PORE-SCALE APPROACH TO DEVELOPING HIGH-PERFORMANCE CAPILLARY EVAPORATOR IN LOOP HEAT PIPE

Masahito NishikawaraToyohashi University of Technology and Worcester Polytechnic Institute

ABSTRACT

Two-phase state in the porous media of loop heat pipe (LHP) evaporator, which is induced by nucleate boiling, is key to enhance the evaporator performance but complicated. To investigate the liquid-vapor (L-V) phase behavior and the relationship with the evaporator heat-transfer coefficient, this work visualizes the L-V phase distribution at the contact surface between the evaporator casing and wick and simulates the two-phase thermal hydraulics in the evaporator by pore network model. The visualization study shows evolution of the L-V phase distribution with changing the heat load and the relationship between the length of the three-phase contact line (TPCL) within the casing, liquid and vapor phase and the heat-transfer coefficient. The simulation work shows effect of pore size distribution of the wick on the heat-transfer coefficient.

NOMENCLATURE

A area (m2)Asat liquid saturated area (m2)AROI area of region of interest (m2)cp specific heat at constant pressure (J/kg K)ΔP pressure difference (Pa)Δ mesh size (m)gi,n flow conductance (m3)hevap evaporator heat-transfer coefficient (W/m2·K)hfg latent heat (J/kg)K permeability (m2)kcase thermal conductivity of the casing (W/m·K)keff effective thermal conductivity of the porous media (W/m·K)Ltri length of the three-phase contact line per unit area (/m)Ll-v length of the boundary line between liquid and vapor phase (m)m mass flux vector (kg/m2·s)P pressure (Pa)Pcap capillary pressure (Pa)Q volumetric flow rate (m3/s)r radius of nucleus bubble (m)rmax the maximum throat radius (m)rmin the minimum throat radius (m)rth throat radius (m)S saturation

TFAWS 2020 – August 18-20, 2020 1

Liquid line Vapor line

CapillaryEvaporator

Condenser

A

Cross-section(A-A')

Heat flux

Heat dissipation

A'

Heat leak

Compensationchamber (CC)

z

GrooveCase

Wick

applyq

grTeT

T temperature (°C)t thickness (m)

θ contact angle (deg)μ viscosity (Pa·s)ν kinetic viscosity (m2/s)ρ density (kg/m3)σ surface tension (N/m)

INTRODUCTION

A thermal-control device known as a loop heat pipe (LHP) has recently attracted attention in various fields. A schematic of an LHP is shown in Figure 1. It comprises a capillary evaporator, condenser, transport line, and compensation chamber (CC). The condenser and transport line are simple pipes. Unlike conventional heat pipes, the porous medium (wick) is solely located in the evaporator; this facilitates longer transport lengths and larger radiation areas. The capillary pressure develops, and liquid evaporates in the wick. The evaporator configuration is the critical part of the performance design. However, an optimal method for designing this component is yet to be established, because the two-phase thermal hydraulics in the capillary evaporator is complicated.

The evaporator design includes wick and groove shape and porous characteristics. This paper focuses on the latter. Enhancement by microscopic approaches such as biporous void structure1, a bilayer wick using carbon nanotubes2, and the unique shape of particles forming the wick3 has been reported, however they are heuristic. Rapidly developing 3D printing technology can make the desired microscopic porous structure4, so it is more valuable to pursue what is the optimized void structure on heat transfer of the capillary evaporator.

The phase state in the wick during an LHP operation is divided into two: liquid saturated and liquid-vapor (L-V) two-phase. The liquid saturated state appears at a relatively low heat flux applied to the evaporator. Evaporation occurs on the L-V interface between the saturated wick and groove. In addition, because the meniscus is along the TPCL within the casing, wick, and grooves, the applied heat is also transported directly by evaporation through it5-7. When high heat flux is

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Figure 1. Schematic of a loop heat pipe.

applied, vapor phase generates inside the wick due to nucleate boiling. Part of the wick is dry momentarily, then the liquid in the CC saturates the wick and finally a two-phase state is formed. On the two-phase state, the L-V interface is inside the wick as well as the wick-groove interface. The heat-transfer coefficient and pressure loss through the wick are affected by the L-V interface shape. The L-V interface shape balances in the flow of the micro-void structure, so microscopic characteristics of the structure can affect thermal performance at a high heat flux.

