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Experimental study of laminar natural convection heat transfer from a vertical cylinder to slush nitrogen under constant heat flux conditions
Cryogenics 71 (2015) 76–81
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Cryogenics journal homepage: www.elsevier.com/locate/cryogenics
Experimental study of laminar natural convection heat transfer from a vertical cylinder to slush nitrogen under constant heat flux conditions Yoonseok Lee, Masamitsu Ikeuchi ⇑ Mayekawa Mfg. Co., Ltd., 2000 Tatsuzawa, Moriya City, Ibaraki 302-0118, Japan
a r t i c l e
i n f o
Article history: Received 27 November 2014 Received in revised form 9 May 2015 Accepted 19 May 2015
Keywords: Slush nitrogen Natural convection Heat transfer coefficient
a b s t r a c t Natural convection heat transfer from a vertical cylinder immersed in slush and subcooled liquid nitrogen and subjected to constant heat fluxes was investigated in order to determine the relative merits of slush nitrogen (SlN2) for immersion cooling. A glass dewar was used as a test vessel in which a cylindrical heater was mounted vertically, and heat transfer measurements were carried out for SlN2 and subcooled liquid nitrogen (LN2) in the laminar flow range. The results revealed advantages of SlN2 over subcooled LN2 in natural convection cooling. The local temperatures of the heated surface surrounded by solid nitrogen particles are measured to increase at much slower rates than in subcooled LN2, which is due to the latent heat of fusion of solid nitrogen. Even after the solid nitrogen particles surrounding the heater are apparently depleted, the average heat transfer coefficients for SlN2 are still found to be greater than those for LN2 with the improvement in heat transfer being larger for lower Grashof number regime. Our analysis also indicates that solid nitrogen particles in close proximity to heated surface do not discourage local convection due to the porous nature of SlN2, making the heat transfer in SlN2 more effective than in the case of solid–liquid phase change of nitrogen involving melting and conduction processes. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Slush nitrogen (SlN2) is a two-phase fluid consisting of fine solid nitrogen particles and liquid nitrogen (LN2). Since 2000 we have studied methods for generating and transporting SlN2 [1] and investigated the flow friction and heat transfer characteristics of SlN2 in a pipe [2] in an attempt to develop a refrigeration system for high temperature superconducting (HTS) power cables. This work confirmed the advantage of solid nitrogen particles in stabilizing the fluid temperature but also revealed the problem of pressure loss increasing with the solid mass fraction of SlN2. It has been recently reported that SlN2 has the same dielectric strength as LN2 [3] and improves overcurrent characteristics of HTS wire, by providing greater stability against thermal runaway, than is obtained with subcooled LN2 [4,5]. To extend the application of SlN2 we have investigated the possible advantages of SlN2 for immersion cooling. The target application is the cooling of HTS transformers using SlN2 as a substitute for subcooled LN2 [6]. Although some work has been done to investigate forced convection characteristics of SlN2 [7–9], little has been done to study natural convection in SlN2 despite its potential applicability, and
⇑ Corresponding author. http://dx.doi.org/10.1016/j.cryogenics.2015.05.008 0011-2275/Ó 2015 Elsevier Ltd. All rights reserved.
it is still unclear what effect solid nitrogen particles have on flow and heat transfer. In this work we investigate natural convection heat transfer from a vertical cylinder to SlN2 and LN2, examining the applicability of SlN2 to immersion cooling system for HTS coils and trying to understand the effects of solid nitrogen particles on natural convection heat transfer.
2. Experimental details The experimental setup consists of a test vessel, a vacuum pump, an agitating unit, and heating and measuring systems as illustrated in Fig. 1. A glass dewar measuring 750 mm long and 150 mm in diameter is used as a test vessel in which a cylindrical heater is installed vertically so that it can be immersed in SlN2 or subcooled LN2. Liquid nitrogen is filled up to the upper boundary of the viewing section and cooled by depressurization. To evacuate nitrogen vapor from the vessel an oil rotary vacuum pump with a discharge rate of 0.6 m3/min is used. SlN2 is generated in the vessel using the freeze–thaw method [1,10]. In producing SlN2, an agitator with four blades is rotated at 60 rpm to break and evenly distribute lumps of solid nitrogen falling from the liquid–vapor interface. A cylindrical heater 100 mm long and 54 mm in diameter was made by winding manganin wire around an FRP bobbin as shown
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Y. Lee, M. Ikeuchi / Cryogenics 71 (2015) 76–81
φ 190 φ 150
vacuum pump
d ¼ 3:93Pr 1=2 ð0:952 þ PrÞ1=4 Gr1=4 ; x x
motor flange
where x denotes an axial distance from the leading edge of the heating section, Pr and Gr are the Prantl and Grashof numbers respectively, and subscript x indicates that the quantity is local. It is known that as long as the thickness of boundary layer is not large compared with the diameter of cylinder, the correlation for the natural convection heat transfer for vertical plates can be applied to vertical cylinders if the following condition is met [12],
DC power supply
logger Ag plated
FRP support FRP support
FRP disk
750
K-type thermocouples
300
viewing section
D 35 P 1=4 ; L GrL
FRP support
heater
agitator
Fig. 1. Schematic diagrams of the test vessel (left) and experimental setup (right). Lengths are in millimeters.
ð2Þ
where D and L denote the diameter and height of cylinder, and GrL is the Grashof number at height L. In this experiment, D = 54 mm, L = 80 mm and GrL < 1.26 1011, satisfying Eq. (2). To evaluate Pr and Gr in Eq. (1) it is necessary to know temperatures of heater surface and fluid. To find the local temperature of heater surface Twx for given heat flux q and ambient fluid temperature T1x we used the relation
T wx ¼ T 1x þ in Fig. 2. Enameled manganin wire with an end-to-end resistance of 50 X and a diameter of 0.2 mm was helically wound around the bobbin core with equal spacing (7.5 mm). The manganin wire was fixed on the bobbin core by electrically insulative material (varnish). Five K-type thermocouples with a diameter of 0.5 mm were then mounted axially spacing 16 mm apart avoiding contacting the manganin wire, on which varnish was applied. After mounting the thermocouples, the bobbin core was coated with thermally conductive epoxy (stycast 2850FT), filling up the gaps between the core and flanges (see Fig. 2) to uniformly produce heat over the heating section. Electric power is supplied to the heater by a regulated DC power supply with a maximum power of 100 W. To measure fluid temperature five thermocouples are used which are of the same type as used on the heater. They are placed at the same axial distances as those on the heater and at a radial distance greater than the thickness of boundary layer. We calculated boundary layer thickness d for the heater using the following equation for d for vertical plates [11]
q ; hx
ð3Þ
where hx denotes a local heat transfer coefficient and is obtained using an empirical correlation [11] given by
Nuxf ¼
hx x
jxf
( ¼
1=5 0:6 Grx Pr f 1=4 0:17 Gr x Prf
5
for 10 < Grx < 1011 for 2 1013 < Grx Pr f < 1016
ð4Þ where Nu represents the Nusselt number, Gr is a modified Grashof number given by
Gr ¼ Gr Nu; and j denotes the thermal conductivity of fluid with subscript f implying that the related properties are evaluated at film tempera1 . Although Eq. (4) was obtained for natural convecture T f ¼ T w þT 2 tion in water, it is also well suited for liquid nitrogen, as will be discussed in Section 3. Since Twx and Nuxf are interdependent, Eqs. (3) and (4) need to be simultaneously solved. We thus iteratively calculated Eqs. (3) and (4) until the average temperature of the
54
10
Tw5
72
80
heating T w3 area (stycast)
56
80
100
Tw 4
1
Tw1
40
Tw 2
24
100
FRP
10
;
*
8
770
vacuum glass dewar
ð1Þ
15 54 Fig. 2. Schematic diagrams of the bobbin used as the body of heater (left) and heater with thermocouples set on it (right). Lengths are in millimeters.
