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Appendix A: Dimensional Equivalentsand Physical Constants
Dimensional Equivalents
Length 1ft ¼ 12 in: ¼ 30:48cm ¼ 0:3048
1m ¼ 100cm ¼ 39:37 in: ¼ 3:28ft
Mass 1 lbm ¼ 0:03108slug ¼ 453:59g ¼ 0:45359kg
1kg ¼ 100g ¼ 0:06852slug ¼ 2:205 lbm
Time 1h ¼ 3600s
1s ¼ 2:778� 10�4 h
Force 1 lbf ¼ 4:448� 105dyne ¼ 4:448N
1N ¼ 105 dyne ¼ 0:2249lbf
Angle 1 � ¼ 1:745� 10�2 rad
1rad ¼ 57:30 �
Temperature 1 �F ¼ 1� R ¼ 0:5556 � C ¼ 0:5556 � K
1 �K ¼� C ¼ 1:8 � R ¼ 1:8 � F�F ¼ 1:8 � Cþ 32�C ¼ 0:5556 �F� 32ð Þ�R ¼� Fþ 459:69�K ¼� Cþ 273:16�R ¼ 1:8 �K�K ¼ 0:5556 � R
Energy 1Btu ¼ 777:66ft lbf ¼ 252cal ¼ 1:054� 1010 erg ¼ 1054J
1J ¼ 107 erg ¼ 0:239cal ¼ 0:7375ft lbf ¼ 9:485� 10�4 Btu
Power 1Btu=h ¼ 2:778� 10�4 Btu=s ¼ 2:929� 106 erg=s ¼ 0:2929W
1W ¼ 107 erg=s ¼ 9:481� 10�4 Btu=s ¼ 3:414Btu=h
Pressure 1 lbf=ft2 ¼ 6:944� 10�3 lbf=in:2 ¼ 4:78:8dyne=cm2 ¼ 47:88N=m2
1lbf=in:2 ¼ 144 lbf=ft2 ¼ 68, 948dyne=cm2 ¼ 6894:8N=m2
1N=m2 ¼ 10dyne=cm2 ¼ 1:450� 10�4 lbf=in:2 ¼ 2:089� 10�2 lbf=ft2
(continued)
© Springer International Publishing Switzerland 2016
B. Zohuri, Heat Pipe Design and Technology, DOI 10.1007/978-3-319-29841-2451
Area 1ft2 ¼ 1:44 in:2 ¼ 929cm2 ¼ 0:0929m2
1m2 ¼ 104cm2 ¼ 1550 in2 ¼ 10:76ft2
Volume 1ft3 ¼ 1728 in:3 ¼ 2:832� 104 cm3 ¼ 0:02832m3
1m3 ¼ 106 cm3 ¼ 6:102 � 104 in:3 ¼ 35:31ft3
1gal US liquidð Þ ¼ 0:13368ft3 ¼ 0:003785m3
Density 1gal US liquidð Þ ¼ 0:13368ft3 ¼ 0:003785m3
1lbm=ft3 ¼ 0:03108slug=ft3 ¼ 1:602� 10�2 g=cm3 ¼ 16:02kg=m3
1kg=m3 ¼ 10�3 g=cm3 ¼ 0:00194slug=ft3 ¼ 0:06242 lbm=ft3
Viscosity (dynamic) 1 lbm=ft h ¼ 8:634� 10�6 slug=ft s ¼ 4:134� 10�3 g=cms ¼4:134� 10�4 kg=ms
1kg=ms ¼ 10g=cms ¼ 2:089� 10�2 slug=ft s ¼ 2:419� 103 lbm=ft h
Thermal
conductivity1Btu=ft hF ¼ 2:778� 10�4 Btu=ft sF ¼ 1:730� 105 erg=cmsK ¼1:730W=mK
1W=mK ¼ 105 erg=cmsK ¼ 1:606� 10�4 Btu=ft sF ¼ 0:578Btu=fthF
Surface tension 1 lbf=ft ¼ 1:459� 104 dyne=cm ¼ 14:59N=m
1N=m ¼ 103 dyne=cm ¼ 0:06854 lbf=ft
Latent heat of
vaporization1Btu=lbm ¼ 32:174Btu=slug ¼ 2:32� 107 erg=g ¼ 2:324� 103 J=kg
1J=kg ¼ 104 erg=g ¼ 1:384� 10�2 Btu=slug ¼ 4:303� 10�4 Btu=lbm
Heat transfer
coefficient1Btu=ft2 hF ¼ 5:674� 103 erg=cm2 sK ¼ 5:674W=m2K
1W=m2K ¼ 103 erg=cm2 sK ¼ 0:1762Btu=ft2 hF
Physical Constants
Gravitational acceleration (standard): g ¼ 32:174ft=s2 ¼ 980:7cm=s2 ¼ 9:807m=s2
Universal gas constant: �R ¼ 1545:2ft lb=molR ¼ 1:987Btu=lbmmolR ¼ 8:314
�107 erg=gmolK ¼ 8:314� 103 J=kgmolK
Mechanical equivalent of heat: J ¼ 777:66ft lbf=Btu ¼ 4:184� 107 erg=cal 1Nm=J
Stefan–Boltzmann constant: �σ ¼ 0:1713� 10�8 Btu=ft2 hR4 ¼ 5:670� 10�5 erg=cm2 sK4
¼ 5:657� 10�8W=m2K4
452 Appendix A: Dimensional Equivalents and Physical Constants
Appendix B: Properties of Solid Materials
Most of the content in this section is from Chi “Heat Pipe Theory and Practice” as
well as “Heat Pipe Design” from B & K Engineering volumes I and II written by
Patrick J. Berennan and Edward J. Kroliczek, published June 1979 under NASA
contract NAS5-23406.
In this appendix, properties of solid materials commonly used for heat pipe
containers and wicks are summarized and presented in graphical format. The
purpose of this appendix is to support the text for what the reader will need to do
to design their task and not necessarily fulfill all the requirements that are needed by
most common handbooks of this nature. For example, the ultimate tensile strength
of materials depends not only on the temperature but also on material processes and
treatment. For the presentation of graphics in this appendix, the average properties
of the most commonly commercially available materials have been used. For more
detailed properties of information and properties of materials, the readers of this
text can refer to the following references:
1. International Critical TableE. W. Washington, McGraw-Hill, New York, 1993.
2. Mechanical Engineers HandbookL. S. Marks, McGraw-Hill, New York, 1967.
3. Cryogenic EngineeringR. B. Scott, Van Nostrand, Princeton, New Jersey, 1959.
4. A Compendium of Properties of Materials at Low TemperatureV. J. Johnson, Wright Air Development Division of Air Research and Develop-
ment Command, Technical Report 60-56, Part I, July 1960, Part II, October 1960.
