# Thermal Performance of Cryogenic Micro-Pin Fin Coolers with Two-Phase Liquid Nitrogen Flows
## 3 Experimental Apparatus and Procedure  
This section visualizes the physical structure of the copper micro-pin fin array. Then, the discussion of the cryogenic micro-pin fin cooler follows. The test rig of the micro-pin fin cooler and the experimental procedure are explained in the following subsection.  
The physical structure of the copper micro-pin fin array is illustrated in Figure 1. The fin width is 150 \(\upmu\)m, the fin heights are 100, 300 and 500 \(\upmu\)m and the gap between adjacent fins is 150 \(\upmu\)m. The number of fins is 1600, and the base area of the array is 12 mm \(\times\) 12 mm.  
The physical structure of the cryogenic micro-pin fin cooler is visualized by showing its cross-sectional view, as presented in Figure 2. A manifold, upper and lower plates and an embedded micro-pin fin array compose the cooler. The base material is copper. The manifold is 55.1 mm long, 24.9 mm wide and 30 mm high. For micro-pin fin arrays, available references [16] show the fin width ranging from 100 to 350 \(\upmu\)m and the fin pitch from 150 to 431 \(\upmu\)m. To obtain high base heat transfer coefficients at reasonable pressure drops, the dimensions of micro-pin fins were selected by considering the values of the references and fabrication capability. The selected values were a width of 150 \(\upmu\)m, height of 300 \(\upmu\)m and pitch of 300 \(\upmu\)m. The base area of the array was 10 mm \(\times\) 10 mm. The working fluid was LN\({}_{2}\), and a heat source, i.e., a hot device, was placed on the top of the cooler.  
Figure 1: Structure of the copper micro-pin fin array.  
Figure 3 illustrates a test rig to investigate the thermofluidic performance of a cryogenic microcooler with a two-phase LN\({}_{2}\) flow. LN\({}_{2}\) flow is controlled by a pressure regulator, and LN\({}_{2}\) is transported through the microcooler. In the microcooler, the heat is absorbed from the hot device. Consequently, the liquid phase changes to the vapor phase. The heat exchanger is used to evaporate the excess of LN\({}_{2}\), and then LN\({}_{2}\) is heated by a water loop maintained at 25 \({}^{\circ}\)C. The test rig utilizes omega E-type thermocouples measuring temperature and cryogenic pressure transducers measuring pressure at the first and the second four-way junctions. The test rig also uses a mass flow meter to monitor the mass flow rate and 3168S for compression fittings and tubing. The flow loop apparatus is insulated with cryogel Z insulation. The measured data are acquired by LabVIEW with an NI 9214 module for temperature and an NI9205 module for voltage.  
Figure 4a,b provides actual images of the micro-pin fin cooler manifold and the assembled LN\({}_{2}\) flow loop apparatus. The thermocouple location and the placement of the resistive heater of the micro-pin fin cooler manifold are shown in Figure 4a. This study also explores the performance of the micro-gap cooler. Its performance is employed as an analysis baseline. The micro-gap cooler, containing an un-finned micro-gap, is structurally quite similar to the micro-pin fin cooler despite having no micro-pin fin. Both the measurement and operating conditions for the micro-gap cooler and the micro-pin fin cooler are very similar.  
Figure 3: Schematic of a test rig to investigate the performance of cryogenic microcoolers with LN\({}_{2}\) flows.  
Figure 2: Cross-section of the cryogenic micro-pin fin cooler.  
Nominal values of measurement accuracy and uncertainty need to be mentioned to assure measurement reliability. The nominal accuracy values are 0.3% for the cryogenic pressure transducer, 1% for the nitrogen mass flow meter, 0.2% for the power supply and \(\pm\)0.5 \({}^{\circ}\)C for the thermocouple. In this study, measurements were repeated two or three times for each mass flow rate. The uncertainty in exit quality was estimated using the method shown in [1], and the estimated typical uncertainty was 3.2%. The measured data should be reliable considering such reasonable values of accuracy and uncertainty.