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Y. Lee, M. Ikeuchi / Cryogenics 71 (2015) 76–81
heater surface converged within 0.0001 K. We evaluated d for the heater in subcooled LN2 with heating power 620 W (q 6 1474 W/m2) according to our experimental conditions. As an example, calculated d for T1x = 65 K and q = 737 W/m2 is presented in Fig. 3. The calculations indicate that the values of d in our experiment do not exceed 2 mm. Considering that the average size of solid nitrogen particles created by the freeze–thaw method described above is about 1.4 mm [1], we set thermocouples for measuring T1x 20 mm away from the heater surface so that solid nitrogen particles may fill the space between the heater and the thermocouples. Since the thermocouples have an uncertainty of ±1.5%, each thermocouple is calibrated such that the triple-point temperature is 63.15 K and the saturation temperature at atmospheric pressure is 77.3 K. In the following, we denote the temperatures of heater surface and ambient fluid at five different axial distances in the order of increasing height as Tw1 to Tw5 and T11 to T15, respectively and the corresponding local heat transfer coefficients as h1 to h5. Natural convection heat transfer measurements are carried out with constant heat fluxes at 1 atm. In the experiment of natural convection in SlN2, SlN2 is generated with the agitator rotating at 60 rpm until the heater is completely buried in solid nitrogen particles (mass fraction 20%), and the agitator is stopped, when SlN2 generation is finished. After the solid nitrogen particles settle down, the vessel is pressurized up to 1 atm by injecting helium gas and then maintained at atmospheric pressure. The temperatures of heater surface and fluid are recorded once per second. The heater is turned on one or two minutes after the start of temperature measurement, and the measurement continues until the fluid in the vessel reaches the saturation temperature. In the case of natural convection in subcooled LN2, LN2 is cooled to the triple point by depressurization. To stabilize the temperatures of heater and fluid at the triple point a small amount of solid nitrogen particles are produced. After solid nitrogen particles melt away, the vessel is pressurized and brought under atmospheric pressure, following the same procedure as for SlN2.
90 −1/2
δ = 3.93xPr 80
(0.952+ Pr) Gr−x 1/4 1 /4
3. Results and discussion To observe laminar natural convection flows of LN2 and SlN2 we applied heater powers of Qe = 5, 10 and 20 W which cause meaningful differences in temperature between the heater surface and fluid. Since some of electric power supplied to heater goes into warming the heater itself, in our analyses we calculated the heat flux transferred from heater to fluid by subtracting from Qe the heat absorbed by heating section as
q¼
1 ðQ qs V s cs DT_ s Þ; As e
where As and Vs represent the surface area and volume of the heating section, respectively, qs and cs are the density and specific heat of stycast 2850FT, and DT_ s represents the increase rate of Twx. It was found that the heater consumed 0.4–0.7% of Qe to heat itself up. Fig. 4 shows the time variations of local temperatures of heater surface and fluid in natural convection in subcooled LN2 with Qe = 20 W. It is observed that immediately after the heater is turned on, temperature stratification develops axially on the heater, and the local temperatures of heated surface and ambient LN2 almost linearly increase keeping their differences constant until bubbles rise. Fig. 5 shows how the differences between Twx and T1x change with time, revealing the relative magnitudes of local heat transfer coefficients hx: the smaller Twx T1x, the larger hx. It is seen in Fig. 5 that Twx T1x remain essentially constant after about 6 min from the start of measurement. This quasi-steady state [13] lasts until bubbles start to form near x = 72 mm when the value of T w5 T 15 starts to decrease (see the distribution of Twx T1x at 22 min in Fig. 5). Once LN2 begins boiling, local temperature differences Twx T1x drastically decrease (and thus hx increase), entering a nucleate boiling regime (see the distribution of Twx T1x at 32 min in Fig. 5). The quasi-steady state region is enclosed by the parallelogram in Fig. 4. Although we stated that the quasi-steady state regime began after 6 min in Fig. 4, the axial distribution of Twx T1x is found to be very close to that in the quasi-steady state about one minute after the heater is on (the distribution of Twx T1x at 2 min in Fig. 5), indicating the quick development of boundary layer on the heater surface. The time variations of Twx and T1x in the case of the heater immersed in SlN2 with heating power Qe = 20 W are presented in
70
Tw1 Tw1 T∞1 T∞1
60
Tw 4 Tw4 T∞ 4 T∞4
Tw3 Tw3 T∞ 3 T∞3
Tw5 TW5 T∞5 T∞5
78
50
temperature [K]
x [mm]
T Tw2 w2 T T∞2 ∞2
80
heat flux q = 737 W/m2
40
ð5Þ
heater surface
30 20
76 74 72 70 68 66
10 0 0.0
bubbles observed
64 62 0.5
1.0
1.5
2.0
δ [mm] Fig. 3. The calculated values of boundary layer thickness d for the natural convection from the vertical cylindrical heater to subcooled liquid nitrogen using Eq. (1). In the calculation the heat flux from the heater is 737 W/m2 (heating power = 10 W), and the temperature of liquid nitrogen beyond d is 65 K.
0 Heater 5 turned on (20 W)
10
15
20
25
30
35
time [min]
Fig. 4. Time variations of temperatures of heater surface and ambient LN2 with heating power Qe = 20 W. The cylindrical heater is initially immersed in subcooled liquid nitrogen. The heater is turned on one minute after the start of measurement. The quasi-steady state regime is enclosed by the dotted parallelogram.
