mu_{f}}{\mu_{w}})^{-0.17} \tag{21}\]  
\[f=(2.917-0.1277\beta+2.016\times 10^{-3}\beta^{2})(5.474-19.02\varphi+18.93 \varphi^{2}-5.34\varphi^{3}) \tag{22}\]  
\[\times\text{Re}_{f}{}^{-[0.2+0.577\sin{[(\pi\beta/45)+2.1]}]} \tag{23}\]  
\[\Delta P_{G}=\rho_{j}gL. \tag{24}\]  
The calculation formula of refrigerant mass in the single phase area is as follows:  
\[m_{j}=\rho_{j}A_{c}L_{c} \tag{25}\]  
(2) The two phase area.  
[PERSON] [33] considered the influence of refrigerant heat flux, steam dryness and average heat flow, and proposed various plate heat exchangers suitable for R134a as refrigerant. Compared with the various condensation heat transfer coefficient formulas proposed earlier, they have a wider application range and are suitable for the establishment of this model.  
\[Nu_{f}=4.118\text{Re}_{eq}{}^{0.4}\text{Pr}_{l}{}^{1/3} \tag{26}\]  
\[\text{Re}_{eq}=\frac{G_{eq}d_{e}}{\mu_{l}} \tag{27}\]  
\[G_{eq}=G\bigg{[}1-x+x(\frac{\rho_{l}}{\rho_{g}})^{0.5}\bigg{]}. \tag{28}\]  
The calculation formula of friction pressure drop in the two-phase region of condensation heat exchange is as follows:  
\[\Delta P_{r}=\Delta P_{f}+\Delta P_{g} \tag{29}\]  
\[\Delta P_{f}=2f\frac{L}{d_{e}}\rho a^{2}(\frac{\mu_{f}}{\mu_{w}})^{-0.17} \tag{30}\]  
\[\Delta P_{g}=\rho_{j}gL \tag{31}\]  
\[f=94.75\text{Re}_{eq}{}^{-0.046}\text{Re}_{l}{}^{-0.4}B\rho^{0.5}(\frac{p}{p _{c}})^{0.8} \tag{32}\]  
\[\text{Re}_{eq}=\frac{G_{eq}d_{e}}{\mu_{l}} \tag{33}\]  
\[Bo=\frac{qA_{r}}{m_{r}h_{fg}}. \tag{34}\]  
The calculation formula of refrigerant mass in the two-phase area is as follows:  
\[m_{j}=\rho_{tp,j}A_{c}L_{c} \tag{35}\]  
\[\rho_{tp,j}=\rho_{g}\alpha+\rho_{l}(1-\alpha) \tag{36}\]  
\[\alpha=(1+(\frac{1-x}{x})(\frac{\rho_{g}}{\rho_{l}})^{0.89}(\frac{\mu_{g}}{ \mu_{l}})^{0.18})^{-1}. \tag{37}\]