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Article

Thermal Performance of Cryogenic Micro-Pin Fin Coolers with Two-Phase Liquid Nitrogen Flows

1
Department of Mechanical Design Engineering, Pukyong National University, Busan 48513, Korea
2
Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA
*
Author to whom correspondence should be addressed.
Submission received: 20 October 2021 / Revised: 11 November 2021 / Accepted: 18 November 2021 / Published: 22 November 2021

Abstract

:
This study experimentally explores the thermofluidic performance of a cryogenic micro-pin fin cooler with two-phase liquid nitrogen flows. The liquid nitrogen cooling system is introduced to investigate the performance of the micro-pin cooler in a cryogenic condition. The result reveals that the nominal value of the base heat transfer coefficients of the micro-pin fin cooler with liquid nitrogen flows, 240 kW/m2-K at a mass flow rate of 2.23 g/s, is an order of magnitude greater than that with FC-72 flows. The result also demonstrates that the base heat transfer coefficient of the micro-pin fin cooler is nearly three times greater than that of the micro-gap cooler, not containing any fins. This study shows the feasibility of the cryogenic micro-pin fin cooler for thermally controlling very high heat density devices such as high-power laser diode bars, of which the heat density can reach 2000 kW/m2.

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.
Krishnamurthy and Peles [10] investigated circular staggered arrays of micro-pin fins with 250 μm height and 100 μm diameter associated with water. It was determined that the nominal value of heat transfer coefficients was 60 kW/m2-K. Qu and Siu-Ho [11] investigated the array of 670 μm-high and 200 μm-wide square pin fins with water. They determined that the nominal value of heat transfer coefficients was 70 kW/m2-K. McNeil and Raeisi [12] explored in-line arrays of 1000 μm-high and 1000 μm-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/m2-K and 3 kPa, respectively. David et al. [13] investigated staggered arrays of 1000 μm-high and 350 μm-wide square pin fins with R-134a. They determined that the nominal value of the base area heat transfer coefficients was 25 kW/m2-K. Resser et al. [1] studied in-line and staggered arrays of 305 μm-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/m2-K for deionized water and 7 kW/m2-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. Zhang et al. [14] investigated the 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. Chen 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 LN2 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 LN2 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 LN2 flow and the micro-pin fin cooler with an FC-72 flow.

2. Correlations

There are several correlations [1,10,11] available to predict the thermofluidic performance of a micro-pin fin array with a two-phase flow. In this study, correlations developed or utilized by Krishnamurthy and Peles [10] were employed because the fin diameter, fin height and fin pitch of their micro-pin fin array were quite similar to those of the micro-pin fin cooler in this investigation. Neither development of new correlations nor evaluation of utilized correlations were the primary objectives of this study. The correlations were only employed to generate auxiliary data associated with FC-72 flows.

2.1. Heat Transfer

Peles [10] used correlations, based on a Chen-type model, to evaluate heat transfer coefficients. Chen [17] defined a heat transfer coefficient for two-phase state, htp, for forced convective boiling in a tube as:
h t p = F · h s p + S · h n b
where F denotes an enhancement factor, hsp denotes a heat transfer coefficient for the single-phase state, S denotes a suppression factor and hnb denotes a heat transfer coefficient for nucleate boiling.
F is defined as the ratio of the two-phase Reynolds number to the liquid Reynolds number and S is defined as the ratio of the effective superheat to the total superheat of the wall. The decrease of S denotes the decrease of the effective superheat, and eventually induces the suppression of the nucleate boiling.
Peles [10] found that convective boiling is the dominant heat transfer mechanism, and thus the nucleate boiling term in Equation (1) is neglected.
htp is re-expressed as:
h t p = F h s p
For a case where P r 1 ,  F is defined as in [10]:
F = ϕ l 2 0.2475
For a case where P r 1 , Equation (3) is multiplied by P r 0.333 by using the method adopted by Bennett et al. [18], as shown below:
F = ϕ l 2 0.2475 P r 0.333
where ϕ l is a two-phase frictional multiplier.
Similar to Zhang and Hibiki [19]’s method, an adjustment parameter ζ is considered, and F is rewritten as:
F = ζ ϕ l 2 0.2475 P r 0.333
Consequently, the two-phase heat transfer coefficient is written as:
h t p = ζ ϕ l 2 0.2475 P r 0.333 h s p
The value of the adjustment parameter, ζ , is 1.4. [20].
A two-phase friction multiplier ϕ l is determined using the correlation proposed by Chisholm and Laird [21], as:
ϕ l 2 = Δ P f t p Δ P f f = 1 + C X v v + 1 X v v 2
where C = 0.24 is an empirically defined constant. X v v is the Martinelli parameter [22], defined as:
X v v = Δ P f / Δ Z f Δ P f / Δ Z v 1 2
Δ P f f = f N G 1 x 2 2 ρ f
Δ P f v = f N G x 2 2 ρ v
where Δ P f / Δ Z f   is the frictional pressure gradient assuming only liquid flows through the channel, Δ P f / Δ Z v   is the frictional pressure gradient assuming only vapor flows through the channel, f is the Blasius type friction factor, N is number of fin rows, G is the mass flux, x is the quality, ρ f is the liquid density and ρ v is the vapor density.
f is defined as [23]:
f = 63.246 R e d 0.7797
where R e d is the Reynolds number ( R e d = G d e / μ ), de is the equivalent diameter of a square micro-pin fin and μ is dynamic viscosity.
In Equation (11), the correlation was developed to predict the experimental results within 5% [23].
In Equation (6), the single-phase heat transfer coefficient term hsp is defined as:
h s p = N u · k f d e
where Nu is the Nusselt number, kf is the thermal conductivity of fluid and de is the equivalent diameter of a fin.
To evaluate Nu, the correlation by Short et al. [24] was utilized, defined as:
N u = 0.76 S t d e 0.16 S l d e 0.2 H f i n d e 0.11 R e 0.33
where St, Sl and Hfin are transverse fin spacing, longitudinal fin spacing and fin height, respectively.

