## 4 Conclusions  
In this research, we developed a one-dimensional, steady-state mathematical model for a novel PCTCS, a system specifically designed for direct CPU cooling in data centers. We conducted simulations by varying key parameters, such as the refrigerant type, the condenser's vertical position, and the cooling water temperature. Our comprehensive investigation delivered a meticulous examination of the internal parameter distribution within the PCTCS, encompassing aspects such as pressure, pressure drop, temperature, thermodynamic quality, void fraction, and heat transfer coefficient. In addition, we proposed temperature and energy efficiency evaluation indices for the system, employed these  
Figure 11: PCTCS parameters in different cooling water temperatures: (**a**) CPUs’ temperature and the maximum temperature difference between cold and heat sources; (**b**) pump power and EERp; (**c**) total pressure drop and subcooling.  
indices to assess the system's performance under various conditions, and based on these assessments, recommended configuration and operation strategies for potential future applications of the system. The following encapsulates the primary conclusions from our study:  
* The constructed model has been validated in harmony with experimental studies, attesting to its precision in simulating the PCTCS;
* The results from our simulations suggest that the PCTCS can efficiently manage CPU power as high as 80 W, attaining an EERp of up to 115, while ensuring that the temperatures of the two CPUs remain at 78.72 \({}^{\circ}\)C and 79.50 \({}^{\circ}\)C--within the CPUs' thermal tolerance limits--when the inlet cooling water temperature is 45 \({}^{\circ}\)C;
* The choice of refrigerant significantly affects the PCTCS's performance. Utilizing R-32 and R-134a as refrigerants results in superior energy efficiency and temperature performance compared to R-113, with R-32 showing the best overall performance. However, the choice of refrigerant necessitates the consideration of factors such as safety, maintenance, and cost in actual applications;
* Increasing the condenser's height decreases the subcooling in the PCTCS's evaporators and condenser. While a higher condenser location improves the PCTCS's energy efficiency, it adversely affects its temperature performance. However, these disparities are marginal, suggesting that the condenser's height exerts a limited effect on the PCTCS's comprehensive performance. In practical applications, this effect can generally be ignored;
* The cooling water temperature significantly influences the PCTCS's performance. A higher cooling water temperature enhances both the temperature performance and energy efficiency of the PCTCS, in addition to facilitating natural cooling and waste heat recovery. Therefore, it is advisable to maximize the cooling water temperature during PCTCS operation, provided the CPU temperature remains within safe limits.  
Conceptualization, L.W. and W.Y.; methodology, L.W.; software, L.W. and H.C.; validation, L.W., H.C., and T.Y.; formal analysis, L.W.; investigation, T.Y.; resources, W.Y.; data curation, H.C.; writing--original draft preparation, L.W.; writing--review and editing, W.Y. and K.R.; visualization, T.Y.; supervision, W.Y. and K.R.; project administration, K.R.; funding acquisition, W.Y. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflict of interest.