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Y. Lee, M. Ikeuchi / Cryogenics 71 (2015) 76–81
80 70
x[mm]
60
T∞5
50 40 30 20
T∞4
10 0 0
1
2
3
4
5
6
7
Tw-T∞ [°C] Fig. 5. Time evolution of Twi T1i (i = 1, . . . , 5) in Fig. 4. The distributions of Twi T1i in the quasi-steady state are represented by solid lines.
Tw 2 T∞ 2
Tw1 T∞1
Tw3 T∞ 3
Tw5 T∞ 5
Tw 4 T∞ 4
Fig. 7. Image of the cylindrical heater in SlN2 at a time between t15 and t14 in Fig. 6. The thermocouple for measuring T15 is apparently revealed from the layer of solid nitrogen particles, while there remain some solid nitrogen particles about the thermocouple for measuring T14.
80 78
temperature [K]
Tðr; tÞ ¼ 63:2 K for r > sðtÞ and t > 0
74
Kq
72
dsðtÞ dt
¼ j
@Tðr;tÞ @r
for t > 0
70
with an initial condition
68
sðt ¼ 0Þ ¼ 0
66
and boundary conditions
64 62 60
9
qcp @Tðr;tÞ ¼ j @r@ r @Tðr;tÞ for 0 < r < sðtÞ and t > 0 > > @t @r =
76
t∞ 5 t∞ 3 t∞ 2 t∞ 4
0 Heater 5 turned on (20 W)
bubbles observed
t∞1
10
15
20
25
all solid N2 melted away
30
35
40
time [min]
Fig. 6. Time variations of temperatures of heater surface and ambient SlN2 with heating power Qe = 20 W. The cylindrical heater is initially immersed in slush nitrogen with all thermocouples buried in solid nitrogen particles. The heater is turned on two minutes after the start of measurement. t1i, i = 1, . . . , 5 denote the times when thermocouple for measuring T1i have apparently emerged from the layer of solid nitrogen particles. The quasi-steady state regime is enclosed by the dotted parallelogram.
Fig. 6. We denote by t1i the time when the thermocouple for measuring T1i with i = 1–5 has clearly come into view with no solid nitrogen particles around it (see Fig. 7 for example). While Twi, i = 1, ... , 5 rapidly increase as soon as the heater is turned on, T1i are observed to remain at the melting point 63.2 K until the thermocouples for measuring T1i are exposed from the layer of solid nitrogen particles. As the solid nitrogen particles surrounding the thermocouples are removed, the flow of fluid around the thermocouples is facilitated by natural convection, building up the boundary layer. Consequently the local fluid temperatures swiftly rise up to catch up with the temperature of ambient liquid nitrogen (for example, see the circled area in Fig. 6). We compared the increase rates of Twx in SlN2 with its solid component in close proximity to the heater with those in solid nitrogen undergoing solid–liquid phase change known as the one-dimensional Stefan problem [14]. Since heat transfer in Stefan problems is driven by conduction and melting, the equations for temperature T and melting front s of melting solid nitrogen in contact with a cylindrical heater with constant heat flux q are given by
j
@Tðr; tÞ jr¼0 ¼ q for t > 0; @r
j
@Tðr; tÞ jr¼rD ¼ 0 for t > 0; @r
> > ;
ð6Þ
where r represents a radial distance from the heater surface, t denotes elapsed time from the heater being turned on, q and cp are the density and heat capacity of liquid nitrogen, respectively, K is the latent heat of fusion of nitrogen, and rD is the radial distance between the heater and dewar. Physical properties of nitrogen were evaluated by engineering software GASPAK [15], and Eq. (6) was solved using the Crank-Nicholson method [16]. The calculated temperatures of heated surface in melting solid nitrogen with Qe = 20 W are plotted in Fig. 8, being compared with Twi, i = 1, . . . , 5 in Fig. 6. It is found that Twi increase at much slower rates than in melting solid nitrogen involving melting and conduction processes, which implies that convection is locally effective due to microcirculation in the porous medium of solid nitrogen particles. Fig. 9 shows the differences between Twx and T1x in Fig. 6 at various times. It is obvious that the local heat transfer improves when the surrounding solid nitrogen particles disappear and natural convection flow fully develops. The values of Twx T1x become practically static, a few minutes after the solid–liquid interface falls below the leading edge of the heating section. It is also worth noting that the maxima of Twx T1x (or minima of hx) at t = t1i, i = 1, . . . , 5 correspond to Twi T1i (or hi). We calculated local heat transfer coefficients in quasi-steady states for SlN2 and LN2 using
hi ¼
q : T wi T 1i
are The results are given in Table 1, and their average values h compared in Fig. 10 which are obtained by
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Y. Lee, M. Ikeuchi / Cryogenics 71 (2015) 76–81
Stefan Pr fan Pr (calculated) lculated)
Tw1 TW1
Tw4 TW
Tw3 TW3
TW2 Tw2
SlN2 SlN 2
Tw5
80
350
72
[W/m2 K]
300
70
h
78
150
76 74
T [K]
LN22 LN
400
68
329.198 329.2
318.938 318.9
351.032 351.0 312.518 312.5
332.5 332.5
282.6 282.602
250 200
100
66
50
64
0
62
Q5W e= 5 W
60 0
10
20
30
40
50
Q20W e = 20 W
Q10W e = 10 W
60 Fig. 10. Comparison of average heat transfer coefficients for a vertical cylinder in slush and subcooled liquid nitrogen.
t [s] Fig. 8. Comparison of temperatures of heated surface in melting solid nitrogen (solid line) and Twi, i = 1, . . . , 5 in Fig. 6 (dotted lines). The heater is turned on with heating power = 20 W at t = 0.
SlN SlN2 2 2.6
LN2 LN2
SlN2:Nu xf = 0.69(Gr*x Pr f )
2.4
0.2
2.2
log Nu xf
80 70
x [mm]
60
2
SlN2: Nu xf = 1.04(Grx* Pr f )
0.18
1.8 1.6
50
1.4
40
1.2
30
1
water
6
7
8
20
9
10
11
12
13
14
log Gr*x Prf
10 Fig. 11. Log–log plots of Nuxf versus Gr x Pr f for a vertical cylinder in slush and subcooled nitrogen (3 106 < Gr x < 1011). Fitted curves for SlN2 using Eq. (7) and correlation for water are also plotted. Fitted curves for subcooled LN2 are omitted, as they are very close to the correlation for water.
0 0
1
2
3
4
5
6
7
Tw-T∞ [°C] Fig. 9. Time evolution of Twi T1i (i = 1, . . . , 5) in Fig. 6. The distributions of Twx T1x in the quasi-steady state are represented by solid lines.
¼1 h L
Table 2 The results of least squares fits to data in Fig. 11 using Eq. (7). Numbers in parentheses are values obtained from least squares fitting with m set to 0.2.
