## Appendix C Geometry-Independent Correlations of CHTCs  
Single-phase:  
* Ditteus-Boettler (originally introduced for single-phase turbulent flows in tubes) \[Nu_{D}=a\cdot Re_{D}{}^{b}\cdot Pr^{c}\] (119)
* Sieder-Tate (originally introduced for single-phase turbulent flows in tubes) \[Nu_{D}=a\cdot Re_{D}{}^{b}\cdot Pr^{c}\bigg{(}\frac{\mu}{\mu_{w}}\bigg{)}^{0.14}\] (120)
* Bogaert-Bolcs (originally introduced for mineral oil in PHEs) \[Nu_{D}=a\cdot Re_{D}{}^{b}\cdot Pr^{(\frac{1}{5}e^{(\frac{6.4}{77.39})})}\bigg{(} \frac{\mu}{\mu_{w}}\bigg{)}^{\frac{0.3}{(Re+6)^{0.125}}}\] (121)
* Kays and Crawford (originally introduced for single-phase turbulent flows in tubes) \[Nu_{D}=\frac{a\cdot Re_{D}{}^{0.8}\cdot Pr}{0.88+2.03\Big{(}Pr^{3}-0.78\Big{)} Re_{D}{}^{-0.1}}\] (122) Condensation:
* [PERSON] et al. (originally introduced for R410 in PHEs) \[h_{L}=a\bigg{(}\frac{\lambda_{L}}{D_{h}}\bigg{)}Re_{L}{}^{0.78}\cdot Pr_{L}{}^ {\frac{1}{3}}\bigg{(}\frac{\mu}{\mu_{w}}\bigg{)}^{0.14}\] (123) \[h_{tp}=\bigg{(}0.25 Co^{-0.45}\cdot Fr_{L}{}^{0.25}+75 Bo^{0.75}\bigg{)}\] (124) where \(Co\), \(Fr_{L}\), and \(Bo\) are convection number, Froud number, and boiling number, respectively represented in the following equations: \[Co=\bigg{(}\frac{\rho_{g}}{\rho_{L}}\bigg{)}\bigg{(}\frac{1-x_{m}}{x_{m}} \bigg{)}^{0.8}\] (125) \[Fr_{L}=\frac{G^{2}}{\rho_{L}{}^{2}\cdot g\cdot D_{h}}\] (126) \[Bo=\frac{q}{G\cdot if_{g}}\] (127)
* [PERSON] et al. (originally introduced for R134a in PHEs) \[h_{Nu}=a\cdot\lambda_{L}\bigg{(}\frac{Re\cdot\mu_{L}}{\rho_{L}\big{(}\rho_{ L}-\rho_{g}\big{)}g}\bigg{)}^{\frac{-1}{3}}\] (128) \[h_{tp}=\sqrt{h_{Nu}{}^{2}+h_{Bogaert}{}^{2}}\] (129) Boiling CHTC correlations:
* [PERSON] et al. (originally introduced for R410 in PHEs) \[h_{L}=0.023 Re_{L}{}^{0.8}\cdot Pr^{0.4}\bigg{(}\frac{\lambda_{L}}{D_{h}}\bigg{)}\] (130) \[h_{pool}=55P_{r}{}^{0.12}(-\ln P_{r})^{-0.55}M^{-0.5}\cdot q^{0.67}\] (131)\[E=1+24,000 Bo^{1.16}+1.37\bigg{(}\frac{1}{X_{tt}}\bigg{)}^{0.86} \tag{25}\] \[S=\Big{(}1+1.15\times 10^{-6}E^{2}\cdot Re_{L}{}^{1.17}\Big{)}^{-1}\] (26) \[h_{tp}=a\cdot E\cdot h_{L}+b\cdot S\cdot h_{pool}\] (27) where \(M\), \(q\), \(X_{tt}\), \(P_{r}\) are molecular weight, heat flux, Martinelli parameter, and reduced pressure, respectively defined as the following: \[X_{tt}=\bigg{(}\frac{1-x_{m}}{x_{m}}\bigg{)}^{0.9}\bigg{(}\frac{\rho_{g}}{\rho _{L}}\bigg{)}^{0.5}\bigg{(}\frac{\mu_{L}}{\mu_{g}}\bigg{)}^{0.1}\] (28) \[P_{r}=\frac{P}{P_{critical}} \tag{29}\]
* [PERSON] et al. (originally introduced for R245 fa and R1233 ZD in PHEs) \[h_{tp}=a\cdot We^{-0.0322}\bigg{(}\frac{\rho_{L}}{\rho_{g}}\bigg{)}^{-0.338} Re_{L}{}^{0.451}\cdot Bd^{-0.469}\] (30) where \(We\), \(Bo\), and \(Bd\) are Weber, Boiling (Equation (A20)), and Bond numbers, respectively defined as follows: \[We=\frac{G^{2}\cdot D_{h}}{\rho_{m}\cdot\sigma}\] (31) \[Bd=\frac{\big{(}\rho_{L}-\rho_{g}\big{)}g\cdot d_{h}{}^{2}}{\sigma}\] (32) where \(G\) and \(\sigma\) are the mass flux and the surface tension, respectively.
* [PERSON] et al. (originally introduced for R134a in PHEs) \[Nu_{tp}=a\cdot Re_{L}{}^{0.5}\cdot Pr_{L}{}^{1/3}\cdot Bo_{eq}{}^{0.3}\frac{ G_{eq}}{G}\] (33) \[G_{eq}=G\bigg{[}(1-x_{m})+x_{m}\bigg{(}\frac{\rho_{L}}{\rho_{g}}\bigg{)}^{0.5} \bigg{]}\] (34) \[Bo_{eq}=\frac{q}{G_{eq}{}^{i}i_{fg}}\] (35)  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**The Empirical Coefficient in** & **Evaporator** & **Condenser** \\
**Equation (32)** & **Evaporator** & **Condenser** \\ \hline a & 9772.82 & 14,660.75 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The calculated empirical coefficients of the hydraulic model of the PHEs of the ORC system.