2.2. Pressure Drop

The local two-phase pressure drop ΔPtp(x) is determined using the equation below [10]:
Δ P t p x = 1 x x i x i x ϕ l 2 Δ P f f d x + Δ P a c c l
The acceleration pressure drop, ΔPaccl is evaluated as [10]:
Δ P a c c l = G 2 x 2 ρ g α + G 2 1 x 2 ρ l 1 α o u t l e t G 2 x 2 ρ g α + G 2 1 x 2 ρ l 1 α inlet
α h = x v g 1 x v l + x v g
α α h = 1 + 0.04503 f 0.34 ln x
where α is the void fraction, α h is the homogenous void fraction, ρg is the gas density, ρl is the liquid density, vg is the gas specific volume, vl is the liquid specific volume and f is the liquid friction factor.

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 μm, the fin heights are 100, 300 and 500 μm and the gap between adjacent fins is 150 μm. The number of fins is 1600, and the base area of the array is 12 mm × 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 μm and the fin pitch from 150 to 431 μm. 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 μm, height of 300 μm and pitch of 300 μm. The base area of the array was 10 mm × 10 mm. The working fluid was LN2, and a heat source, i.e., a hot device, was placed on the top of the cooler.
Figure 3 illustrates a test rig to investigate the thermofluidic performance of a cryogenic microcooler with a two-phase LN2 flow. LN2 flow is controlled by a pressure regulator, and LN2 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 LN2, and then LN2 is heated by a water loop maintained at 25 °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 316SS 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 LN2 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.
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 ±0.5 °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.

