# Thermal Performance of Cryogenic Micro-Pin Fin Coolers with Two-Phase Liquid Nitrogen Flows
## 4 Results and Discussion
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Property** & **Unit** & **N\({}_{2}\)** & **FC-72** \\ \hline Molecular weight & & 28 & 338 \\ Boiling temperature & K & 77.3 & 329.1 \\  & \({}^{\circ}\)C & \(-\)195.9 & 56 \\ Liquid enthalpy & kJ/kg & \(-\)122.1 & 59.8 \\ Latent heat of vaporization & kJ/kg & 198.8 & 84.7 \\ Vapor enthalpy & kJ/kg & 76.7 & 144.5 \\ Liquid density & kg/m\({}^{3}\) & 806 & 1680 \\ Vapor density & kg/m\({}^{3}\) & 4.6 & 13 \\ Kinematic viscosity of liquid & 10\({}^{6}\) m\({}^{2}\)/s & 0.19 & 0.38 \\ Liquid specific heat & kJ/kg-K & 2.041 & 1.1 \\ Liquid thermal conductivity & W/m-K & 0.135 & 0.057 \\ Thermal diffusivity & 10\({}^{6}\) m\({}^{2}\)/s & 0.082 & 0.031 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Descriptions of N\({}_{2}\) and FC-72’s properties [25; 26; 27; 28]. Figure 6: (**a**) Base heat transfer coefficient and (**b**) pressure drop of the cryogenic micro-gap cooler as a function of exit quality. compared with FC-72. The comparison of crucial thermofluidic properties implies that N\({}_{2}\) might be better than FC-72 for heat transfer enhancement in both sensible and latent heat transfer modes. Figures 7 and 8 present the base heat transfer coefficient, hbase, and the pressure drop, \(\Delta\)Pt\({}_{\text{tp}}\), of the cryogenic micro-pin fin and micro gap coolers. Both hbase and \(\Delta\)Pt\({}_{\text{tp}}\) values are shown with various exit quality values for various mass flux values of LN\({}_{2}\) and FC-72. In Figures 7 and 8, fin, gap, value of g/s and value of \(\mu\)m denote a micro-pin fin cooler, micro-gap cooler, mass flux and fin height,  
array can explain the considerably better heat transfer performance with the micro-pin fin cooler. The trend of the hbase of the micro-pin fin cooler can be seen to differ from that of the micro-gap cooler. The difference of the two-phase heat transfer behavior with the exit quality between the micro-pin fin cooler and the micro-gap cooler might be explained by the nearly three times greater exit quality associated with the micro-pin fin cooler, in terms of average quality value, than that with the micro-gap cooler. The result shown in Figure 7 visualizes the feasibility of the cryogenic micro-pin fin cooler when thermally managing very high heat density devices such as high power laser diode (LD) bars [16], of which the heat density can reach 2000 kW/m\({}^{2}\). For example, the cryogenic micro-pin fin cooler may control such a high power laser diode bar at an excess temperature, i.e., the temperature difference between the LD bar and the LN2 flow, of about 10 K.  
Figure 8 shows that \(\Delta\)Ptp values of the micro-pin fin cooler increase as the exit quality for both LN2 and FC-72 flows increases. The pressure drop is fundamentally affected by various physical parameters including local quality, fluid velocity, characteristic length, viscosity and density. Although explaining the pressure drop behavior for either LN2 or FC-72 flow is quite challenging due to the complicated mechanism of interrelated effects of aforementioned parameters, increasing momentum dissipation induced by the increase of the vapor fraction may explain such an increase of \(\Delta\)Ptp values. Figure 8 shows that the values of \(\Delta\)Ptp with LN2 are greater than those with FC-72. It can also be seen that the values of \(\Delta\)Ptp with the micro-pin fin cooler are greater than those with the micro gap cooler. The effect of the micro-pin fin array on the pressure drop along the microcooler should be understood for better design of the micro-pin fin cooler. Hence, physical aspects of the considerably greater values of \(\Delta\)Ptp with the micro-pin fin cooler compared with the micro gap cooler should be rigorously investigated, employing sophisticated measurement tools, in a future study. In Figures 7 and 8, the correlation prediction can be seen to roughly agree with the measurement.