5 X h i Dxi i¼1
c m
with Dxi = 16 mm being the span of the ith temperature measure for SlN are found to be 5–12% larger than for subment section. h 2 cooled LN2, although the degree of enhancement in heat transfer decreases with the increase of heat load. It is quite clear that the solid nitrogen particles deposited at the bottom of the vessel improve natural convection heat transfer. Since no apparent motion of solid particles was observed during heat transfer measurements, we infer that the temperature gradient between solid and liquid nitrogen may encourage natural convection flow.
SlN2
LN2
Water
1.04 (0.69) 0.18 (0.20)
0.90 (0.63) 0.19 (0.20)
0.60 0.20
The following functional form including a modified Grashof number Gr⁄ is extensively used to obtain correlation for heat transfer with constant heat fluxes [11,13,17,18], m
Nuxf ¼ cðGrx Prf Þ ;
ð7Þ
where c and m are constants to be determined, and all the related properties in Eq. (7) are evaluated at local film temperatures.
Table 1 Local heat transfer coefficients for the vertical cylinder in slush and subcooled liquid nitrogen (unit: W/m2 K). x (mm)
8 24 40 56 72
SlN2
LN2
Qe = 5 W
Qe = 10 W
Qe = 20 W
Qe = 5 W
Qe = 10 W
Qe = 20 W
441.7 327.7 303.6 253.9 267.9
464.2 329.1 318.5 262.3 272.0
522.8 336.8 322.3 284.1 289.1
415.8 273.6 271.3 229.4 222.9
457.6 301.8 276.1 246.2 280.9
484.9 321.3 299.5 272.7 284.2
Y. Lee, M. Ikeuchi / Cryogenics 71 (2015) 76–81
Fig. 11 shows the local heat transfer correlations for SlN2 and LN2 obtained from the data in quasi-steady states for Qe = 5, 10 and 20 W (3 106 < Grx < 1011). The empirical correlation for water, Eq. (4) is also plotted for comparison. Values of c and m are determined by least squares fit, and their fitted values are presented in Table 2. The results indicate that Eq. (4) applies to subcooled LN2 in the laminar region, although it has already been reported that subcooled LN2 in forced convection obeys the conventional Colburn equation [1]. As for SlN2, the local Nusselt numbers are about 10% larger compared with subcooled LN2 due to the enhancement in heat transfer as discussed above. Although Nuxf are shifted upwards relative to those for LN2 in Fig. 11, the natural convection in SlN2 still displays the characteristics of laminar flow (m 0.2). 4. Summary We have investigated natural convection heat transfer from a vertical cylinder to SlN2 and subcooled LN2 with constant heat fluxes in laminar flow range and confirmed advantages of SlN2 over LN2. It has been observed that the local temperatures of heated surface surrounded by solid nitrogen particles increase at much slower rates than in subcooled LN2, demonstrating the increased cooling capacity of SlN2 due to the latent heat of fusion of solid nitrogen. After the heated surface completely emerges from solid nitrogen particles, entering the fully developed natural convection regime, average heat transfer coefficients for SlN2 are observed to be somewhat (5–12% in this work) larger than for LN2, while the improvement in heat transfer is larger for lower Gr x . We infer that the large temperature gradient caused by solid nitrogen particles deposited at the bottom may facilitate natural convection flow, although further research is needed to clarify the effect of solid particles in SlN2 on natural convection. We have also found that the presence of solid nitrogen particles near the heated surface does not discourage local convection due to the porous nature of SlN2, making the heat transfer in SlN2 better than in melting solid nitrogen involving melting and conduction processes. Acknowledgments We are deeply grateful to Dr. S. Fuchino, National Institute of Advanced Industrial Science & Technology, Japan for offering us a
81
glass dewar as well as useful discussion and also express our sincere thanks to Dr. M. Murakami, honorary professor of University of Tsukuba, Japan for helpful advice. References [1] Matsuo K, Ikeuchi M, Machida A, Yasuda K. Fundamental study of pipe flow and heat transfer characteristics of slush nitrogen. Adv Cryog Eng 2006;51:1033–40. [2] Ikeuchi M, Machida A, Ono R, Matsuo K. Fundamental study of heat transfer characteristics of flowing slush nitrogen. Teion Kogaku 2007;42:96–101 [in Japanese]. [3] Fuchino S. Dielectric breakdown characteristics of slush nitrogen. National Convention Record IEE Japan: No. 5-133; 2009 [in Japanese]. [4] Uryu T, et al. Experiment on overcurrent characteristics of HTS tapes in slush nitrogen. National Convention Record IEE Japan: No. 5-134; 2009 [in Japanese]. [5] Momotari H, et al. Numerical simulation on over-current characteristics of HTS tapes in slush nitrogen. National Convention Record IEE Japan: No. 5-135; 2009 [in Japanese]. [6] Schwenterly B, Pleva E. HTS transformer development. Presentation for DOE peer review; 2010, June 30. [7] Takakoshi T, Murakami M, Ikeuchi M, Matsuo K, Tsukahara R. PIV measurement of slush nitrogen flow in a pipe. Adv Cryog Eng 2006;51:1025–32. [8] Ohira K, Nakagomi K, Takahashi N. Pressure-drop reduction and heat-transfer deterioration of slush nitrogen in horizontal pipe flow. Cryogenics 2011;51:563–74. [9] Ohira K, Ota A, Mukai Y, Hosono T. Numerical study of flow and heat-transfer characteristics of cryogenic slush fluid in a horizontal circular pipe (SLUSH3D). Cryogenics 2012;52:428–40. [10] Haberbusch MS, McNelis NB. Comparison of the continuous freeze slush hydrogen technique to the freeze/thaw Tecjnique. NASA Technical Memorendum; 1996. p. 10732. [11] Holman JP. Heat transfer. 5th ed. International: McGraw-Hill Book Co.; 1981 [chapter 7]. [12] Gebhart B. Heat transfer. 2nd ed. New York: McGraw-Hill Book Co; 1970 [chapter 8]. [13] Fujii T, Takeuchi M, Fujii M, Suzaki K, Uehara H. Experiments on naturalconvection heat transfer from the outer surface of a vertical cylinder to liquids. Int J Heat Mass Transfer 1970;13:753–87. [14] Alexiades V, Solomon AD. Mathematical modeling of melting and freezing processes: basic concepts and applications. Taylor & Francis; 1992. [15] GASPAK v3.32. Colorado, Horizon Technologies; 1999. [16] Press WH, Teukolosky SA, Vetterling WT, Flannery BP. Numerical recipes in FORTRAN. 2nd ed. Cambridge University Press; 1994 [chapter 19]. [17] Globe S, Dropkin D. Natural convection heat transfer in liquids confined by two horizontal plates and heated from below. Trans ASME J Heat Transfer 1959;81:24–8. [18] Metais B, Eckert ERG. Forced, mixed and free convection regimes. Trans ASME J Heat Transfer 1964;86:295–6.