This paper investigates the L-V phase displacement in the capillary evaporator and try to find how to design the porous structure. The L-V phase displacement on the contact surface between the casing and wick using visualization evaporator during LHP operation is observed and effect of pore size distribution is explored by pore network simulation.

EXPERIMENTAL SETUP

The capillary evaporator visualizations performed so far6, 8-12 were on the cross-section in the axial direction of the evaporator. In particular, if the thermo-fluid behavior is two-dimensional in nature, it is sufficient to understand the behavior on the cross-section only. However, the actual behavior is three-dimensional in nature. Therefore, the behavior on the contact surface is important. This study focuses on the parallel plane to the contact surface between the evaporator casing and wick. The previous work13 developed the transparent evaporator using a quartz glass tube as the casing with a low thermal conductivity of 1.38 W/mK14. This work improves the casing material to sapphire tube with a high thermal conductivity of 46 W/mK14 to reproduce practical use.

To visualize the evaporator during the LHP operation, a sapphire tube is used for the evaporator casing formed with a transparent indium-tin-oxide (ITO) heater (Figure 2). The heater consists of transparent conductive film made of ITO and Au electrodes at both ends of the film to apply electricity. The electric resistance of the heater is 20 Ω. The heater length is the same as the groove length i.e., 45 mm. Both ends connect to the CC and vapor line using ICF flanges. A urethane

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Flow

Flow

Pressuregauge

Vapor line

Evaporator CCLiquid line

Condenser

Charging portfrom chiller

to chiller

Differential pressure gauge

Valve

CameraLight

370 mm

800 mm

Heating and observing section (45 mm)

Wick CCCase

Figure 2. Visualization loop heat pipe.

sponge was used as a wick to ensure the sealing between the groove and CC and to provide a strong contact between the casing and wick. The sponge has a larger diameter than the casing’s inner diameter. The void of the sponge is open. The pore radius and the porosity are 15 μm and 75%, respectively. 20 axial grooves of 1 mm in depth, 1 mm in width and 45 mm in length and no circumferential ones are machined. HFE7000 is selected as a working fluid taking tolerability and wettability to the wick into account. The main dimensions are as follows: outer diameters of vapor line, condenser, liquid line, CC, evaporator casing, and wick are 6.4 mm, 6.4 mm, 6.4 mm, 19 mm, 15.0 mm, and 13.0 mm, and lengths of them are 470 mm, 955 mm, 540 mm, 150 mm, 150 mm, and 50 mm, respectively. After installation of the wick into the sapphire tube, the capillary capability of the developed evaporator was tested by the bubble point method. The bubble point pressure is comparable with the capillary pressure developed by the pore radius of the wick; 4.5 kPa. In the condenser, a meandering stainless-steel tube is embedded in a plate cooled by a chiller. The temperature of the LHP was measured by thermocouples. Two pressure transducers are assembled to measure the pressure difference between the inlet of the vapor line and the outlet of the liquid line and saturation pressure. Data was acquired every 5 s. An image of the evaporator was taken by a single-micro-lens reflex camera to observe the L-V phase state, and the captured images were distinguished between the vapor and liquid phase region by binarization. The frame rate was 30 fps and the pixel size was 20 μm. The LHP was covered with thermal insulators except for around the observation area. Heat loss from the evaporator to ambient is measured and was 4 W at 70 °C of evaporator temperature. The experimental condition is as follows: step heat load of 10-80-10 W (0.56-4.5 W/cm2), sink temperature of 10 °C, room temperature 20 °C, and operating temperature limit of 70 °C.