© Springer International Publishing Switzerland 2016
B. Zohuri, Heat Pipe Design and Technology, DOI 10.1007/978-3-319-29841-2453
01
2
3
4
56789
2
3
4
56789
2
3
4
5
6789
101
102
103
250
Ti
Fe
Ni
SS 304
500 750
Cu
Al
1000Temperature, R
The
rmal
con
duct
ivity
, Btu
/ft.h
r.F
1250 1500 1750
Fig. B.1 Thermal conductivity of several solid materials Chi �R ¼ 0:556 �K, 1Btu=fthF ¼ð 1:730W=mKÞ [2]
454 Appendix B: Properties of Solid Materials
0
100
200
300
400
500
600
500 1000
Cu
Ni
Ti
Al
Fe
SS 304
1500Temperature, R
Den
sity
, lbm
/ft3
2000 2500
Fig. B.2 Density of several solid materials Chi �R ¼ 0:556 �K, 1 lbm=ft3 ¼ 16:02 kg=m3� �
[2]
Appendix B: Properties of Solid Materials 455
0
20
40
60
80
100
500 1000
Cu
Ni
Ti
AlFe
SS 304
1500
Temperature, R
Ulti
mat
e te
nsile
str
ess,
kps
i
2000 2500
Fig. B.3 Ultimate tensile strength of several solid materials Chi 1� R ¼ð 0:5556 �K, 1 kpsi ¼6:895� 106 N=m2Þ [2]
456 Appendix B: Properties of Solid Materials
Com
posi
tion
Pro
pert
ies
at 3
00 K
Mel
ting
Poi
nt(K
)
Alu
min
um
Pur
e93
327
02
2770
903
875
883
1825
231
449
385
420
355
380
384
322
129
447
447
237
97.1
302
65 473
237
163
787
240
186
925
231
218
186
1042
174
161
126
106
90.8
78.7
185
301
1114
2191
2604
2823
3018
3227
3519
203
203
99.3
222
111
384
90.9
80.7
71.3
65.4
616
682
61.9
57.2
779
937
49.4
581
542
484
242
94.7
198
159
192
482
252
413
356
42 785
41 ——
—
6574
7513
714
995
17 237
362
232
190
327
109
134
94.0
69.5
54.7
574
680
975
32.3
975
28.7
609
654
31.4
609
654
42.2
680
53.1
574
43.3
32.8
28.3
32.1
490
65.7
490
384
80.6
384
216
95.6
215
96.8
43.2
27.3
19.8
17.4
17.4
337
290
323
124
311
131
348
298
135
357
284
140
375
270
145
395
255
155
19360
395
425
460
545
5259
393
397
379
417
366
433
352
451
339
480
990
73.0
68.2
59.2
48.4
29.1
117
14 17 33.9
6.71
34.7
127
23.1
20.7
177
168
200
96.8
93.7
401
52 54 110
23 59.9
317
80.2
72.7
2790
1850
8650
7160
8933
8800
8780
8530
755
1550
594
2118
1358
1293
1104
1188
1439
1211
1336
1810
8920
5360
1930
0
1810
7870
Allo
y 20
24-T
6(4.
5% C
u, 1
.5%
Mg,
0.6
% M
n)
Allo
y 19
5,ca
st (
4.5%
Cu)
Ber
ylliu
m
Cad
miu
m
Chr
omiu
m
Cop
per
Pur
e
Com
mer
cial
bro
nze
(90°
Cu,
10%
Al)
Pho
spho
r ge
ar b
ronz
e (8
8%C
u,11
%S
n)
Car
trid
ge b
rass
(70
%C
u,30
%Z
n)
Con
stan
tan
(55%
Cu,
45%
Ni)
Ger
man
ium
Gol
d
Iron P
ure
Arm
co(9
9.75
% p
ure)
Pro
pert
ies
at V
ario
us T
empe
ratu
res
k(W
/m. K
)cP(I
/kg.
K)
rk
(kg/
m3 )
(l/kg
. K)
c p(W
/m. K
)
a1x
106
(m2 /s
)10
0 K
200
K20
0 K
2500
K40
0 K
600
K80
0 K
1000
K12
00 K
1500
K
Fig.B.4
Properties
ofsolidmaterials[3]
Appendix B: Properties of Solid Materials 457
Car
bon
Ste
els
7832
434
434
63.9
60.5
17.7
56.7
487
58.7
487
49.8
501
42.2
487
38.2
492
42.0
492
46.8
492
17.3
512
16.6
515
15.2
504
15.8
513
39.7
118
179
141
125
143
224
132
134
261
142
126
275
118
285
112
295
105
208
9890
230
280
459
86
36.7
34.0
31.4
559
585
606
18.9
21.9
24.7
557
18.3
21.3
24.2
602
576
550
19.8
22.6
25.4
28.0
31.7
682
640
611
582
559
585
606
9.2
272
402
12.6
36.7
575
39.1
575
42.1
575
20.0
688
22.8
25.4
36.3
28.2
969
33.3
688
34.5
688
26.9
969
27.4
969
559
685
1090
559
48.8
39.2
685
37.4
699
35.0
559
44.0
582
39.7
685
1169 31
.3
1168 29
.3
971
27.6
48.0
39.2
30.0
18.8
7832
7817
446
51.9
14.9
11.6
41.0
434
8131
7822
444
442
37.7
42.3
10.9
12.2
14.1
3.91
3.95
3.48
3.71
24.1
53.7
7858
7836
8055
1670
7900
8238
7978
1134
0
1024
0
8900
8400
8510
8570
129
251
444
420
439
265
138
90.7
23.0
164
232
383
107
80.2
65.6
67.6
530
562
71.8
76.2
82.6
616
594
592
485
14 480
13.5
17.0
20.5
24.0
27.6
33.0
79.1
72.1
67.5
64.4
626
546
61.3
510
58.2
473
55.2
10.3
372
52.6
16 525
545
21
8.7
55.2
3.4
3.1
23.6
12 11.7
53.7
601
2894
1728
1672
1665
2741
477
468
480
480
443
48.9
15.1
14.9
13.4
14.2
35.3
Pla
in c
arbo
n(M
n ≤
–1%
,Si ≤
0.1
%)
AIS
I 101
0
Car
bon-
silic
on (
Mn
≤ 1%
,0.1
% <
Si ≤
0.6
%)
Chr
omiu
m(lo
w)s
teel
s
1 C
r-
1 C
r-V
(0.
2%C
,1.0
2% C
r,0.
15%
V)
Sta
inle
ss s
teel
s
AIS
I 302
AIS
I 304
AIS
I 316
AIS
I 347
Lead
Mol
ybde
num
Nic
kel
Pur
e
Nic
hrom
e (8
0%N
i,20%
Cr)
Inco
nel X
-750
(73%
Ni,1
5%C
r,6.
7%F
e)
Nio
biumCr-
Mo-
Si (
0.18
%C
,0.6
5%C
r,0.
23%
Mo,
0.6%
Si)
Mo(
0.16
%C
,1%
Cr,
0.54
%M
o,0.
6%S
i)
1 2
1 21 4
Car
bon-
man
gane
se-s
ilico
n (1
%<
Mn≤
1.6
5%,
0
.1%
<S
i≤0.
6%)
Fig.B.5
Properties
ofsolidmaterials[3]
458 Appendix B: Properties of Solid Materials
Com
posi
ton
Pro
pert
ies
at 3
00K
Mel
ting
Poi
nt
(K)
Pc p
ka 1
x106
(kg/
m3 )
(l/kg
.K)
(W/m
-K)
(m2 /3
)
1800
1685
1235
505
1953
3660
1663
016
2
712
235
227
522
132
4717
.4
100
K20
0 K
200
K40
0 K
600
K80
0 K
1000
K12
00 K
1500
K25
00 K
52
——
——
——
5965
6973
76
884
264
98.9
790
425
239 62
.2
243
20.4
551
159
137
61.9
867
412
250
19.4
591
633
145
125
137
142
19.7
20.7
675
620
113
152
686
107
100
167
95 176
157
118
148
22.0
24.5
262
396
913
277
379
946
292
992
361
967
42.2
31.2
25.7
22.7
556
430
225 73
.3
215
24.5
465
186
122
259
444
187
85.2
188
30.5
300
208
87
89.2
174
40.1
9.32
68.3
148
429
66.6
21.9
174
2330
1050
0
7310
4500
1930
0
Pro
pert
ies
at V
ario
us T
empe
ratu
res
k(W
/m-Kk
P()
/Kg-
K)
Allo
y60P
t-40
Rh
(60%
Pt,4
0%R
h)
Sili
con
Silv
er
Tin
Tita
nium
Tun
gste
n
Fig.B.6
Properties
ofsolidmaterials[3]
Appendix B: Properties of Solid Materials 459
References
1. Berennan, P. J., & Kroliczek, E. J. (1979). Heat pipe design. From B & K Engineering Volume
I and II. NASA contract NAS5-23406.