Contents lists available at ScienceDirect
Cryogenics journal homepage: www.elsevier.com/locate/cryogenics
Experimental study of laminar natural convection heat transfer from a vertical cylinder to slush nitrogen under constant heat flux conditions Yoonseok Lee, Masamitsu Ikeuchi ⇑ Mayekawa Mfg. Co., Ltd., 2000 Tatsuzawa, Moriya City, Ibaraki 302-0118, Japan
a r t i c l e
i n f o
Article history: Received 27 November 2014 Received in revised form 9 May 2015 Accepted 19 May 2015
Keywords: Slush nitrogen Natural convection Heat transfer coefficient
a b s t r a c t Natural convection heat transfer from a vertical cylinder immersed in slush and subcooled liquid nitrogen and subjected to constant heat fluxes was investigated in order to determine the relative merits of slush nitrogen (SlN2) for immersion cooling. A glass dewar was used as a test vessel in which a cylindrical heater was mounted vertically, and heat transfer measurements were carried out for SlN2 and subcooled liquid nitrogen (LN2) in the laminar flow range. The results revealed advantages of SlN2 over subcooled LN2 in natural convection cooling. The local temperatures of the heated surface surrounded by solid nitrogen particles are measured to increase at much slower rates than in subcooled LN2, which is due to the latent heat of fusion of solid nitrogen. Even after the solid nitrogen particles surrounding the heater are apparently depleted, the average heat transfer coefficients for SlN2 are still found to be greater than those for LN2 with the improvement in heat transfer being larger for lower Grashof number regime. Our analysis also indicates that solid nitrogen particles in close proximity to heated surface do not discourage local convection due to the porous nature of SlN2, making the heat transfer in SlN2 more effective than in the case of solid–liquid phase change of nitrogen involving melting and conduction processes. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Slush nitrogen (SlN2) is a two-phase fluid consisting of fine solid nitrogen particles and liquid nitrogen (LN2). Since 2000 we have studied methods for generating and transporting SlN2 [1] and investigated the flow friction and heat transfer characteristics of SlN2 in a pipe [2] in an attempt to develop a refrigeration system for high temperature superconducting (HTS) power cables. This work confirmed the advantage of solid nitrogen particles in stabilizing the fluid temperature but also revealed the problem of pressure loss increasing with the solid mass fraction of SlN2. It has been recently reported that SlN2 has the same dielectric strength as LN2 [3] and improves overcurrent characteristics of HTS wire, by providing greater stability against thermal runaway, than is obtained with subcooled LN2 [4,5]. To extend the application of SlN2 we have investigated the possible advantages of SlN2 for immersion cooling. The target application is the cooling of HTS transformers using SlN2 as a substitute for subcooled LN2 [6]. Although some work has been done to investigate forced convection characteristics of SlN2 [7–9], little has been done to study natural convection in SlN2 despite its potential applicability, and
⇑ Corresponding author. http://dx.doi.org/10.1016/j.cryogenics.2015.05.008 0011-2275/Ó 2015 Elsevier Ltd. All rights reserved.
it is still unclear what effect solid nitrogen particles have on flow and heat transfer. In this work we investigate natural convection heat transfer from a vertical cylinder to SlN2 and LN2, examining the applicability of SlN2 to immersion cooling system for HTS coils and trying to understand the effects of solid nitrogen particles on natural convection heat transfer.
2. Experimental details The experimental setup consists of a test vessel, a vacuum pump, an agitating unit, and heating and measuring systems as illustrated in Fig. 1. A glass dewar measuring 750 mm long and 150 mm in diameter is used as a test vessel in which a cylindrical heater is installed vertically so that it can be immersed in SlN2 or subcooled LN2. Liquid nitrogen is filled up to the upper boundary of the viewing section and cooled by depressurization. To evacuate nitrogen vapor from the vessel an oil rotary vacuum pump with a discharge rate of 0.6 m3/min is used. SlN2 is generated in the vessel using the freeze–thaw method [1,10]. In producing SlN2, an agitator with four blades is rotated at 60 rpm to break and evenly distribute lumps of solid nitrogen falling from the liquid–vapor interface. A cylindrical heater 100 mm long and 54 mm in diameter was made by winding manganin wire around an FRP bobbin as shown
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φ 190 φ 150
vacuum pump
d ¼ 3:93Pr 1=2 ð0:952 þ PrÞ1=4 Gr1=4 ; x x
motor flange
where x denotes an axial distance from the leading edge of the heating section, Pr and Gr are the Prantl and Grashof numbers respectively, and subscript x indicates that the quantity is local. It is known that as long as the thickness of boundary layer is not large compared with the diameter of cylinder, the correlation for the natural convection heat transfer for vertical plates can be applied to vertical cylinders if the following condition is met [12],
DC power supply
logger Ag plated
FRP support FRP support
FRP disk
750
K-type thermocouples
300
viewing section
D 35 P 1=4 ; L GrL
FRP support
heater
agitator
Fig. 1. Schematic diagrams of the test vessel (left) and experimental setup (right). Lengths are in millimeters.
ð2Þ
where D and L denote the diameter and height of cylinder, and GrL is the Grashof number at height L. In this experiment, D = 54 mm, L = 80 mm and GrL < 1.26 1011, satisfying Eq. (2). To evaluate Pr and Gr in Eq. (1) it is necessary to know temperatures of heater surface and fluid. To find the local temperature of heater surface Twx for given heat flux q and ambient fluid temperature T1x we used the relation
T wx ¼ T 1x þ in Fig. 2. Enameled manganin wire with an end-to-end resistance of 50 X and a diameter of 0.2 mm was helically wound around the bobbin core with equal spacing (7.5 mm). The manganin wire was fixed on the bobbin core by electrically insulative material (varnish). Five K-type thermocouples with a diameter of 0.5 mm were then mounted axially spacing 16 mm apart avoiding contacting the manganin wire, on which varnish was applied. After mounting the thermocouples, the bobbin core was coated with thermally conductive epoxy (stycast 2850FT), filling up the gaps between the core and flanges (see Fig. 2) to uniformly produce heat over the heating section. Electric power is supplied to the heater by a regulated DC power supply with a maximum power of 100 W. To measure fluid temperature five thermocouples are used which are of the same type as used on the heater. They are placed at the same axial distances as those on the heater and at a radial distance greater than the thickness of boundary layer. We calculated boundary layer thickness d for the heater using the following equation for d for vertical plates [11]
q ; hx
ð3Þ
where hx denotes a local heat transfer coefficient and is obtained using an empirical correlation [11] given by
Nuxf ¼
hx x
jxf
( ¼
1=5 0:6 Grx Pr f 1=4 0:17 Gr x Prf
5
for 10 < Grx < 1011 for 2 1013 < Grx Pr f < 1016
ð4Þ where Nu represents the Nusselt number, Gr is a modified Grashof number given by
Gr ¼ Gr Nu; and j denotes the thermal conductivity of fluid with subscript f implying that the related properties are evaluated at film tempera1 . Although Eq. (4) was obtained for natural convecture T f ¼ T w þT 2 tion in water, it is also well suited for liquid nitrogen, as will be discussed in Section 3. Since Twx and Nuxf are interdependent, Eqs. (3) and (4) need to be simultaneously solved. We thus iteratively calculated Eqs. (3) and (4) until the average temperature of the
54
10
Tw5
72
80
heating T w3 area (stycast)
56
80
100
Tw 4
1
Tw1
40
Tw 2
24
100
FRP
10
;
*
8
770
vacuum glass dewar
ð1Þ
15 54 Fig. 2. Schematic diagrams of the bobbin used as the body of heater (left) and heater with thermocouples set on it (right). Lengths are in millimeters.
