# Thermal Performance of Cryogenic Micro-Pin Fin Coolers with Two-Phase Liquid Nitrogen Flows
## 1 Introduction  
Consistent demand for electronic and photonic devices with high heat density or heat flux, such as microelectronics, power amplifiers, laser diode bars and concentrated photovoltaic cells, necessitates aggressive cooling technologies [1]. Recently, two-phase flows in micro-pin fin arrays have been getting more attention [2; 3; 4; 5]. Extensive research has been conducted for single-phase flow in either micro-channels or micro-pin fin arrays [6; 7; 8; 9]. Nevertheless, two-phase heat transfer with micro-pin fin arrays is relatively less investigated compared with the single-phase cases.  
[PERSON] and [PERSON] [10] investigated circular staggered arrays of micro-pin fins with 250 \(\upmu\)m height and 100 \(\upmu\)m diameter associated with water. It was determined that the nominal value of heat transfer coefficients was 60 kW/m\({}^{2}\)-K. [PERSON] and [PERSON] [11] investigated the array of 670 \(\upmu\)m-high and 200 \(\upmu\)m-wide square pin fins with water. They determined that the nominal value of heat transfer coefficients was 70 kW/m\({}^{2}\)-K. [PERSON] and [PERSON] [12] explored in-line arrays of 1000 \(\upmu\)m-high and 1000 \(\upmu\)m-wide square pin fins with R-113. It was determined that the nominal values of heat transfer coefficients and pressure drops were 3.5 kW/m\({}^{2}\)-K and 3 kPa, respectively. [PERSON] et al. [13] investigated staggered arrays of 1000 \(\upmu\)m-high and 350 \(\upmu\)m-wide square pin fins with R-134a. They determined that the nominal value of the base area heat transfer coefficients was 25 kW/m\({}^{2}\)-K. [PERSON] et al. [1] studied in-line and staggered arrays of 305 \(\upmu\)m-high square pin fins. The working fluids were deionized water and HFE-7200. The nominal values of base area heat transfer coefficients were 30 kW/m\({}^{2}\)-K for deionized water and 7 kW/m\({}^{2}\)-K for HFE-7200, respectively. The nominal values of pressure drops were 35 kPa for deionized water and 30 kPa for HFE-7200, respectively.  
Cryogenic cooling could be a more effective solution for the performance and reliability of devices with an extreme heat density such as LD bars. [PERSON] et al. [14] investigatedthe flow boiling mechanism through micro-tubes with liquid nitrogen. The explored tube diameters were 0.531, 0.834, 1.042 and 1.931 mm. It was claimed that nucleate boiling for the low mass quality region and convection evaporation for the high mass quality region govern heat transfer. Their study results found the critical heat flux (CHF) with micro-tubes to be higher compared with classical channels and the CHF increased with the mass flux. [PERSON] et al. [15] explored heat transfer mechanisms of boiling liquid nitrogen flow through a horizontal tube. The internal diameter of the tube was 1.98 mm. They proposed a correlation considering the effects of convective evaporation and nucleate boiling to predict heat transfer coefficients in the channel. To the best of our knowledge, only one piece of research [16] has been reported for cryogenic cooling with micro-pin fin arrays, though research on cryogenic cooling in micro- or mini-tubes, as mentioned, has been consistently conducted.  
This paper extends the preceding literature [16] focusing on thermofluidic characteristics of cryogenic LN\({}_{2}\) flow in micro-coolers. This paper begins by introducing and discussing correlations predicting the heat transfer and pressure drop in micro-pin fin arrays with a two-phase flow. Then, the paper discusses the experimental apparatus and procedure for exploring the thermofluidic performance of the cryogenic micro-pin fin cooler with LN\({}_{2}\) flow. Finally, this paper discusses the thermofluidic performance of the cryogenic micro-pin fin cooler, compares the performance between the cryogenic micro-pin fin cooler and the cryogenic micro-gap cooler and explores the effect of the refrigerant by comparing the performance between the cryogenic micro-pin fin cooler with an LN\({}_{2}\) flow and the micro-pin fin cooler with an FC-72 flow.