2. Chi, S. W. (1976). Heat pipe theory and practice. New York: McGraw-Hill.
3. Peterson, G. P. (1994). An introduction to heat pipes—Modeling, testing and applications.New York: John Wiley & Sons.
460 Appendix B: Properties of Solid Materials
Appendix C: Properties of Fluids
Most of the content in this section is from Chi “Heat Pipe Theory and Practice” as
well as “Heat Pipe Design” from B & K Engineering Volumes I and II written by
Patrick J. Berennan and Edward J. Kroliczek, published in June 1979 under NASA
contract NAS5-23406.
Fluid properties relevant to heat pipe performance in this text are presented in
this appendix in graphical presentation format for nine working fluids which are:
1. Neon
2. Nitrogen
3. Methane
4. Ammonia
5. Methanol
6. Water
7. Mercury
8. Potassium
9. Sodium
It is often necessary to collect these nine properties for each fluid from different
sources. Properties of liquid metal were first compiled by Deverall, Kemme, and
Florschuetz and by Frank, Smith, and Taylor. Refer to the following:
1. Sonic Limitation and Startup Problems of Heat PipesJ. E. Deverall, J. E. Kemme and L. W. Florschuetz, Los Alamos National
Laboratory, Report LA-4818, September 1970.
2. Heat Pipe Design ManualS. Frank, J. T. Smith and K. M. Taylor, Martin Marietta Corporation, Report
MND-3288, February 1967.
Properties of mercury have been compiled by Deverall.
3. Mercury as a Heat Pipes FluidDeverall, Los Alamos National Laboratory, LA-4300, October 1969.
© Springer International Publishing Switzerland 2016
B. Zohuri, Heat Pipe Design and Technology, DOI 10.1007/978-3-319-29841-2461
Properties of modern-temperature fluids have been compiled by:
4. Heat Pipe Design HandbookBienert and Skrabek and Taylor, Dynatherm Corporation, Report to NASA,
Contract No. NAS9-11927, August 1972.
5. Heat Pipe Design ManualS. Frank, J. T. Smith and K. M. Taylor, Martin Marietta Corporation, Report
MND-3288, February 1967.
Properties of cryogenic fluids have been compiled by Chi in the following
reference along with his computer codes that have been described in Chap. 3.
6. Mathematical Modeling of Cryogenic Heat PipesS. W. Chi, NASA CR-116175, September 1970.
The above compilations have been the sources of property values used in the
preparation of the graphs presented in this appendix.
Also, Reay and Kew [3] are providing a good list of properties of working fluids
for the following fluids:
Fluids listed
1. Helium
2. Ammonia
3. Acetone
4. Flutec PP2
5. Heptane
6. Flutec PP9
7. Mercury
8. Potassium
9. Lithium
10. Nitrogen
11. Water
12. High-temperature organics
13. Pentane
14. Cesium
15. Methanol
16. Sodium
17. Ethanol
Properties listed:
Latent heat of evaporation Vapor dynamic viscosity
Liquid density Vapor pressure
Vapor density Vapor-specific heat
Liquid thermal conductivity Liquid surface tension
Liquid dynamic viscosity
462 Appendix C: Properties of Fluids
2
2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9
3
4
56789
2
3
4
56789
2
3
4
56789
101
1101
Ne
Hg K Na
N2
CH
4
NH
3
CH
3OH
H2O
102 103 104
102
103
Temperature, R
Vap
or p
ress
ure,
pv
psia
Fig. C.1 Saturation pressure of several heat pipe working fluids Chi [2] �R ¼ð0:556� K, 1 psi ¼ 6:895� 103 N=m2Þ
Appendix C: Properties of Fluids 463
2
2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9
3
4
56789
2
3
4
56789
2
3
4
56789
1
10–1
101
Ne
Hg
K
Na
N2
CH4
NH3
CH3OHH2O
102 103 104
101
102
2
3
4
56789
2
3
4
56789
2
3
4
56789
101
1
102
103
Temperature, R
Den
sity
, lbm
/ft3
Fig. C.2 Saturation density of several heat pipe working fluids Chi [2] 1� R ¼ð0:5556� K, 1 lbm=ft3 ¼ 1:602 kg=m3Þ
464 Appendix C: Properties of Fluids
2
2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9
3
4
56789
2
3
4
56789
2
3
4
56789
10–5
10–4
101
Ne
Hg
K
Na
N2CH4
NH3
CH
3 OH
H2O
102 103 104
10–3
10–2
2
3
4
56789
2
3
4
56789
2
3
4
56789
10–2
1
10–1
10–3
Temperature, R
Sur
face
tens
ion,
lbf/f
t
Fig. C.3 Viscosity of several heat pipe working fluids at saturation state Chi [2] 1� R ¼ð0:5556� K, 1 lbm=ft h ¼ 4:134� 10�4 kg=m sÞ
Appendix C: Properties of Fluids 465
2
2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9
3
4
56789
2
3
4
56789
2
3
4
56789
10–3
10–2
101
Ne
Hg
K
NaN2
CH4
NH3
H2O
CH3OH
102 103 104
10–1
1
2
3
4
56789
2
3
4
56789
2
3
4
56789
10–1
101
1
10–2
Temperature, R
Vis
cosi
ty, l
bm/ft
.hr
Fig. C.4 Surface tension of saturated liquid for several heat pipe working fluids Chi [2]
1� R ¼ 0:5556� K, 1 lbf=ft ¼ 14:59 N=mð Þ
466 Appendix C: Properties of Fluids
2
2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9
3
4
56789
2
3
4
56789
2
3
4
56789
102
101
101
Ne
Hg
K
Na
N2
CH4
NH3
CH3OH
H2O
102 103 104
103
104
Temperature, R
Late
nt h
eat o
f vap
oriz
atio
n, B
tu/lb
m
Fig. C.5 Latent heat of vaporization for several heat pipe working fluids Chi [2]
1� R ¼ 0:5556� K, 1 Btu=lbm ¼ 2:324� 103 J=kg� �
Appendix C: Properties of Fluids 467
2
2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9
3
4
56789
2
3
4
56789
2
3
4
56789
10–2
10–1
101
Ne
Hg
K
Na
N2
CH4
NH3H2O
CH3OH
102 103 104
1
101
2
3
4
56789
2
3
4
56789
2
3
4
56789
1
102
101
10–1
Temperature, R
The
rmal
con
duct
ivity
, Btu
/ft.h
r.F
Fig. C.6 Liquid thermal conductivity for several heat pipe working fluids at saturated state Chi
[2] 1� R ¼ 0:5556� K, 1 Btu=ft h F ¼ 1:730 W=m Kð Þ
468 Appendix C: Properties of Fluids
–271
–270
–269
–268
–203
–200
–195
–190
–185
–180
–175
–170
–160
–150
210.
020
5.5
198.
019
0.0
183.
017
3.7
163.
215
2.7
124.
266
.8
830.
081
8.0
798.
077
8.0
758.
073
2.0
702.
067
2.0
603.
047
4.0
1.84
3.81
7.10
10.3
913
.68
22.0
533
.80
45.5
580
.90
194.
00
0.15
00.
146
0.13
90.
132
0.12
50.
117
0.11
00.
103
0.08
90.
075
2.48
1.94
1.51
1.26
1.08
0.95
0.86
0.80
0.72
0.65
0.48
0.51
0.56
0.60
0.65
0.71
0.77
0.83
1.00
1.50
0.48
0.74
1.62
3.31
4.99
6.69
8.37
1.07
19.3
728
.80
1.08
31.
082
1.07
91.