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 LN2 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 LN2 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(Ts − Tinf)]. q is the heat transfer rate, A is the base area, Ts is the surface temperature and Tinf is the fluid temperature. The result shows the decrease of hbase values ranging from 273 to 201 kW/m2-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 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 LN2 flow, as a function of exit quality. The results show hbase values ranging from 92 to 103 kW/m2-K and ΔPtp values ranging from 55 to 69 kPa associated with a mass flux of 3.2 g/s, and hbase values ranging from 85 to 89 kW/m2-K and ΔPtp values ranging from 39 to 48 kPa associated with a mass flux of 2.3 g/s. Both greater hbase and ΔPtp 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 LN2 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 N2 and FC-72, as shown in Table 1.
Table 1 shows that N2 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 compared with FC-72. The comparison of crucial thermofluidic properties implies that N2 might be better than FC-72 for heat transfer enhancement in both sensible and latent heat transfer modes.
Figure 7 and Figure 8 present the base heat transfer coefficient, hbase, and the pressure drop, ΔPtp, of the cryogenic micro-pin fin and micro gap coolers. Both hbase and ΔPtp values are shown with various exit quality values for various mass flux values of LN2 and FC-72. In Figure 7 and Figure 8, fin, gap, value of g/s and value of μm denote a micro-pin fin cooler, micro-gap cooler, mass flux and fin height, respectively.
The analysis of FC-72 is either based on measured or correlation-evaluated results. The correlations shown in Equations (6)–(17) were used to evaluate hbase and ΔPtp values for similar fin height and mass flux conditions compared to the LN2 micro-pin fin cooler.
Figure 7 reveals that the nominal value of hbase of the micro-pin fin cooler with LN2 flow is nearly an order of magnitude greater than that of the micro-pin fin cooler with FC-72 flow, showing the average value with LN2 of 240 kW/m2-K and that with FC-72 of 23 kW/m2-K. In this comparison, the mass flux and fin height are 2.23 g/s and 300 μm, respectively. The superior thermofluidic properties of LN2 may explain this interesting result.
Figure 7 shows the average hbase value of the micro-gap cooler with LN2 flow is 78 kW/m2-K at a mass flux of 2.23 g/s and fin height of 300 μm. This result demonstrates that the hbase value with the micro-pin fin cooler could be about three times greater than that with the micro-gap cooler. The effect of surface area enhancement by the micro-fin 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/m2. 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 ΔPtp 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 ΔPtp values.
Figure 8 shows that the values of ΔPtp with LN2 are greater than those with FC-72. It can also be seen that the values of ΔPtp 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 ΔPtp 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 Figure 7 and Figure 8, the correlation prediction can be seen to roughly agree with the measurement. This discrepancy might be explained by the difference of fin heights and flow rates between the measurement and prediction, the characteristics of correlations fundamentally developed using water data and the very complicated physical behavior of LN2 flow through the micro-pin fin cooler. As previously mentioned, it should be noted that the evaluation of the correlations was not a primary objective of this study. The correlations [10] were utilized to provide supplementary data associated with FC-72 flows and to check the general trends of the measurement data.

5. Conclusions

This study aimed to investigate the thermofluidic performance of a cryogenic micro-pin fin cooler with an LN2 flow. The experimental apparatus was implemented for measurement. Heat transfer coefficient and pressure drop values were carefully measured. Supplementary results of the heat transfer coefficient and pressure drop with FC-72 flows were generated, employing correlations utilized from the literature. The surface area effect of the micro-pin fin array on the thermofluidic performance was explored by comparing the micro-pin fin cooler with the micro-gap cooler. The refrigerant effect on the thermofluidic performance of the micro-pin fin cooler was also explored by comparing the case with the LN2 flow to the case with the FC-72 flow.
Several interesting results were found in this study. First, the study revealed that the nominal value of the base heat transfer coefficient, hbase, of the micro-pin fin cooler with an LN2 flow was 250 kW/m2-K at a mass flow rate of 2.23 g/s, which was an order of magnitude greater than that with a FC-72 flow. This interesting result might be explained by superior thermofluidic properties of LN2 when compared with FC-72. Second, the study result demonstrated that the hbase value with the micro-pin fin cooler could be about three times greater than that with the micro-gap cooler. This was mainly due to the affirmative effect of the surface area enhancement by the micro-fin array. Third, the result revealed the potential capability of the cryogenic micro-pin fin cooler to thermally manage very high heat density devices, e.g., high power laser diode bars, of which the heat density can reach 2000 kW/m2. Last, the results found that the pressure drop, ΔPtp, values of the micro-pin fin cooler increased with increases of the exit quality for both LN2 and FC-72 flows. The increase of the vapor fraction caused an increase of momentum dissipation. This mechanism may explain such an increase of ΔPtp values.

Author Contributions

Conceptualization, K.J.K., B.H. and A.B.-C.; methodology, K.J.K.; software, H.H.Y.; validation, H.H.Y. and W.N.; formal analysis, H.H.Y.; investigation, W.N.; resources, B.H. and A.B.-C.; data curation, K.J.K. and H.H.Y.; writing—original draft preparation, K.J.K.; writing—review and editing, K.J.K.; visualization, H.H.Y.; supervision, K.J.K., B.H. and A.B.-C.; project administration, K.J.K., B.H. and A.B.-C.; funding acquisition, K.J.K., All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2019R1F1A1061585).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data are contained within the article.

Conflicts of Interest

The authors declare no conflict of interest.

