## 2 Basic Analysis of Prediction Models and Model Verification  
### Analysis of Key Thermophysical Properties  
For two-phase liquid immersion cooling technology, its main heat transfer mechanism is nucleate boiling and the condensation of the coolants. For the boiling process, based on bubble dynamics and heat transfer [43; 44], the hot wall of electronics must have a certain superheat (more than the boiling point of the liquid) for bubbles to be generated constantly when the coolants boil. According to the condition of the force and thermal equilibrium between the bubbles and surrounding liquid [45], the required superheat (\(T_{w}-T_{s}\)) can be obtained by Equation (1):  
\[T_{w}-\ T_{s}=\frac{2\sigma T_{s}}{\Delta Hr}\left(\frac{1}{\rho_{V}}-\frac{1 }{\rho_{L}}\right) \tag{1}\]  
where \(T_{w}\) is the wall temperature, K; \(T_{s}\) is the saturated temperature of the coolants, K; \(\sigma\) is the surface tension, N/m; \(\Delta H\) is the latent heat of evaporation, kJ/kg; \(\rho_{V}\) and \(\rho_{L}\) are the vapor and the liquid phase densities, respectively, kg/m\({}^{3}\); and \(r\) is the bubble core radius, m. The latent heat of evaporation \(\Delta H\) can be obtained by the Clausius-Clapeyron equation, as shown in Equation (2) [43]:  
\[\Delta H=\frac{dp_{s}}{dT_{s}}T_{s}\left(\frac{1}{\rho_{V}}-\frac{1}{\rho_{L}}\right) \tag{2}\]  
where \(dp_{s}/dT_{s}\) is the rate of change in saturation pressure with saturation temperature, Pa/K. As the superheat (\(T_{w}-T_{s}\)) increases, the number of bubbles increases. When the bubbles converge and cover the hot wall of the electronics, heat transfer begins to deteriorate. The heat flux corresponding to this heat transfer transition is the critical heat flux (CHF). The CHF of coolants can be estimated by using a modified formula based on the Zuber equation [46], as shown in Equation (3):  
\[\mathrm{CHF}=K\Delta H\rho_{V}{}^{0.5}[\sigma g(\rho_{L}-\rho_{V})]^{0.25} \tag{3}\]  
where \(K\) is the empirical coefficient related to the coolants and \(g\) is the gravity acceleration, m/s\({}^{2}\). Equations (1)-(3) indicate that the saturated vapor pressure, the liquid and vapor densities, and the surface tension are the important properties for the nucleate boiling.  
Except for the boiling process, the condensation process is also essential in two-phase liquid immersion cooling systems. The heat transfer coefficient of condensation can be calculated by the model designed by [PERSON] et al. [47], based on tubular condensers, as shown in Equation (4):  
\[\mathrm{HTC}=0.729\left[\frac{\Delta Hg\lambda_{L}^{3}\rho_{L}}{\eta_{L}D_{o} (T_{s}-T_{o})}\right]^{0.25} \tag{4}\]where HTC is the heat transfer coefficient, W/(m\({}^{2}\cdot\)K); \(\lambda_{L}\) is the liquid thermal conductivity, W/(m\(\cdot\)K); \(\eta_{L}\) is the liquid dynamic viscosity, Pa\(\cdot\)s; \(D_{o}\) is the outer diameter of the condenser pipe, m; and \(T_{o}\) is the outer wall temperature of the condenser pipe, K. Equation (4) indicates that liquid dynamic viscosity and thermal conductivity are important thermophysical properties.  
In summary, the key thermophysical properties of the coolants used in two-phase liquid immersion cooling systems mainly include the saturated vapor pressure, density, surface tension, viscosity, thermal conductivity and latent heat of vaporization.