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x

z

y

Lz

Ly

LxLiquid phase

Evaporatorcase

Wick(porous)

Groove

Contact surface

Vapor phase=1.5 mm

=4.0 mm

=3.5 mm

Void BulkVapor phaseL-V interfaceLiquidphase

vP

lP

Throat(cylinder)Pore(sphere)

Modeling

PORE NETWORK MODEL

Numerical modelIn the simulation, the flow in the capillary structure was represented by a pore network model (PNM) while the energy conservation of the casing and wick were solved. The computational domain corresponding to a portion of the periodic structure of a capillary evaporator is shown in Figure 3. The domain is a cuboid with the size of 4.0 × 3.5 × 1.5 mm (Lx × Ly × Lz) and consists of a stainless-steel casing, a wick, and grooves. The groove height is 1 mm, the casing thickness is 1.0 mm, and the contact surface between the casing and wick is 50% of the Lx × Lz area. A constant saturation temperature and pressure are imposed to the groove and CC. The energy conservation considering conduction and convection, and the heat conduction, are solved for the wick and casing.

c p m⋅∇ T=keff ∇2 T (1)

k case ∇2T=0 (2)

Depending on the heat flux applied to the evaporator, the wick phase state is divided into saturated with a liquid for the low heat flux and unsaturated with a liquid and vapor for the high heat flux. In the simulation, the transition condition to an unsaturated state is given by

Figure 3. Computational domain and schematic illustration of the pore network model. Groove height and case thickness is 1 mm and the ratio of the wick-casing contact surface to the casing bottom surface is 0.5.

T−T sat ( P )>ΔT nuc=2 σT sat

ρv rh fg(3)

ΔTnuc is the threshold of nucleation based on boiling critical superheat15. In this model, r is set as the mode pore radius of the wick. The L-V interface in the wick is calculated so that the pressure difference between the vapor and liquid on the interface balances the local capillary pressure. Figure 3 shows a schematic illustration of the PNM for the fluid simulation. The PNM divides the voids of the porous structure into spherical pores and cylindrical throats. Unlike the continuum approach used for solving flows in porous media, the PNM allows a distribution of

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the pore radius and corresponding local variables. Since local voids are represented as simple shapes associated with throats and pores in the pore network, the present model allows analysis of a greater quantity of pores. The local capillary pressure, Pcap is expressed by

Pcap=2σ cosθ

rth(4)

Temperature dependence of surface tension is considered using the property software REFPROP16. A contact angle assumes 0°. The mass flow rate in the throat between neighboring pores was proportional to the pressure difference of the pores. Considering mass conservation at a pore i, the following equation with respect to pressure was applied,

∑n=1

6 g i,n

ν (P i−Pn )=0 (5)

gi,n is proportional to the quadruplicate throat radius, and inversely proportional to the throat length. It should be noted that n was six for the three-dimensional lattice, which corresponds to the coordinate number. The pressure was obtained from the solution of Eq. (5). Then, the mass flow rate in the throats was calculated. The mesh size was 0.1 mm. The simulation used the following values for the heat-transfer coefficient i.e., 100 W/m2K for the heat-transfer coefficient between the wick and CC, and 1.0 × 105 W/m2K for the contact heat-transfer coefficient between the casing and wick. Zero pressure loss through the transport line is given. The boundary between the dry wick and groove was insulated thermally.

Samples of Porous MediaSamples with different radius distributions have to be generated although the macroscopic characteristics of K/reff are the same. To meet the above condition, K is adjusted to fit the same value in all samples. In this work, the mode value is used as representative of rth distribution. rth

is allocated on the lattice grid and generated to fit the distribution with the gamma distribution whose probability density function is expressed with

f ( x )= 1Γ (k )θk xk−1 exp(− x

θ ).

(6)

Distribution profile is determined by k and θ. θ is set to fit the mode rth with 1.2 μm, which is the real value in the ref17. Profile dispersion is adjusted by changing k. Σ* defined with following equation18 is introduced to express the dispersion quantitatively,

Σ∗¿ ( rmax−r min )/ Δ . (7)

K can be obtained by solving Eq.(5) after sample generation. Porous media of cross-section A and thinness t is set in the computer, then Eq.(5) is solved with given ΔP as a boundary condition, finally the flow rate though the porous media is calculated. The computational permeability Kcomp is calculated with Darcy’s law,

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0

0.2

0.4

0.6

0.8

1

0 4 8 12 16

Volume

frac

tion

Pore radius (μm)

17.0*

10.0* 055.0*

035.0*

017.0* 0014.0*

017.0*

Meas.Sim.