077
1.07
41.
072
1.07
01.
068
1.06
31.
059
1.05
40.
985
0.87
00.
766
0.66
20.
561
0.46
40.
367
0.18
50.
110
22.8
23.6
20.9 4.0
148.
314
0.7
128.
011
3.8
26.0
17.0
10.0 8.5
1.81
2.24
2.77
3.50
3.90
3.70
2.90
1.34
0.20
0.30
0.60
0.90
0.06
0.32
1.00
2.29
2.04
52.
699
4.61
96.
642
0.26
0.19
0.09
0.01
Hel
ium
Nitr
ogen
Liqu
idvi
scos
.cP
x 1
02
Liqu
idvi
scos
.cP
x 1
01
vapo
urvi
scos
.cP
x 1
03
vapo
urvi
scos
.cP
x 1
02
Vap
our
pres
s.B
ar
Vap
our
pres
s.B
ar
Vap
our
spec
ific
heat
kJ/
kg°C
Vap
our
spec
ific
heat
kJ/
kg°C
Liqu
id s
urfa
ce
tens
ion
N/m
x 1
03
Liqu
id s
urfa
ce
tens
ion
N/m
x 1
02
Tem
p °C
Tem
p °C
Late
nt h
eat
kJ/k
g
Late
nt h
eat
kJ/k
g
Liqu
idde
nsity
kg/m
3
Liqu
idde
nsity
kg/m
3
Vap
our
dens
itykg
/m3
Vap
our
dens
itykg
/m3
Liqu
id th
erm
alco
nduc
tivity
W/m
°C x
10-2
Liqu
id th
erm
alco
nduc
tivity
W/m
°C
Fig.C.7
Workingfluid
properties
ofhelium
[3]
Appendix C: Properties of Fluids 469
Am
mon
ia
Tem
p ˚C
Tem
p ˚C
Late
nthe
atkJ
/kg
Late
nthe
atkJ
/kg
Liqu
idde
nsity
Kg/
m3
Liqu
idde
nsity
Kg/
m3
Vap
our
dens
ityK
g/m
3
Vap
our
dens
ityK
g/m
3
Liqu
id th
erm
alco
nduc
tivity
W/m
˚C
Liqu
id th
erm
alco
nduc
tivity
W/m
˚C
Liqu
idvi
scos
.cP
Liqu
idvi
scos
.cP
Vap
our
visc
os.
cP x
102
Vap
our
visc
os.
cP x
102
Liqu
id s
urfa
cete
nsio
nN
/mx
102
Liqu
id s
urfa
cete
nsio
nN
/mx
102
Vap
our
pres
s.B
ar Vap
our
pres
s.B
ar
Vap
our
spec
ific
heat
kJ/k
g ˚C
Vap
our
spec
ific
heat
kJ/k
g ˚C
120
100
806040200––– 204060 –20
428
699
891
1026
1101
1187
1263
1338
1384
1343
374.4
455.1
505.7
545.2
579.5
610.3
638.6
665.5
690.4
714.4
0.03
0.05
1.62
3.48
6.69
12.00
20.49
34.13
54.92
113.16
0.29
40.30
30.30
40.29
80.28
60.27
20.25
50.23
50.21
20.18
40.07
0.11
0.15
0.17020
0.22
0.25
0.260.29
0.36
1.891.60
1.40
1.27
1.16
1.01
0.92
0.85
0.79
0.72
90.44
63.12
40.90
29.80
15.34
8.46
4.24
1.93
0.76
0.27
2.29
22.26
02.21
02.18
02.16
02.15
02.12
52.10
02.07
52.05
0
0.15
005
000.76
71.36
71.83
32.13
32.48
03.09
03.57
44.06
2
Pentan
e
120
100806040200
269.7
295.7
329.1
342.3
355.5
366.9
378.3
390.0
509.4
537.6
563.0
585.0
607.0
625.5
644.0
663.0
25.20
16.54
10.61
6.51
4.35
2.20
0.75
0.01
0.12
20.12
40.12
70.12
80.13
30.13
80.14
30.14
9
0.12
00.12
80.14
70.17
40.20
00.24
20.28
30.34
4
0.90
0.81
0.74
0.69
0.63
0.58
0.53
0.51
13.81
7.19
3.89
2.28
1.52
0.76
0.24
0.10
1.16
41.08
81.05
01.02
10.97
10.92
20.87
40.82
5
0.68
0.83
0.97
0.17
0.371.58
1.79
0.01
Fig.C.8
Workingfluid
properties
ofam
monia
[3]
470 Appendix C: Properties of Fluids
Ace
tone
Met
hano
l
Tem
p°C
Tem
p°C
Late
nthe
atkJ
/kg
Late
nthe
atkJ
/kg
Liqu
idde
nsity
kg/m
3
Liqu
idde
nsity
kg/m
3
Vap
our
dens
itykg
/m3
Vap
our
dens
itykg
/m3
Liqu
id th
erm
alco
nduc
tivity
W/m
°C
Liqu
id th
erm
alco
nduc
tivity
W/m
°C
Liqu
idvi
scos
. cP
Liqu
idvi
scos
. cP
Vap
our
visc
os.
cP x
102
Vap
our
visc
os.
cP x
102
Vap
our
pres
s.B
ar
Vap
our
pres
s.B
ar
Vap
our
spec
ific
heat
kJ/k
g°C
Vap
our
spec
ific
heat
kJ/
kg°C
Liqu
id s
urfa
cete
nsio
nN
/m x
102
Liqu
id s
urfa
cete
nsio
nN
/m x
102
–40
–20 0 20 40 60 80 100
120
140
–50
–30
–10 10 30 50 70 90 110
130
150
1194
1187
1182
1175
1155
1125
1085
1035 98
092
085
0
843.
583
3.5
818.
780
0.5
782.
076
4.1
746.
272
4.4
703.
668
5.2
653.
2
0.01
0.01
0.04
0.12
0.31
0.77
1.47
3.01
5.64
9.81
15.9
0
0.21
00.
208
0.20
60.
204
0.20
30.
202
0.20
10.
199
0.19
70.
195
0.19
3
1.70
01.
300
0.94
50.
701
0.52
10.
399
0.31
40.
259
0.21
10.
166
0.13
8
0.72
0.78
0.85
0.91
0.98
1.04
1.11
1.19
1.26
1.31
1.38
0.01
0.02
0.04
0.10
0.25
0.55
1.31
2.69
4.98
7.86
8.94
1.20
1.27
1.34
1.40
1.47
1.54
1.61
1.79
1.92
1.92
1.92
3.26
2.95
2.63
2.36
2.18
2.01
1.85
1.66
1.46
1.25
1.04
660.
061
5.6
564.
055
2.0
536.
051
7.0
495.
047
2.0
426.
139
4.4
860.
084
5.0
812.
079
0.0
768.
074
4.0
719.
068
9.6
660.
363
1.8
0.03
0.10
0.26
0.64
1.05
2.37
4.30
6.94
11.0
218
.61
0.20
00.
189
0.18
30.
181
0.17
50.
168
0.16
00.
148
0.13
50.
126
0.80
00.
500
0.39
50.
323
0.26
90.
226
0.19
20.
170
0.14
80.
132
0.68
0.73
0.78
0.82
0.86
0.90
0.95
0.98
0.99
1.03
0.01
0.03
0.10
0.27
0.60
1.15
2.15
4.43
6.70
10.4
9
2.00
2.06
2.11
2.16
2.22
2.28
2.34
2.39
2.45
2.50
3.10
2.76
2.62
2.37
2.12
1.86
1.62
1.34
1.07
0.81
Fig.C.9
Workingfluid
properties
ofacetone[3]
Appendix C: Properties of Fluids 471
Flu
tec
PP
2
Tem
p °C
Tem
p °C
–30
–10
10 30 50 70 90 110
130
160
–30
939.