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Y. Lee, M. Ikeuchi / Cryogenics 71 (2015) 76–81
heater surface converged within 0.0001 K. We evaluated d for the heater in subcooled LN2 with heating power 620 W (q 6 1474 W/m2) according to our experimental conditions. As an example, calculated d for T1x = 65 K and q = 737 W/m2 is presented in Fig. 3. The calculations indicate that the values of d in our experiment do not exceed 2 mm. Considering that the average size of solid nitrogen particles created by the freeze–thaw method described above is about 1.4 mm [1], we set thermocouples for measuring T1x 20 mm away from the heater surface so that solid nitrogen particles may fill the space between the heater and the thermocouples. Since the thermocouples have an uncertainty of ±1.5%, each thermocouple is calibrated such that the triple-point temperature is 63.15 K and the saturation temperature at atmospheric pressure is 77.3 K. In the following, we denote the temperatures of heater surface and ambient fluid at five different axial distances in the order of increasing height as Tw1 to Tw5 and T11 to T15, respectively and the corresponding local heat transfer coefficients as h1 to h5. Natural convection heat transfer measurements are carried out with constant heat fluxes at 1 atm. In the experiment of natural convection in SlN2, SlN2 is generated with the agitator rotating at 60 rpm until the heater is completely buried in solid nitrogen particles (mass fraction 20%), and the agitator is stopped, when SlN2 generation is finished. After the solid nitrogen particles settle down, the vessel is pressurized up to 1 atm by injecting helium gas and then maintained at atmospheric pressure. The temperatures of heater surface and fluid are recorded once per second. The heater is turned on one or two minutes after the start of temperature measurement, and the measurement continues until the fluid in the vessel reaches the saturation temperature. In the case of natural convection in subcooled LN2, LN2 is cooled to the triple point by depressurization. To stabilize the temperatures of heater and fluid at the triple point a small amount of solid nitrogen particles are produced. After solid nitrogen particles melt away, the vessel is pressurized and brought under atmospheric pressure, following the same procedure as for SlN2.
90 −1/2
δ = 3.93xPr 80
(0.952+ Pr) Gr−x 1/4 1 /4
3. Results and discussion To observe laminar natural convection flows of LN2 and SlN2 we applied heater powers of Qe = 5, 10 and 20 W which cause meaningful differences in temperature between the heater surface and fluid. Since some of electric power supplied to heater goes into warming the heater itself, in our analyses we calculated the heat flux transferred from heater to fluid by subtracting from Qe the heat absorbed by heating section as
q¼
1 ðQ qs V s cs DT_ s Þ; As e
where As and Vs represent the surface area and volume of the heating section, respectively, qs and cs are the density and specific heat of stycast 2850FT, and DT_ s represents the increase rate of Twx. It was found that the heater consumed 0.4–0.7% of Qe to heat itself up. Fig. 4 shows the time variations of local temperatures of heater surface and fluid in natural convection in subcooled LN2 with Qe = 20 W. It is observed that immediately after the heater is turned on, temperature stratification develops axially on the heater, and the local temperatures of heated surface and ambient LN2 almost linearly increase keeping their differences constant until bubbles rise. Fig. 5 shows how the differences between Twx and T1x change with time, revealing the relative magnitudes of local heat transfer coefficients hx: the smaller Twx T1x, the larger hx. It is seen in Fig. 5 that Twx T1x remain essentially constant after about 6 min from the start of measurement. This quasi-steady state [13] lasts until bubbles start to form near x = 72 mm when the value of T w5 T 15 starts to decrease (see the distribution of Twx T1x at 22 min in Fig. 5). Once LN2 begins boiling, local temperature differences Twx T1x drastically decrease (and thus hx increase), entering a nucleate boiling regime (see the distribution of Twx T1x at 32 min in Fig. 5). The quasi-steady state region is enclosed by the parallelogram in Fig. 4. Although we stated that the quasi-steady state regime began after 6 min in Fig. 4, the axial distribution of Twx T1x is found to be very close to that in the quasi-steady state about one minute after the heater is on (the distribution of Twx T1x at 2 min in Fig. 5), indicating the quick development of boundary layer on the heater surface. The time variations of Twx and T1x in the case of the heater immersed in SlN2 with heating power Qe = 20 W are presented in
70
Tw1 Tw1 T∞1 T∞1
60
Tw 4 Tw4 T∞ 4 T∞4
Tw3 Tw3 T∞ 3 T∞3
Tw5 TW5 T∞5 T∞5
78
50
temperature [K]
x [mm]
T Tw2 w2 T T∞2 ∞2
80
heat flux q = 737 W/m2
40
ð5Þ
heater surface
30 20
76 74 72 70 68 66
10 0 0.0
bubbles observed
64 62 0.5
1.0
1.5
2.0
δ [mm] Fig. 3. The calculated values of boundary layer thickness d for the natural convection from the vertical cylindrical heater to subcooled liquid nitrogen using Eq. (1). In the calculation the heat flux from the heater is 737 W/m2 (heating power = 10 W), and the temperature of liquid nitrogen beyond d is 65 K.
0 Heater 5 turned on (20 W)
10
15
20
25
30
35
time [min]
Fig. 4. Time variations of temperatures of heater surface and ambient LN2 with heating power Qe = 20 W. The cylindrical heater is initially immersed in subcooled liquid nitrogen. The heater is turned on one minute after the start of measurement. The quasi-steady state regime is enclosed by the dotted parallelogram.
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Y. Lee, M. Ikeuchi / Cryogenics 71 (2015) 76–81
80 70
x[mm]
60
T∞5
50 40 30 20
T∞4
10 0 0
1
2
3
4
5
6
7
Tw-T∞ [°C] Fig. 5. Time evolution of Twi T1i (i = 1, . . . , 5) in Fig. 4. The distributions of Twi T1i in the quasi-steady state are represented by solid lines.