Throat

Table 1. Pore radius characteristics of samples.

K comp=μ⋅At⋅ΔP

Q .(8)

Kcomp is adjusted by multiplying all gi,n by a constant to fit the same value of 2.00×10-14 m2. Six samples are generated with different Σ* as shown in Figure 4 and Error: Reference source notfound. Sample no. 5 is fitted to the real porous media in the Ref17. The above process of porous sample generation is used in the evaporator simulation.

RESUTLS AND DISCUSSION

Visualization at the contact surface between the evaporator casing and wickThe test results of the LHP with the visualization evaporator are shown in Figure 5. The evaporator temperature presents U-shape. It was observed that the phase state in the wick core is two-phase at less than 15 W and is liquid-saturated at more than 20 W. It is considered that the two-phase state leads large heat leak to the CC, resulting in high evaporator temperature. Nucleate boiling was observed at 15 W. The evaporator temperature was over the limit at 90 W.

Figure 4. Pore radius distribution of samples.

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0

10

20

30

40

50

60

70

80

90

100

0

10

20

30

40

50

60

70

0 5000 10000 15000 20000

Hea

t loa

d [W

]

Tem

p [℃

]

Time [s]

Te Tv1 Tv2 Tv3 Tl Tcc Heat load [W]

Hea

t loa

d [W

]

Hea

t flu

x [W

/cm

2 ]

5.6

5.1

4.5

3.9

3.4

2.8

2.2

1.7

1.1

0.6

0

Figure 5. Temperature history. U-shape is observed.

The evaporator heat-transfer coefficients, saturation and TPCL length in a steady-state are shown in Figure 6. Figure 7 shows binarized images at each heat load. The L-V phase distribution was calculated by subtracting the initial saturated image from time sequences. Average saturation S and TPCL length Ltri are calculated with

S=A sat / AROI . (9)

. (10)

Although hevap could not be calculated at 20 and 25 W due to small temperature difference, hevap

increases right after the nucleate boiling and then decreases with heat load increasing. The saturation drops after the nucleate boiling and then decreases with the heat load increasing. On the

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0

0.2

0.4

0.6

0.8

1

0

1000

2000

3000

4000

5000

6000

7000

0 20 40 60 80

Satu

ratio

n

hev

ap[W

/m2K

]

Heat load [W]

Unmeasurable hevap with small ΔT

20 25

Before NB

After NB

0

1

2

3

4

5

6

7

8

9

10

0

1000

2000

3000

4000

5000

6000

7000

0 20 40 60 80

TPCL

leng

th [/

mm

]

hev

ap[W

/m2K

]

Heat load [W]20 25

(a) (b)

□Vapor Phase ■Liquid Phase

10 W

15 W(Before NB)

20 W

25 W

30 W

35 W

15 W(Boiling incipience)

15 W(Steady state)

40 W

45 W

50 W

55 W

60 W

65 W

70 W

75 W

Figure 6. (a)Relation of saturation to the heat-transfer coefficient. (b)Relation of the TPCL length to the heat-transfer coefficient.

Figure 7. Observed phase distribution at the contact surface between the evaporator casing and wick. White is vapor phase and black is liquid phase.

other hand, the TPCL length increases after the nucleate boiling, and reaches the peak at 20 W, then decreases with the heat load increasing. It is considered that the TPCL length has a strong relationship with the evaporator heat-transfer coefficient rather than the saturation. At the boiling incipience, most parts are dry, afterwards, liquid saturates. The stable phase distribution shows that liquid phases are scattered when the heat-transfer coefficient is high at 20 and 25 W, while the liquid phase is compact at higher heat load.

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0200400600800

1,0001,2001,4001,6001,8002,000

0 5,000 10,000 15,000 20,000 25,000 30,000 35,000

h eva

p(W

/m2 K

)

Heat flux (W/m2)

Calc.

Exp.

2Φ

Validation of pore network simulationThe developed model has been validated with two LHP results. One of the comparisons is shown in Figure 8. The evaporator has a PTFE porous wick and ethanol is used as the working fluid. The transport length is 1 m and the cylindrical evaporator is 12 mm diameter. The detailed description is found in the Ref19. The comparison of measured heat-transfer coefficient with simulated one shows rough agreement. The simulation presents two-phase transition at 1.2 W/cm2.

