# Thermal Performance of Cryogenic Micro-Pin Fin Coolers with Two-Phase Liquid Nitrogen Flows
## 4 Results and Discussion  
In this section, the thermofluidic performance of the cryogenic micro-pin fin cooler is discussed. Then, it is compared with that of the cryogenic micro-gap cooler. In the following analysis, the thermofluidic performance of the cryogenic micro-pin fin cooler with LN\({}_{2}\) will be compared with the performance, either measured or predicted using correlations, of the micro-pin fin cooler with FC-72. Figure 5a,b shows the base heat transfer coefficient and pressure drop of the cryogenic micro-pin fin cooler, associated with LN\({}_{2}\) flow, as a function of exit quality. The exit quality values range from 7.5 to 30%. All the results shown in Figure 5a,b were obtained using the test rig shown in Figure 4a,b. The applied chip heater powers were 30, 70 and 96 W.  
hbase denotes a base heat transfer coefficient, defined as q/[A(T\({}_{\mathrm{s}}-T_{\mathrm{inf}}\))]. q is the heat transfer rate, A is the base area, T\({}_{\mathrm{s}}\) is the surface temperature and T\({}_{\mathrm{inf}}\) is the fluid temperature. The result shows the decrease of hbase values ranging from 273 to 201 kW/m\({}^{2}\)-K and the increase of pressure drop values ranging from 227 to 253 kPa as the exit quality increases. This reduction of the hbase value with the increase of the exit quality value might  
Figure 4: (**a**) Micro-pin fin cooler manifold; (**b**) Assembled LN\({}_{2}\) flow loop apparatus. Figure 5: (**a**) Base heat transfer coefficient and (**b**) pressure drop of the cryogenic micro-pin fin cooler as a function of exit quality. be explained by the decrease of the mass flow rate as the power dissipation and vapor fraction increase. Figure 6a,b shows the base heat transfer coefficient and the pressure drop of the cryogenic micro-gap cooler, associated with two mass flux values of LN\({}_{2}\) flow, as a function of exit quality. The results show h\({}_{\text{base}}\) values ranging from 92 to 103 kW/m\({}^{2}\)-K and \(\Delta\)Pt\({}_{\text{tp}}\) values ranging from 55 to 69 kPa associated with a mass flux of 3.2 g/s, and h\({}_{\text{base}}\) values ranging from 85 to 89 kW/m\({}^{2}\)-K and \(\Delta\)Pt\({}_{\text{tp}}\) values ranging from 39 to 48 kPa associated with a mass flux of 2.3 g/s. Both greater h\({}_{\text{base}}\) and \(\Delta\)Pt\({}_{\text{tp}}\) values with a greater mass flux imply conflicting aspects, i.e., affirmative and negative effects, of the increase of the mass flux. It should be noted that the value and range of the exit quality used for Figure 6a,b are considerably smaller than those for Figure 5a,b. FC-72 is one of the widely utilized fluids for the research of two-phase flow heat transfer with mini or micro-channels. In this study, the micro-pin fin array with FC-72 flow was used as a baseline to evaluate the thermofluidic performance of the LN\({}_{2}\) micro-pin fin cooler. Prior to a detailed discussion regarding the thermofluidic performance with two fluids, it is useful to discuss the thermofluidic properties of N\({}_{2}\) and FC-72, as shown in Table 1.  
Table 1 shows that N\({}_{2}\) has about a 252-K lower boiling temperature, nearly twice the latent heat of vaporization, nearly twice the liquid specific heat, 2.4 times larger thermal conductivity, about half the kinematic viscosity and 2.6 times greater thermal diffusivity