Tw 2 T∞ 2
Tw1 T∞1
Tw3 T∞ 3
Tw5 T∞ 5
Tw 4 T∞ 4
Fig. 7. Image of the cylindrical heater in SlN2 at a time between t15 and t14 in Fig. 6. The thermocouple for measuring T15 is apparently revealed from the layer of solid nitrogen particles, while there remain some solid nitrogen particles about the thermocouple for measuring T14.
80 78
temperature [K]
Tðr; tÞ ¼ 63:2 K for r > sðtÞ and t > 0
74
Kq
72
dsðtÞ dt
¼ j
@Tðr;tÞ @r
for t > 0
70
with an initial condition
68
sðt ¼ 0Þ ¼ 0
66
and boundary conditions
64 62 60
9
qcp @Tðr;tÞ ¼ j @r@ r @Tðr;tÞ for 0 < r < sðtÞ and t > 0 > > @t @r =
76
t∞ 5 t∞ 3 t∞ 2 t∞ 4
0 Heater 5 turned on (20 W)
bubbles observed
t∞1
10
15
20
25
all solid N2 melted away
30
35
40
time [min]
Fig. 6. Time variations of temperatures of heater surface and ambient SlN2 with heating power Qe = 20 W. The cylindrical heater is initially immersed in slush nitrogen with all thermocouples buried in solid nitrogen particles. The heater is turned on two minutes after the start of measurement. t1i, i = 1, . . . , 5 denote the times when thermocouple for measuring T1i have apparently emerged from the layer of solid nitrogen particles. The quasi-steady state regime is enclosed by the dotted parallelogram.
Fig. 6. We denote by t1i the time when the thermocouple for measuring T1i with i = 1–5 has clearly come into view with no solid nitrogen particles around it (see Fig. 7 for example). While Twi, i = 1, ... , 5 rapidly increase as soon as the heater is turned on, T1i are observed to remain at the melting point 63.2 K until the thermocouples for measuring T1i are exposed from the layer of solid nitrogen particles. As the solid nitrogen particles surrounding the thermocouples are removed, the flow of fluid around the thermocouples is facilitated by natural convection, building up the boundary layer. Consequently the local fluid temperatures swiftly rise up to catch up with the temperature of ambient liquid nitrogen (for example, see the circled area in Fig. 6). We compared the increase rates of Twx in SlN2 with its solid component in close proximity to the heater with those in solid nitrogen undergoing solid–liquid phase change known as the one-dimensional Stefan problem [14]. Since heat transfer in Stefan problems is driven by conduction and melting, the equations for temperature T and melting front s of melting solid nitrogen in contact with a cylindrical heater with constant heat flux q are given by
j
@Tðr; tÞ jr¼0 ¼ q for t > 0; @r
j
@Tðr; tÞ jr¼rD ¼ 0 for t > 0; @r
> > ;
ð6Þ
where r represents a radial distance from the heater surface, t denotes elapsed time from the heater being turned on, q and cp are the density and heat capacity of liquid nitrogen, respectively, K is the latent heat of fusion of nitrogen, and rD is the radial distance between the heater and dewar. Physical properties of nitrogen were evaluated by engineering software GASPAK [15], and Eq. (6) was solved using the Crank-Nicholson method [16]. The calculated temperatures of heated surface in melting solid nitrogen with Qe = 20 W are plotted in Fig. 8, being compared with Twi, i = 1, . . . , 5 in Fig. 6. It is found that Twi increase at much slower rates than in melting solid nitrogen involving melting and conduction processes, which implies that convection is locally effective due to microcirculation in the porous medium of solid nitrogen particles. Fig. 9 shows the differences between Twx and T1x in Fig. 6 at various times. It is obvious that the local heat transfer improves when the surrounding solid nitrogen particles disappear and natural convection flow fully develops. The values of Twx T1x become practically static, a few minutes after the solid–liquid interface falls below the leading edge of the heating section. It is also worth noting that the maxima of Twx T1x (or minima of hx) at t = t1i, i = 1, . . . , 5 correspond to Twi T1i (or hi). We calculated local heat transfer coefficients in quasi-steady states for SlN2 and LN2 using
hi ¼
q : T wi T 1i
are The results are given in Table 1, and their average values h compared in Fig. 10 which are obtained by
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Y. Lee, M. Ikeuchi / Cryogenics 71 (2015) 76–81
Stefan Pr fan Pr (calculated) lculated)
Tw1 TW1
Tw4 TW
Tw3 TW3
TW2 Tw2
SlN2 SlN 2
Tw5
80
350
72
[W/m2 K]
300
70
h
78
150
76 74
T [K]
LN22 LN
400
68
329.198 329.2
318.938 318.9
351.032 351.0 312.518 312.5
332.5 332.5
282.6 282.602
250 200
100
66
50
64
0
62
Q5W e= 5 W
60 0
10
20
30
40
50
Q20W e = 20 W
Q10W e = 10 W
60 Fig. 10. Comparison of average heat transfer coefficients for a vertical cylinder in slush and subcooled liquid nitrogen.
t [s] Fig. 8. Comparison of temperatures of heated surface in melting solid nitrogen (solid line) and Twi, i = 1, . . . , 5 in Fig. 6 (dotted lines). The heater is turned on with heating power = 20 W at t = 0.
SlN SlN2 2 2.6
LN2 LN2
SlN2:Nu xf = 0.69(Gr*x Pr f )
2.4
0.2
2.2
log Nu xf
80 70
x [mm]
60
2
SlN2: Nu xf = 1.04(Grx* Pr f )
0.18
1.8 1.6
50
1.4
40
1.2
30
1
water
6
7
8
20
9
10
11
12
13
14
log Gr*x Prf
10 Fig. 11. Log–log plots of Nuxf versus Gr x Pr f for a vertical cylinder in slush and subcooled nitrogen (3 106 < Gr x < 1011). Fitted curves for SlN2 using Eq. (7) and correlation for water are also plotted. Fitted curves for subcooled LN2 are omitted, as they are very close to the correlation for water.
0 0
1
2
3
4
5
6
7
Tw-T∞ [°C] Fig. 9. Time evolution of Twi T1i (i = 1, . . . , 5) in Fig. 6. The distributions of Twx T1x in the quasi-steady state are represented by solid lines.
¼1 h L
Table 2 The results of least squares fits to data in Fig. 11 using Eq. (7). Numbers in parentheses are values obtained from least squares fitting with m set to 0.2.