Another validation shown in Table 2 is comparison with the visualization LHP results. The evaporator has a quartz porous wick and acetone is used as the working fluid. The evaporator temperature, saturation and phase distribution at the contact surface are compared. The simulated evaporator temperature agrees well with the measured one, but the phase distribution doesn’t agree completely. In both of experiment and simulation, however, liquid phase remains along the TPCL. The simulation showed that the residual liquid is low temperature, therefore, the cooled liquid sites on the contact surface can contribute enhancement of the heat-transfer coefficient. The simulation could reproduce such a specific characteristic which makes large impact on the heat transfer.

Figure 8. Comparison of an LHP test and PN simulation (PTFE porous – Ethanol19).

Table 1. Comparison of visualization and PN simulation (Quartz porous – Acetone20). Black shows liquid phase and white is vapor phase.

Te(°C)

S Phase distribution at the contact surface

Exp. 114 0.63

Sim. 115 0.5845 mm

z

Residual liquid phase

Vapor phase Liquid phase

x

Groove

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L-V interface shape of SS-Ammonia

Low heat flux

High heat flux0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

0.0E+00 1.0E-06 2.0E-06 3.0E-06 4.0E-06

hev

ap(W

/m2K)

qapply

1×10-6 2×10-6 3×10-6 4×10-60

SS-R134a

PTFE-R134a

SS-Ammonia

PTFE-AmmoniaSS-Acetone

PTFE-Acetone

2Φ

T lim.

T lim.

V.P.V.P.

V.P.

V.P.

qmax_v^

^

(a) (b)

Effect of pore size distributionSix cases of the evaporator configuration are simulated with two wicks of SS and PTFE porous media and three working fluids of ammonia, R134a, and acetone.

Design method difference depending on working fluid

Figure 9a shows the evaporator heat-transfer coefficient, hevap of sample no. 5 on each evaporator. hevap with ammonia and R134a has a local maximum in the two-phase state. No L-V interface is inside the wick of SS- Ammonia at the lowest heat flux, as shown in Figure 9b. Then, the size of the vapor phase increases with the heat flux increasing. For the evaporator with acetone, after transition to the two-phase state, the L-V interface is not stable inside the wick, then the vapor phase penetrates at a relatively low heat flux. When the vapor penetration occurs, the evaporator losses a pumping function then the operation stops. Considering the ratio of pressure loss between the liquid and vapor phase, the ratio is expressed with kinetic viscosity ratio of liquid and vapor based on Darcy’s law. The ratios of ammonia, R134a, and acetone are 4, 1.5, 15, respectively. For acetone, pressure loss per unit length through the vapor phase is 15 times higher than that through liquid phase, so it is difficult to keep the L-V interface inside the wick once the wick sate transits to two-phase. In conclusion, optimization of microscopic characteristics of the wick is not effective for the fluid with a high kinetic viscosity ratio of vapor to liquid, and enhancement by macroscopic characteristics is effective as well as by wick shape.

Figure 9. (a) hevap as a function of non-dimensional heat flux. Σ* is 0.017. Applied heat flux to the evaporator is normalized with figure of merit. Boundary between saturated and two-phase wick and the operating limits when vapor phase penetrates to the CC or evaporator temperature reaches a critical point are depicted with |, VP, and T lim, respectively. (b) Evolution of the L-V interface shape of SS-Ammonia evaporator.

Effect of pore radius distribution

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PTFE-ammonia

Σ* high3,000

T lim.

L-V interface shape(PTFE-ammonia 6.1W/cm2)

Σ*0.017 Σ*0.0014

Σ*0.035

Σ*0.1

Σ*0.055

Σ*0.17

Casing

0

2,000

4,000

6,000

8,000

0.0 20.0 40.0 60.0

hev

ap(W

/m2K

)

qapply (W/cm2)

0.17 0.1 0.0550.035 0.017 0.0014

SS-ammonia Σ* high

0

V.P.

T lim.