482
5.0
0.02
0.17
73.
401.
251.
311.
371.
441.
511.
581.
651.
721.
78
2.76
2.66
2.57
2.44
2.31
2.17
2.04
1.89
1.75
0.01
0.02
0.03
0.10
0.29
0.76
1.43
2.66
4.30
0.75
0.80
0.85
0.91
0.97
1.02
1.07
1.13
1.18
2.20
1.50
1.02
0.72
0.51
0.37
0.28
0.21
0.17
30.
170
0.16
80.
166
0.16
50.
163
0.16
00.
159
0.03
0.05
0.38
0.72
1.32
2.59
5.17
9.25
813.
079
8.0
781.
076
2.2
743.
172
5.3
704.
167
8.7
928.
790
4.8
888.
687
2.3
858.
383
2.1
786.
673
4.4
–10
10 30 50 70 90 110
130
106.
219
4218
860.
441.
392.
966.
4311
.79
21.9
934
.92
57.2
110
3.63
0.13
0.63
75.
200
0.98
1.03
1.07
1.12
1.17
1.22
1.26
1.31
0.01
0.72
0.81
0.92
1.01
1.07
1.11
1.17
1.25
1.33
1.45
1.90
1.71
1.52
1.32
1.13
0.93
0.73
0.52
0.32
0.01
0.02
0.09
0.22
0.39
0.62
1.43
2.82
4.83
8.76
1.36
1.43
3.50
02.
140
1.43
51.
005
0.72
00.
543
0.42
90.
314
0.16
7
0.62
60.
613
0.60
10.
588
0.57
50.
563
0.55
00.
537
0.51
8
1829
1773
1716
1660
1599
1558
1515
1440
103.
199
.896
.391
.887
.082
.176
.570
.359
.1
Late
nthe
atkJ
/kg
Late
nthe
atkJ
/kg
Liqu
idde
nsity
kg/m
3
Liqu
idde
nsity
kg/m
3
Liqu
id th
erm
alco
nduc
tivity
W/m
°C
Liqu
id th
erm
alco
nduc
tivity
W/m
°C
Vap
our
dens
itykg
/m3
Vap
our
dens
itykg
/m3
Liqu
idvi
scos
. cP
Liqu
idvi
scos
. cP
Eth
anol
Vap
our
visc
os.
cPx1
02
Vap
our
visc
os.
cPx1
02
Vap
our
Pre
ss.
Bar
Vap
our
Pre
ss.B
ar
Vap
our
spec
ific
heat
kJ/k
g°C
Vap
our
spec
ific
heat
kJ/
kg°C
Liqu
id s
urfa
cete
nsio
nN
/mx1
02
Liqu
id s
urfa
cete
nsio
nN
/mx1
02
Fig.C.10
Workingfluid
properties
offlutecPP2[3]
472 Appendix C: Properties of Fluids
Wat
er
Hep
tane
Tem
p°C
−20
384.
037
2.6
362.
235
1.8
341.
533
1.2
319.
630
5.0
715.
50.
010.
170.
490.
971.
452.
313.
716.
08
0.14
30.
690.
570.
600.
530.
430.
340.
290.
240.
210.
18
0.63
0.66
0.70
0.74
0.77
0.82
0.01
0.02
0.08
0.20
0.32
0.62
1.10
1.85
0.83
0.87
0.92
0.97
1.02
1.05
1.09
1.16
2.42
2.21
2.01
1.81
1.62
1.43
1.28
1.10
0.14
10.
140
0.13
90.
137
0.13
50.
133
0.13
2
699.
0
683.
066
7.0
649.
063
1.0
612.
059
2.0
20 40 60 80 100
120
2024
4824
0223
5923
0922
5822
0021
39
2003
1967
2074
998.
299
2.3
983.
097
2.0
958.
094
5.0
928.
0
888.
086
5.0
909.
0
0.02
0.05
0.13
0.29
0.60
1.12
1.99
5.16
7.87
3.27
0.60
31.
000.
960.
021.
817.
286.
966.
626.
265.
895.
505.
064.
664.
293.
89
1.89
1.91
1.95
2.01
2.09
2.21
2.38
2.62
2.91
0.07
0.20
0.47
1.01
2.02
3.90
6.44
10.0
416
.19
1.04
1.12
1.19
1.27
1.34
1.41
1.49
1.57
1.65
0.65
0.47
0.36
0.28
0.23
0.20
0.17
0.15
0.14
0.63
00.
649
0.66
80.
680
0.68
20.
683
0.66
90.
659
0.67
9
40 60 80 100
120
140
160
180
2000
Vap
our
spec
fic h
eat
kJ/k
g°C
Vap
our
spec
fic
heat
kJ/
kg°C
Late
nthe
atkJ
/kg
Liqu
id s
urfa
cete
nsio
nN
/m x
102
Liqu
id s
urfa
cete
nsio
nN
/m x
102
Liqu
idde
nsity
kg/m
3
Vap
our
dens
itykg
/m3
Liqu
idvi
scos
.cP
Liqu
idvi
scos
.cP
x10
2
Vap
our
pres
sB
ar
Vap
our
pres
s.B
ar
Liqu
id th
enna
lco
nduc
tivity
W/m
°C
Tem
p°C
Late
nthe
atkJ
/kg
Liqu
idde
nsity
kg/m
3
Vap
our
dens
itykg
/m3
Liqu
idvi
scos
.cP
Vap
our
visc
os.
cP x
102
Liqu
id th
enna
lco
nduc
tivity
W/m
°C
Fig.C.11
Workingfluid
properties
ofheptane[3]
Appendix C: Properties of Fluids 473
Flu
tec
PP
9
Hig
h T
empe
ratu
re O
rgan
ic (
Dip
heny
l-Dip
heny
l Oxi
de E
utec
tic)
Vap
our
viac
os.
cPx1
02
Vap
our
visc
os.
cPx1
02
Vap
our
pres
s.B
ar
Vap
our
pres
s.B
ar
Vap
our
spec
ific
heat
kJ/k
g °C
Vap
our
spec
ific
heat
kJ/k
g °C
Liqu
id s
urfa
cete
nsio
nN
/mx1
02
Liqu
id s
urfa
cete
nsio
nN
/mx1
02
Liqu
idvi
scos
. cP
Liqu
idvi
scos
.cP
Liqu
id th
erm
alco
nduc
tivity
W/m
°C
Liqu
id th
erm
alco
nduc
tivity
W/m
°C
Tem
p°C
Tem
p°C
–30 0 30 60 90 120
150
180
225
100
150
200
250
300
350
400
450
354.
033
8.0
321.
030
1.0
278.
025
1.0
219.
018
5.0
992.
095
1.0
905.
085
8.0
809.
075
5.0
691.
062
5.0
0.03
0.22
0.94
3.60
8.74
19.3
741
.89
81.0
0
0.13
10.
125
0.11
90.
113
0.10
60.
099
0.09
30.
086
0.97
0.57
0.39
0.27
0.20
0.15
0.12
0.10
0.67
0.78
0.89
1.00
1.12
1.23
1.34
1.45
0.01
0.05
0.25
0.88
2.43
5.55
10.9
019
.00
1.34
1.51
1.67
1.81
1.95
2.03
2.11
2.19
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.03
Late
nthe
atkJ
/kg
Late
nthe
atkJ
/kg
Liqu
idde
nsity
kg/m
3
Liqu
idde
nsity
kg/m
3
Vap
our
dens
itykg
/m3
Vap
our
dens
itykg
/m3
103.
098
.494
.590
.286
.183
.077
.470
.859
.4
2098
2029
1960
1891
1822
1753
1685
1604
1455
0.01
0.01
0.12
0.61
1.93
4.52
11.8
125
.13
63.2
7
0.06
00.