5 X h i Dxi i¼1
c m
with Dxi = 16 mm being the span of the ith temperature measure for SlN are found to be 5–12% larger than for subment section. h 2 cooled LN2, although the degree of enhancement in heat transfer decreases with the increase of heat load. It is quite clear that the solid nitrogen particles deposited at the bottom of the vessel improve natural convection heat transfer. Since no apparent motion of solid particles was observed during heat transfer measurements, we infer that the temperature gradient between solid and liquid nitrogen may encourage natural convection flow.
SlN2
LN2
Water
1.04 (0.69) 0.18 (0.20)
0.90 (0.63) 0.19 (0.20)
0.60 0.20
The following functional form including a modified Grashof number Gr⁄ is extensively used to obtain correlation for heat transfer with constant heat fluxes [11,13,17,18], m
Nuxf ¼ cðGrx Prf Þ ;
ð7Þ
where c and m are constants to be determined, and all the related properties in Eq. (7) are evaluated at local film temperatures.
Table 1 Local heat transfer coefficients for the vertical cylinder in slush and subcooled liquid nitrogen (unit: W/m2 K). x (mm)
8 24 40 56 72
SlN2
LN2
Qe = 5 W
Qe = 10 W
Qe = 20 W
Qe = 5 W
Qe = 10 W
Qe = 20 W
441.7 327.7 303.6 253.9 267.9
464.2 329.1 318.5 262.3 272.0
522.8 336.8 322.3 284.1 289.1
415.8 273.6 271.3 229.4 222.9
457.6 301.8 276.1 246.2 280.9
484.9 321.3 299.5 272.7 284.2
Y. Lee, M. Ikeuchi / Cryogenics 71 (2015) 76–81
Fig. 11 shows the local heat transfer correlations for SlN2 and LN2 obtained from the data in quasi-steady states for Qe = 5, 10 and 20 W (3 106 < Grx < 1011). The empirical correlation for water, Eq. (4) is also plotted for comparison. Values of c and m are determined by least squares fit, and their fitted values are presented in Table 2. The results indicate that Eq. (4) applies to subcooled LN2 in the laminar region, although it has already been reported that subcooled LN2 in forced convection obeys the conventional Colburn equation [1]. As for SlN2, the local Nusselt numbers are about 10% larger compared with subcooled LN2 due to the enhancement in heat transfer as discussed above. Although Nuxf are shifted upwards relative to those for LN2 in Fig. 11, the natural convection in SlN2 still displays the characteristics of laminar flow (m 0.2). 4. Summary We have investigated natural convection heat transfer from a vertical cylinder to SlN2 and subcooled LN2 with constant heat fluxes in laminar flow range and confirmed advantages of SlN2 over LN2. It has been observed that the local temperatures of heated surface surrounded by solid nitrogen particles increase at much slower rates than in subcooled LN2, demonstrating the increased cooling capacity of SlN2 due to the latent heat of fusion of solid nitrogen. After the heated surface completely emerges from solid nitrogen particles, entering the fully developed natural convection regime, average heat transfer coefficients for SlN2 are observed to be somewhat (5–12% in this work) larger than for LN2, while the improvement in heat transfer is larger for lower Gr x . We infer that the large temperature gradient caused by solid nitrogen particles deposited at the bottom may facilitate natural convection flow, although further research is needed to clarify the effect of solid particles in SlN2 on natural convection. We have also found that the presence of solid nitrogen particles near the heated surface does not discourage local convection due to the porous nature of SlN2, making the heat transfer in SlN2 better than in melting solid nitrogen involving melting and conduction processes. Acknowledgments We are deeply grateful to Dr. S. Fuchino, National Institute of Advanced Industrial Science & Technology, Japan for offering us a
81
glass dewar as well as useful discussion and also express our sincere thanks to Dr. M. Murakami, honorary professor of University of Tsukuba, Japan for helpful advice. References [1] Matsuo K, Ikeuchi M, Machida A, Yasuda K. Fundamental study of pipe flow and heat transfer characteristics of slush nitrogen. Adv Cryog Eng 2006;51:1033–40. [2] Ikeuchi M, Machida A, Ono R, Matsuo K. Fundamental study of heat transfer characteristics of flowing slush nitrogen. Teion Kogaku 2007;42:96–101 [in Japanese]. [3] Fuchino S. Dielectric breakdown characteristics of slush nitrogen. National Convention Record IEE Japan: No. 5-133; 2009 [in Japanese]. [4] Uryu T, et al. Experiment on overcurrent characteristics of HTS tapes in slush nitrogen. National Convention Record IEE Japan: No. 5-134; 2009 [in Japanese]. [5] Momotari H, et al. Numerical simulation on over-current characteristics of HTS tapes in slush nitrogen. National Convention Record IEE Japan: No. 5-135; 2009 [in Japanese]. [6] Schwenterly B, Pleva E. HTS transformer development. Presentation for DOE peer review; 2010, June 30. [7] Takakoshi T, Murakami M, Ikeuchi M, Matsuo K, Tsukahara R. PIV measurement of slush nitrogen flow in a pipe. Adv Cryog Eng 2006;51:1025–32. [8] Ohira K, Nakagomi K, Takahashi N. Pressure-drop reduction and heat-transfer deterioration of slush nitrogen in horizontal pipe flow. Cryogenics 2011;51:563–74. [9] Ohira K, Ota A, Mukai Y, Hosono T. Numerical study of flow and heat-transfer characteristics of cryogenic slush fluid in a horizontal circular pipe (SLUSH3D). Cryogenics 2012;52:428–40. [10] Haberbusch MS, McNelis NB. Comparison of the continuous freeze slush hydrogen technique to the freeze/thaw Tecjnique. NASA Technical Memorendum; 1996. p. 10732. [11] Holman JP. Heat transfer. 5th ed. International: McGraw-Hill Book Co.; 1981 [chapter 7]. [12] Gebhart B. Heat transfer. 2nd ed. New York: McGraw-Hill Book Co; 1970 [chapter 8]. [13] Fujii T, Takeuchi M, Fujii M, Suzaki K, Uehara H. Experiments on naturalconvection heat transfer from the outer surface of a vertical cylinder to liquids. Int J Heat Mass Transfer 1970;13:753–87. [14] Alexiades V, Solomon AD. Mathematical modeling of melting and freezing processes: basic concepts and applications. Taylor & Francis; 1992. [15] GASPAK v3.32. Colorado, Horizon Technologies; 1999. [16] Press WH, Teukolosky SA, Vetterling WT, Flannery BP. Numerical recipes in FORTRAN. 2nd ed. Cambridge University Press; 1994 [chapter 19]. [17] Globe S, Dropkin D. Natural convection heat transfer in liquids confined by two horizontal plates and heated from below. Trans ASME J Heat Transfer 1959;81:24–8. [18] Metais B, Eckert ERG. Forced, mixed and free convection regimes. Trans ASME J Heat Transfer 1964;86:295–6.