(a) (b)

Table 3. Correlation between hevap and variables with respect to L-V interface.Ltri

AintDvp

Scont

S

Liquid phaseVapor phase

Figure 11. Representative variables with respect to L-V interface in the two-phase wick.

Figure 10a shows hevap of the evaporator with ammonia. The maximum heat flux is higher with higher Σ*. The heat flux where hevap is a local maximum increases with Σ* increasing. The L-V interface shape is smooth at the lowest Σ* and the shape of Σ*=0.035 is complicated as shown in Figure 10b.

To find what shape has a high heat-transfer coefficient, five variables are considered as characteristics of the L-V interface shape as shown in Figure 11: length of the TPCL Ltri, Area of the L-V interface Aint, Depth of vapor pocket Dvp, Saturation of the wick S, and saturation on the contact surface Scont. The correlations with hevap are calculated and listed in Error: Referencesource not found3. Ltri is positively correlated with hevap. Therefore, enhancement of Ltri is effective on the high hevap. As shown in Figure 12a, hevap linearly increases with Ltri. Ltri is affected by Σ* as shown in Figure 12b. The case in which Ltri is the longest of 4.34 is Σ*=0.035 and qapply=6.1 W/cm2. Ltri is the longest with middle Σ* in simulation conditions. In the simulation, permeability of the all simulated wicks is set as a constant. However, it is difficult in reality that only pore distribution changes and permeability keep a constant. Therefore, more consideration on hevap enhancement by control of pore size distribution is needed.

Figure 10. Effect of pore radius distribution on (a) hevap and (b) L-V interface shape. VP, and T lim show the operating limits when vapor phase penetrates to the CC or evaporator temperature reaches a critical point.

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y = 386 x + 1,387

0

500

1,000

1,500

2,000

2,500

3,000

0 1 2 3 4 5

hev

ap(W

/m2K)

Ltri

0

1

2

3

4

5

0 20 40 60

Ltri

qapply (W/cm2)

0.17 0.1 0.0550.035 0.017 0.0014

Liquid phase

Vapor phase

4.34

Σ*

Ltri = 4.34T lim.

(a) (b)

Figure 11. (a)Relation between hevap and Ltri in the PTFE-ammonia LHP. (b) Ltri as a function of heat flux on each radius distribution. Ltri is normalized by the length of saturated wick. The inset shows the interface shape of the maximum Ltri. T lim shows the operating limit when evaporator temperature reaches a critical point.

CONCLUSIONS

To establish the design methods of microscopic characteristics of the porous media, two-phase thermal hydraulics in the LHP evaporator are investigated. A visualization evaporator using a sapphire tube and a urethane sponge observed scattered liquid sites on the contact surface between the casing and wick during LHP operation. 3D pore-network simulation demonstrated that the TPCL length has positive correlation with the evaporator heat-transfer coefficient and the TPCL length has a maximum at moderate dispersion of pore radius in some cases. The TPCL length may be optimized by adjusting pore size distribution.

CONTACT

Masahito Nishikawara was born in Aichi, Japan, in 1988. He received the B.Eng., M.Eng., and Dr. Eng. degrees from Nagoya University, Nagoya, Japan, in 2010, 2012, and 2015, respectively. Since 2015, he has been with the Department of Mechanical Engineering, Toyohashi University of Technology, Toyohashi, Japan, where he is currently an Assistant Professor. Since June 2019, he has also been a Visiting Researcher with the Department of Mechanical Engineering, Worcester Polytechnic Institute, Worcester, MA, USA. His current research interests include advanced heat transfer devices with capillarity and electrohydrodynamics (EHD), such as loop heat pipes and EHD pumps.

Email: nishikawara@me.tut.ac.jp

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REFERENCES

1. H. Li, Z. C. Liu, B. B. Chen, W. Liu, C. Li, and J. Yang, “Development of biporous wicks for flat-plate loop heat pipe,” Exp. Therm. Fluid Sci., Vol. 37, pp. 91–97, 2012.

2. E. Terrado, R. Molina, E. Natividad, M. Castro, P. Erra, D. Mishkinis, A. Torres, and M. T. Martínez, “Modifying the heat transfer and capillary pressure of loop heat pipe wicks with carbon nanotubes,” The Journal of Physical Chemistry C, Vol. 115, pp. 9312-9319, 2011.