059
0.05
70.
056
0.05
40.
053
0.05
20.
051
0.04
9
5.77
3.31
1.48
0.94
0.65
0.49
0.38
0.30
0.21
0.82
0.90
1.06
1.18
1.21
1.23
1.26
1.33
1.44
0.00
0.00
0.01
0.03
0.12
0.28
0.61
1.58
4.21
0.80
0.87
0.94
1.02
1.09
1.15
1.23
1.30
1.41
2.36
2.08
1.80
1.52
1.24
0.95
0.67
0.40
0.01
Fig.C.12
Workingfluid
properties
offlutecPP9[3]
474 Appendix C: Properties of Fluids
Liqu
idde
nsity
kg/m
3
Vap
our
dens
itykg
/m3
Liqu
idvi
scos
.cP
Mer
cury
Cae
sium
Vap
our
visc
os.
cP x
102
Vap
our
pres
sB
ar
Liqu
id th
enna
lco
nduc
tivity
W/m
°C
Vap
our
spec
ific
heat
kJ/k
g°C
Liqu
id s
urfa
cete
nsio
nN
/m x
102
Tem
p°C
Late
nthe
atkJ
/kg
Liqu
idde
nsity
kg/m
3
Vap
our
dens
itykg
/m3 x
102
Liqu
idvi
scos
.cP
Vap
our
visc
os.
cP x
102
Vap
our
pres
s B
arLi
quid
then
nal
cond
uctiv
ityW
/m°C
Vap
our
spec
ific
heat
kJ/k
g°C
x 1
0
Liqu
id s
urfa
cete
nsio
nN
/m x
102
Tem
p°C
150
308.
813
230
0.01
9.99
1.09
0.39
0.01
1.04
4.45
4.15
4.00
3.82
3.74
3.61
3.41
3.25
3.15
3.03
2.75
1.04
1.04
1.04
1.04
1.04
1.04
1.04
1.04
1.04
1.04
0.18
0.44
1.16
2.42
4.92
8.86
15.0
323
.77
34.9
563
.00
0.48
0.53
0.61
0.66
0.70
0.75
0.81
0.87
0.95
1.10
0.96
0.93
0.89
0.86
0.83
0.80
0.79
0.78
0.78
0.77
11.2
311
.73
12.1
812
.58
12.9
613
.31
13.6
213
.87
14.1
514
.80
0.60
1.73
4.45
8.75
16.8
028
.60
44.9
265
.75
94.3
917
0.00
1299
512
880
1276
312
656
1250
812
308
1215
412
054
1196
211
800
303.
830
1.8
298.
929
6.3
293.
829
1.3
288.
828
6.3
283.
527
7.0
250
300
350
400
450
500
550
600
650
750
375
530.
417
400.
0120
.76
0.25
2.20
0.02
1.56
1.56
1.56
1.56
1.56
1.56
1.56
1.56
1.56
1.56
5.81
5.61
5.36
5.11
4.81
4.51
4.21
3.91
3.66
3.41
0.04
0.09
0.16
0.36
0.57
1.04
1.52
2.46
3.41
2.30
2.40
2.50
2.55
2.60
2.67
2.75
2.28
2.90
0.23
0.22
0.20
0.19
0.18
0.17
0.17
0.16
0.16
20.5
120
.02
19.5
218
.83
18.1
317
.48
16.8
316
.18
15.5
3
0.01
0.02
0.03
0.07
0.10
0.18
0.26
0.40
0.55
1730
1720
1710
1700
1690
1680
1670
1655
1640
520.
451
5.2
510.
250
2.8
495.
349
0.2
485.
247
7.8
470.
3
425
475
525
575
625
675
725
775
825
Late
nthe
atkJ
/kg
Fig.C.13
Workingfluid
properties
ofmercury
[3]
Appendix C: Properties of Fluids 475
350
400
450
500
550
600
650
700
750
800
850
500
600
700
800
900
1000
1100
1200
1300
4370
4243
4090
3977
3913
3827
3690
3577
3477
70.0
864
.62
60.8
157
.81
53.3
549
.08
45.0
841
.08
37.0
8
828.
180
5.4
763.
575
7.3
745.
472
5.4
690.
866
9.0
654.
0
9.50
9.04
8.69
8.44
8.16
7.86
7.51
7.12
6.72
6.32
5.92
2093
2078
2060
2040
2020
2000
1980
1969
1938
1913
1883
51.0
849
.08
47.0
845
.08
43.3
141
.81
40.0
838
.08
36.3
134
.81
33.3
1
0.00
20.
006
0.01
50.
031
0.06
20.
111
0.19
30.
314
0.48
60.
716
1.05
4
0.00
30.
013
0.05
00.
134
0.30
60.
667
1.30
62.
303
3.62
2
0.21
0.19
0.18
0.17
0.15
0.14
0.13
0.12
0.12
0.11
0.10 0.24
0.21
0.19
0.18
0.17
0.16
0.16
0.15
0.15
0.18
0.19
0.20
0.22
0.23
0.24
0.25
0.26
0.27
0.01
0.04
0.15
0.47
1.25
2.81
5.49
9.59
15.9
1
9.04
9.04
9.04
9.04
9.04
9.04
9.04
9.04
9.04
1.51
1.42
1.33
1.23
1.13
1.04
0.95
0.86
0.77
0.15
0.16
0.16
0.17
0.17
0.18
0.19
0.19
0.20
0.20
0.21
0.01
0.01
0.02
0.05
0.10
0.19
0.35
0.61
0.99
1.55
2.34
5.32
5.32
5.32
5.32
5.32
5.32
5.32
5.32
5.32
5.32
5.32
763.
174
8.1
735.
472
5.4
715.
470
5.4
695.
468
5.4
675.
466
5.4
653.
1
Tem
p °C
Late
nthe
atkJ
/kg
Liqu
idde
nsity
kg/m
3
Vap
our
dens
itykg
/m3
Liqu
id th
erm
alco
nduc
tivity
W/m
°C
Liqu
idvi
scos
. cP
Pot
asiu
m
Sod
ium
Vap
our
visc
os.
cP ×
102
Vap
our
pres
s.B
ar
Vap
our
spec
ific
heat
kJ/k
g °C
Liqu
id s
urfa
cete
nsio
nN
/m ×
102
Tem
p °C
Late
nthe
atkJ
/kg
Liqu
idde
nsity
kg/m
3
Vap
our
dens
itykg
/m3
Liqu
id th
erm
alco
nduc
tivity
W/m
°C
Liqu
idvi
scos
.cP
Vap
our
visc
os.
cP ×
10
Vap
our
pres
s.B
ar
Vap
our
spec
ific
heat
kJ/k
g °C
× 1
0
Liqu
id s
urfa
cete
nsio
nN
/m ×
102
Fig.C.14
Workingfluid
properties
ofpotassium
[3]
476 Appendix C: Properties of Fluids
Tem
p °C
Late
nthe
atkJ
/kg
Liqu
idde
nsity
kg/m
3
Vap
our
dens
itykg
/m3
Liqu
id th
erm
alco
nduc
tivity
W/m
°C
Liqu
idvi
scos
.cP
Lith
ium
Vap
our
visc
os.
cP ×
102
Vap
our
pres
s.B
ar
Vap
our
spec
ific
heat
kJ/k
g°C
Liqu
id s
urfa
cete
nsio
nN
/m ×
102
1030
1130
1230
1330
1430
1530
1630
1730
2050
045
00.
005
67 69 70 69 68 65 62 59
0.24
0.24
0.23
0.23
0.23
0.23
0.23
0.23
0.53
20.
532
0.53
20.
532
0.53
20.
532
0.53
20.