Nomenclature

A base area [m2]
C constant in Equation (7)
d e equivalent diameter of a fin [m]
F enhancement factor
f friction factor
G mass flux [kg/m2s]
H f i n fin height [m]
h heat transfer coefficient [W/m2-k]
h b a s e base heat transfer coefficient [W/m2-k]
k thermal conductivity [W/m-k]
N number of fin rows in longitudinal direction
N u Nusselt number
P r Prandtl number
Δ P pressure drop [Pa]
Δ P f pressure drop due to friction [Pa]
Δ P accl pressure drop due to acceleration [Pa]
q heat transfer rate [W]
R e Reynolds number
S suppression factor
S t transverse fin spacing [m]
S L longitudinal fin spacing [m]
T i n f fluid temperature [°C]
T s surface temperature [°C]
X Martinelli parameter
x quality
Greek symbols
α void fraction
ρ density [kg/m3]
μ dynamic viscosity [Pa·s]
ν specific volume [m3/kg]
ϕ l two-phase frictional multiplier
ζ adjustment parameter
Subscripts
d diameter
f fluid
g gas
h homogenous flow model
l liquid
nb nucleate boiling
sp single-phase
tp two-phase
v vapor
vv viscous-viscous

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Figure 1. Structure of the copper micro-pin fin array.
Figure 1. Structure of the copper micro-pin fin array.
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Figure 2. Cross-section of the cryogenic micro-pin fin cooler.
Figure 2. Cross-section of the cryogenic micro-pin fin cooler.
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Figure 3. Schematic of a test rig to investigate the performance of cryogenic microcoolers with LN2 flows.
Figure 3. Schematic of a test rig to investigate the performance of cryogenic microcoolers with LN2 flows.
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Figure 4. (a) Micro-pin fin cooler manifold; (b) Assembled LN2 flow loop apparatus.
Figure 4. (a) Micro-pin fin cooler manifold; (b) Assembled LN2 flow loop apparatus.
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Figure 5. (a) Base heat transfer coefficient and (b) pressure drop of the cryogenic micro-pin fin cooler as a function of exit quality.
Figure 5. (a) Base heat transfer coefficient and (b) pressure drop of the cryogenic micro-pin fin cooler as a function of exit quality.
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Figure 6. (a) Base heat transfer coefficient and (b) pressure drop of the cryogenic micro-gap cooler as a function of exit quality.
Figure 6. (a) Base heat transfer coefficient and (b) pressure drop of the cryogenic micro-gap cooler as a function of exit quality.
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Figure 7. Base heat transfer coefficient of the cryogenic micro-pin fin and micro-gap coolers as a function of exit quality for various mass fluxes of LN2 and FC-72.
Figure 7. Base heat transfer coefficient of the cryogenic micro-pin fin and micro-gap coolers as a function of exit quality for various mass fluxes of LN2 and FC-72.
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Figure 8. Pressure drop of the cryogenic micro-pin fin and micro-gap coolers as a function of exit quality for various mass fluxes of LN2 and FC-72.
Figure 8. Pressure drop of the cryogenic micro-pin fin and micro-gap coolers as a function of exit quality for various mass fluxes of LN2 and FC-72.
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Table 1. Descriptions of N2 and FC-72’s properties [25,26,27,28].
Table 1. Descriptions of N2 and FC-72’s properties [25,26,27,28].
PropertyUnitN2FC-72
Molecular weight 28338
Boiling temperatureK77.3329.1
°C−195.956
Liquid enthalpykJ/kg−122.159.8
Latent heat of vaporizationkJ/kg198.884.7
Vapor enthalpykJ/kg76.7144.5
Liquid densitykg/m38061680
Vapor densitykg/m34.613
Kinematic viscosity of liquid106 m2/s0.190.38
Liquid specific heatkJ/kg-K2.0411.1
Liquid thermal conductivityW/m-K0.1350.057
Thermal diffusivity106 m2/s0.0820.031
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Kim, K.J.; Yang, H.H.; Noh, W.; Han, B.; Bar-Cohen, A. Thermal Performance of Cryogenic Micro-Pin Fin Coolers with Two-Phase Liquid Nitrogen Flows. Appl. Sci. 2021, 11, 11071. https://0-doi-org.brum.beds.ac.uk/10.3390/app112211071

AMA Style

Kim KJ, Yang HH, Noh W, Han B, Bar-Cohen A. Thermal Performance of Cryogenic Micro-Pin Fin Coolers with Two-Phase Liquid Nitrogen Flows. Applied Sciences. 2021; 11(22):11071. https://0-doi-org.brum.beds.ac.uk/10.3390/app112211071

Chicago/Turabian Style

Kim, Kyoung Joon, Hyeon Ho Yang, Wooheon Noh, Bongtae Han, and Avram Bar-Cohen. 2021. "Thermal Performance of Cryogenic Micro-Pin Fin Coolers with Two-Phase Liquid Nitrogen Flows" Applied Sciences 11, no. 22: 11071. https://0-doi-org.brum.beds.ac.uk/10.3390/app112211071

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