3. B. Wangaskar, S. Khandekar, and K. Balani, “Effect of Particle Morphology on Transport Parameters of Loop Heat Pipes,” Proc. Joint 19th International Heat Pipe Conference and 13th International Heat Pipe Symposium, No. LHP1_4, 2018.

4. B. Richard, D. Pellicone, W. Anderson, “Loop Heat Pipe Wick Fabrication via Additive Manufacturing,” Proc. Joint 19th International Heat Pipe Conference and 13th International Heat Pipe Symposium, No. PS1_22, 2018.

5. A.S. Demidov, E.S. Yatsenko, Investigation of heat and mass transfer in the evaporation zone of a heat pipe operating by the ‘inverted meniscus’ principle, Int. J. Heat Mass Transfer, Vol. 37, pp. 2155–2163, 1994

6. K Odagiri and H Nagano, “Characteristics of phase-change heat transfer in a capillary evaporator based on microscale infrared/visible observation,” Int. J. Heat Mass Transfer, Vol. 130, pp. 938-945, 2019.

7. Y. Yamada, M. Nishikawara, H. Yanada, and Y. Ueda, “Performance prediction of a loop heat pipe considering evaporation from the meniscus at the three-phase contact line,” Proc. Joint 19th International Heat Pipe Conference and 13th International Heat Pipe Symposium, No. LHP3_2, 2018.

8. Liao, Q. and Zhao, T.S, “A visual study of phase-change heat transfer in a two-dimensional porous structure with a partial heating boundary,” Int. J. Heat Mass Transf., Vol. 43, pp. 1089–1102, 2000.

9. Launay, S. Mekni, N, “Specifically designed loop heat pipe for quantitative characterisation,” Proc. 15th International Heat Pipe Conference, 2010.

10. Hatakenaka, R., Okamoto, A., Mase, Y., Murakami, M., and Iikura, H., “Visualization of Internal Fluid Behavior in a Miniature Loop Heat Pipe using Neutron Radiography,” 41st Int. Conf. Environ. Syst., 2011.

11. Xu, J., Zhang, L., Xu, H., Zhong, J., Xuan, J., “Experimental investigation and visual observation of loop heat pipes with two-layer composite wicks,” Int. J. Heat Mass Transf., Vol. 72, pp, 378–387, 2014.

12. Mottet, L., Coquard, T., and Prat, M., “Three dimensional liquid and vapour distribution in the wick of capillary evaporators,” Int. J. Heat Mass Transf., Vol. 83, pp. 636–651, 2015.

13. M. Nishikawara, Y. Ueda and H. Yanada, “Static and dynamic liquid-vapor phase distribution in the capillary evaporator of a loop heat pipe,” Microgravity Science and Technology, Vol. 31, pp. 61-71, 2019.

14. Japan society of thermophysical properties, Thermophysical properties handbook, Yokendo p. 216-217, 2008. (in Japanese)

15. The Japan Society of Mechanical Engineers ed., Heat transfer, the Japan Society of Mechanical Engineers, p. 131, 2014. (in Japanese)

16. E.W. Lemmon, M.L. Huber, and M.O. McLinden, NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 9.1, National

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Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, 2013.

17. M. Nishikawara and H. Nagano, “Parametric Experiments on a Miniature Loop Heat Pipe with PTFE Wicks,” International Journal of Thermal Sciences, Vol. 85, pp. 29-39, 2014

18. Prat, M. and Bouleux, F., “Drying of capillary porous media with a stabilized front in two dimensions,” Phys. Rev. E., Vol. 60, pp. 647–5656, 1999.

19. Nishikawara, M., Nagano, H., Mottet, L., and Prat, M., “Formation of unsaturated regions in the porous wick of a capillary evaporator,” Int. J.Heat Mass Transf., Vol. 89, pp. 588–595, 2015.

20. M. Nishikawara, Y. Ueda and H. Yanada, “Static and dynamic liquid-vapor phase distribution in the capillary evaporator of a loop heat pipe,” Microgravity Science and Technology, Vol. 31, Issue 1, pp. 61-71, 2019.

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