532
0.07
0.17
0.45
0.96
1.85
3.30
5.30
8.90
1.67
1.74
1.83
1.91
2.00
2.10
2.17
2.26
2.90
2.85
2.75
2.60
2.40
2.25
2.10
2.05
0.01
30.
028
0.05
70.
108
0.19
30.
340
0.49
0
440
430
420
410
405
400
398
2010
020
000
1970
019
200
1890
018
500
1820
0
Fig.C.15
Workingfluid
properties
oflithium
[3]
Appendix C: Properties of Fluids 477
References
1. Berennan, P. J., & Kroliczek, E. J. (1979). Heat pipe design. From B & K Engineering Volume
I and II. NASA contract NAS5-23406.
2. Chi, S. W. (1976). Heat pipe theory and practice. New York: McGraw-Hill.
3. Reay, D., & Kew, P. (2006). Heat pipes theory, design and application (5th Ed.). Oxford:
Butterworth-Heinemann.
478 Appendix C: Properties of Fluids
Appendix D: Different Heat Pipe DesignExamples
Different design examples from different resources and references are presented in
this appendix to help the reader to have better understanding and approach to design
a heat pipe under different conditions and functional requirement while heat pipe is
operating under normal condition.
Design Example 1
This example is part of The Effects of Transverse Vibration on the Performance of
an Axial Groove Wick Heat Pipe, Master’s thesis, By Kenneth A. Carpenter,
December 1994. Defense Technical Information Center under Accession Number:
ADA289349
An experimental investigation was performed to determine the effects of trans-
verse vibrations on the performance of an ammonia–aluminum axial groove wick
heat pipe. Theoretical calculations predicted performance degradation due to the
working fluid being shaken out of the upper capillary grooves.
A bench top shaker was used to apply transverse, sinusoidal vibrations of 30, 35,
and 40 Hz, corresponding to peak acceleration amplitudes of 1.84 g, 2.50 g, and
3.27 g, respectively.Maximumheat throughput,Q submax, of the vibrating heat pipe
was measured. A comparison of these values and static Q sub max values indicated
degradation in heat pipe performance. A mean performance deterioration of 27.6 W
was measured for the 1.84 g case, an average degradation of 12.9% from static heat
pipe performance. At 2.50 g peak acceleration, the degradation rose to 37.3 W, an
average decrease of 14.8% from static performance. An average deterioration in
performance of 28.1% was recorded for the 3.27 g case. This amounted to a mean
performance degradation of 69.3 W. The results of this investigation revealed that
transverse, sinusoidal vibrations have a detrimental impact on the performance of an
ammonia/axial groove wick heat pipe. Further, the performance degradation
increases with increasing vibration peak acceleration amplitude.
© Springer International Publishing Switzerland 2016
B. Zohuri, Heat Pipe Design and Technology, DOI 10.1007/978-3-319-29841-2479
Heat Pipe Geometry
Heat pipe performance is as much a function of the wick geometry as it is a function
of the working fluid. The heat pipe for this experiment was supplied by Dynatherm
Corporation. It was an axial groove wick heat pipe of extruded aluminum. For a
working fluid, the heat pipe was charged with 8.6 g of anhydrous ammonia.
Figure D.1 shows the tested heat pipe in cross section, while Table D.1 presents
critical heat pipe dimensions. The tested heat pipe is shown in profile in Fig. D.2
and includes the dimensions for the evaporator, adiabatic, and the condenser
sections
Heat Transport Limits
All heat pipes are constrained by four operating heat transport limits. These are the
sonic limit, the entrainment limit, the capillary limit, and the boiling limit. The heat
transport limits are functions of the heat pipe geometry, the working fluid proper-
ties, and the heat pipe operational environment. This last category includes heat
pipe inclinations, heat pipe section lengths, and other external influences.
11.379 mm
11.379 mm
α
9.398 mm
Fig. D.1 Heat pipe cross-
sectional drawing
Table D.1 Heat pipe cross-
sectional parametersLand thickness (bottom) t1 0.020 in. 0.508 mm
Groove opening (top) w 0.025 in. 0.635 mm
Groove opening (bottom) wb 0.048 in. 1.219 mm
Groove depth δ 0.055 in. 1.397 mm
Groove angle α 13.9� 0.2426 rad
Number of grooves n 17 17
480 Appendix D: Different Heat Pipe Design Examples
The complete explanations and derivations for the heat transport limits of the
tested heat pipe are provided below. Table D.2 is a representation of the theoretical
operating limits of the tested heat pipe. Column 1 of this table gives the heat pipe
operating temperature, which is the temperature of the adiabatic section of the heat
pipe. The remaining columns give the values for the four heat transport limits at the
various operating temperatures. An examination of Table D.2 reveals that for the
anticipated operating temperature range of 40–80 �C, the boiling limit was expected
to constrain the maximum heat transport of the test article since it has the lowest
heat transport value for the entire operating range. However, as Chi points out [2],
the boiling limit of a heat pipe must be verified experimentally.
Experimental investigation showed the theoretical boiling limit to be overly
conservative. This agrees with the findings of Brennan and Kroliczek [1]. They
point out that boiling limit models are very conservative.
In their work, they found that the theoretical boiling limit could be an order of
magnitude lower than the actual boiling limit. The true heat transport limit in the
operating temperature range of 40–80 �C proved to be the capillary limit.
Heat pipes are subject to four different heat transport limits, depending upon the
portion of the operational range in which they are being used. These limits are, from
the lowest operating temperature to the highest, as follows: sonic limit, entrainment
limit, capillary limit, and boiling limit. Table D.2 is a summary of the four
abovementioned limits, and they are summarized as follows.
Evaporator
10.7442 cm
Adiabatic section
36.5906 cm
62.3367 cm66.1467 cm
Condenser section
15.0019 cm
Fig. D.2 Heat pipe profile view
Table D.2 Theoretical heat transport limits
Top QS,max Qe,max Qc,max Qb,max
Operating
temperature (�C)Sonic
limit (W)
Entrainment
limit (W)
Capillary
limit (W)
Boiling
limit (W)
40 99,050 529.29 289.09 18.22
50 124,740 543.15 263.78 12.69
60 158,550 554.04 234.78 8.58
70 202,230 558.36 202.64 5.63
80 256,760 551.02 168.05 3.59
Appendix D: Different Heat Pipe Design Examples 481
Sonic Limit Analysis
When the vapor leaving the evaporator, or if there exists an adiabatic section,
reaches the sonic limit, then Eq. (2.20) (or Eq. (D.1) here) can be used and is
presented here again. This equation for the sonic heat transport limit was first
derived by Levy [3] and is known as the Levy equation. Chi has reproduced the
derivation of this equation as well [2]:
QSmax¼ Avρ0λ
γ0RvT0
2 γ0 þ 1ð Þ� �1=2
ðEq:D:1ðor Eq:2:20ÞÞ
where
QSmax¼ Sonic heat transport limit (W).
Av¼Vapor core cross-sectional area (m2).
ρ0¼Vapor density at stagnation temperature (kg/m3).
λ¼Latent heat of vaporization (J/kg).
γ0¼ Specific gas constant.
Rv¼Vapor gas constant (J/kg K)
T0¼ Stagnation temperature (K).
The sonic heat transport limit for this heat pipe example is represented in
Fig. D.3.
