# A Review of Pool-Boiling Processes Based on Bubble-Dynamics Parameters
## 6 Boiling-Heat-Transfer Coefficient h and Heat Flux q
### Boiling Heat Transfer Coefficient \(h\)  
It has been widely recognized that it is possible to predict the boiling heat transfer coefficient through modeling theoretical or empirical relational equations from experimental data. These correlations also reduce time and economic cost compared to measuring experimentally. Therefore, it is necessary to explore the boiling heat transfer coefficients (HTC) for various combinations of surfaces and liquids. [PERSON] and [PERSON] [121] analyzed the bubble detachment diameters and liquid properties during pool boiling with pure liquids. An experiential model was obtained as shown in Equation (50). Based on these correlations, the factors affecting the boiling heat transfer coefficient include liquid thermal conductivity, bubble detachment diameter, heat flux, saturation temperature, and so on. \[h=0.1\bigg{(}\frac{k_{l}}{D_{d}}\bigg{)}\bigg{(}\frac{qD_{d}}{k_{l}T_{sat}} \bigg{)}^{0.67}\bigg{(}\frac{\rho_{v}}{\rho_{l}}\bigg{)}^{0.156}\bigg{(}\frac{ h_{l\gamma}D_{d}^{2}}{\alpha_{l}^{2}}\bigg{)}^{0.371}\bigg{(}\frac{\alpha_{l}^{2} \rho_{l}}{\sigma D_{d}}\bigg{)}^{0.35}\bigg{(}\frac{\mu_{l}C_{pl}}{k_{l}} \bigg{)}^{-0.16} \tag{50}\]  
[PERSON] and [PERSON] [122] conducted pool boiling experiments on a wide range of liquids. Based on a large amount of experimental data, semi-empirical correlations of boiling heat transfer coefficients were established. The predicted correlations for hydrocarbons, refrigerants, and other liquids are shown in Equations (51)-(53), respectively. For hydrocarbons  
\[h=0.0546\bigg{(}\frac{k_{l}}{D_{d}}\bigg{)}\bigg{[}\bigg{(}\frac{\rho_{v}}{\rho _{l}}\bigg{)}^{0.5}\bigg{(}\frac{qD_{d}}{k_{l}T_{sat}}\bigg{)}\bigg{]}^{0.67} \bigg{(}\frac{\rho_{l}-\rho_{v}}{\rho_{l}}\bigg{)}^{-4.33}\bigg{(}\frac{h_{l \gamma}D_{d}^{2}}{\alpha_{l}^{2}}\bigg{)}^{0.248} \tag{51}\]  
For refrigerants  
\[h=207\bigg{(}\frac{k_{l}}{D_{d}}\bigg{)}\bigg{(}\frac{qD_{d}}{k_{l}T_{sat}} \bigg{)}^{0.745}\bigg{(}\frac{\rho_{v}}{\rho_{l}}\bigg{)}^{0.581}\bigg{(}\frac {\
u_{l}}{\alpha_{1}}\bigg{)}^{0.53} \tag{52}\]  
For other liquids  
\[h=0.23\bigg{(}\frac{k_{l}}{D_{d}}\bigg{)}\bigg{(}\frac{qD_{d}}{k_{l}T_{sat}} \bigg{)}^{0.674}\bigg{(}\frac{\rho_{v}}{\rho_{l}}\bigg{)}^{0.297}\bigg{(}\frac {h_{l\gamma}D_{d}^{2}}{\alpha_{l}^{2}}\bigg{)}^{0.371}\bigg{(}\frac{\alpha_{l} ^{2}\rho_{l}}{\sigma D_{d}}\bigg{)}^{0.35}\bigg{(}\frac{\rho_{l}-\rho_{v}}{\rho _{l}}\bigg{)}^{-1.73} \tag{53}\]  
[PERSON] et al. [123] performed a boiling experiment on a horizontal smooth tube, with an outer diameter of 19 mm, with various refrigerants. They reduced the heat flux from 8 W/cm\({}^{2}\) isotropic to 1 W/cm\({}^{2}\). The Equation (54) was proposed based on their experimental data, which described the relationship between the boiling heat transfer coefficient and the detachment diameter, the heat flux, the thermal diffusivity, the liquid saturation temperature and the thermophysical properties, where \(c=0.855\bigg{(}\frac{\rho_{v}}{\rho_{l}}\bigg{)}^{0.309}\)\(p_{r}^{-0.437}\), \(p_{r}\) and \(T_{r}\), respectively, are the reduced pressure and the reduced temperature, i.e., the ratios of the measured values to the critical values. \[h=10\bigg{(}\frac{k_{l}}{D_{d}}\bigg{)}\bigg{(}\frac{qD_{d}}{k_{l}T_{sat}} \bigg{)}^{c}p_{r}^{0.1}(1-T_{r})^{-1.4}\bigg{(}\frac{\rho_{l}-\rho_{v}}{\rho_{l }}\bigg{)}^{0.33}\bigg{(}\frac{\
u_{l}}{\alpha_{l}}\bigg{)}^{-0.25} \tag{54}\]  
[PERSON] et al. [124] investigated the experimental data of a nucleate boiling pool with several flammable coolants, refined the Equation (54) and obtained Equation (55), which was found to agree with the experimental results within an error of \(\pm 5.3\%\).