2400.00E+00
5.00E+04
1.00E+05
1.50E+05
2.00E+05
2.50E+05
3.00E+05
3.50E+05
4.00E+05
4.50E+05
5.00E+05
250 260 270 280 290 300 310
Operating Temperature (Degrees Kelvin)
Hea
t Tra
nspo
rt L
imit
(Wat
ts)
320 330 340 350 360 370 380 390 400
Fig. D.3 Sonic heat transport limit
482 Appendix D: Different Heat Pipe Design Examples
Entrainment Limit Analysis
The entrainment limit is a result of the interactions of the vapor stream and the
liquid stream. The interface between these opposite flowing streams is a mutual
shear layer. If the relative velocity between the two streams is great enough, liquid
droplets will be torn from the liquid stream and become entrained in the vapor
stream [1]. When this occurs, evaporator wick dryout follows rapidly [2]. Chi
derives the equation for computing the entrainment heat transport limit:
Qemax¼ Avλ
σρv2rh, s
� �1=2ðEq:D:2Þ
where
Qemax¼Entrainment heat transport limit (W).
Av¼Vapor core cross-sectional area (m2)
λ¼Latent heat of vaporization (J/kg).
σ¼ Surface tension coefficient (N/m).
ρv¼Vapor density (kg/m3).
rh,s¼Hydraulic radius of wick at vapor/wick interface (m).
The entrainment heat transport limit for the heat pipe used in this experiment is
represented in Fig. D.4.
2400
50
100
150
200
250
300
350
400
450
500
550
250 260 270 280 290 300 310
Operating Temperature (Degrees Kelvin)
Hea
t Tra
nspo
rt L
imit
(Wat
ts)
320 330 340 350 360 370 380 390 400
Fig. D.4 Entrainment heat transport limit
Appendix D: Different Heat Pipe Design Examples 483
Capillary or Wick Limit Analysis
The capillary limit occurs when liquid is evaporating more rapidly than capillary
forces can replenish the liquid. This condition results in local wick dryout and
increased wall temperatures [1]. Chi [2] has derived the equations for determining
the capillary or wick heat transport limit:
Qcmax¼ QLð Þcmax
12Lc þ La þ 1
2Le
� � ðEq:D:3Þ
with
QLð Þcmax¼
2σrc� ΔP⊥ � ρlgLt sinΦ
� �Fl þ Fvð Þ ðEq:D:4Þ
where
Fl ¼ μlKAwρlλ
ðEq:D:5Þ
and
Fv ¼ f vRevð Þμv2r2hvAvρvλ� � ðEq:D:6Þ
where
Qcmax¼Capillary heat transport limit (W).
Lc¼Length of condenser section (m).
La¼Length of adiabatic section (m).
Le¼Length of evaporator section (m).
Lt¼Total length of the heat pipe (m).
σ¼ Surface tension coefficient (N/m).
rc¼Effective pore radius (m).
rh¼Hydraulic vapor radius.
ΔP⊥ ¼Hydrostatic pressure perpendicular to pipe axis (N/m2).
ρl¼Liquid density (kg/m3).
ρv¼Vapor density (kg/m3).
λ¼Heat of vaporization (J/kg).
Φ¼Heat pipe inclination (radians).
g¼Gravitational force (9.81m/s3).
Fl¼Liquid frictional coefficient.
Fv¼Vapor frictional coefficient.
μl¼Liquid viscosity (kg/m s).
484 Appendix D: Different Heat Pipe Design Examples
μv¼Vapor viscosity (kg/m s).
K¼Effective wick permeability (m�2).
fv¼Vapor drag coefficient.
Rev¼Reynolds number.
Aw¼Wick cross-sectional area (m2).
For this example, some simplifications can be made to Eq. (D.4). Since there is
no connection between the grooves in the tested heat pipe, the hydrostatic pressure
term, ΔP⊥, is zero. The heat pipe was maintained in a nearly horizontal position
throughout the test; therefore, the pipe inclination angle, Φ is zero. These simpli-
fications reduce Eq. (D.4) to
QLð Þcmax¼
2σrc
� �Fl þ Fvð Þ ðEq:D:7Þ
The effective wick permeability used in Eq. (D.5) is a function of the wick
geometry. For the axial groove wick used in this study, the equation for the effective
wick permeability of the trapezoidal shaped groove is assumed by Brennan and
Kroliczek [1]:
K ¼ 0:435wδþ δ2 tan α� �1=2w02 2δ
cos α 1� sin αð Þþw
h i28><>:
9>=>; ðEq:D:8Þ
where
K¼Effective wick permeability (m�2).
w¼Groove width at the inner radius (m).
δ¼Groove depth (m).
α¼Groove angle (�).The capillary or wick heat transport limit for the heat pipe used in this example is
shown below (Fig. D.5);
Boiling Limit Analysis
The boiling limit results when the heat flux density is great enough to cause the
saturation vapor pressure at the interface between the wick and the wall to exceed
the liquid pressure at the same point. When this occurs, vapor bubbles form in the
liquid stream. These bubbles cause hot spots and restrict liquid circulation, leading
to wick dryout [2]. The heat transport limit at which this occurs is known as the
boiling limit. Chi derives the equation for computing the boiling heat transport
limit:
Appendix D: Different Heat Pipe Design Examples 485
Qbmax¼ 2πLekeTv
λρvln ri=rvð Þ2σ
rn� Pc
� ðEq:D:9Þ
where
Qbmax¼Boiling heat transport limit (W).
Le¼Evaporator section length (m).
ke¼Effective thermal conductivity of the liquid or saturated wick matrix
(W/m K).
Tv¼Vapor temperature (K).
λ¼Latent heat of vaporization (J/kg).
ρv¼Vapor density (kg/m2).
ri¼ Inside radius of pipe (m).
rv¼Vapor core radius (m).
σ¼ Surface tension coefficient (N/m).
rn¼Boiling nucleation radius (m).
Pc¼Capillary pressure (N/m2).
The effective thermal conductivity, Ke, used in Eq. (D.9) is highly dependent
upon the wick geometry. Chi gives the equation for finding the effective thermal
conductivity of an axially grooved heat pipe;
ke ¼ wkl 0:185wfkw þ δklð Þ þ wfklkwδð Þwþ wfð Þ 0:185wfkw þ δklð Þ ðEq:D:10Þ
2400
50
100
150
200
250
300
350
250 260 270 280 290 300 310Operating Temperature (Degrees Kelvin)
Hea
t Tra
nspo
rt L
imit
(Wat
ts)
320 330 340 350 360 370 380 390 400
Fig. D.5 Capillary or wick heat transport limit
486 Appendix D: Different Heat Pipe Design Examples
where
wf¼Groove fin thickness (m).
w¼Groove width (m).
δ¼Groove depth (m).
kl¼Liquid thermal conductivity (W/m K).
kw¼Wall thermal conductivity (W/m K).
The radius of nucleation, r, used in Eq. (D.9) is also a function of the boiling
surface [2]. A wide range of values for r have been reported. Chi gives typical
nucleation radii of 254–2540 nm, while Silverstein reports values ranging from 1 to
7 μm (Silverstein [3] Page 162). A third source, Brennan and Kroliczek, give typical
nucleation radii of 1–10 μm [1]. Brennan and Kroliczek also point out that the
boiling limit model is very conservative. Even using their lower limit for nucleation
radius, they’ve found that the model boiling limit can easily be an order of
magnitude lower than the actual measured boiling limit. The boiling limit for the
heat pipe used in this experiment, using Chi’s lower limit of 254 nm, is represented
in Fig. D.6.
Note: Recommended Values for Nucleation Site Radius [3]. It is reasonable to
assume that the nucleation site radius in properly fabricated and conditioned heat
pipes lies within the range of 1–7 μm. A value of 3 μm is suggested for preliminary
design purpose.
Evaluation of this Example
The heat transport for this investigation was based on an anticipated heat pipe
operating temperature of 313–353 K (40–80 �C). Based on the theoretical curves
shown in Figs. D.3, D.4, D.5, and D.6, the boiling heat transport limit is expected to
2400
100
50
150
250
350
450
550
200
300
400
500
600
650
250 260 270 280 290 300 310Operating Temperature (Degrees Kelvin)
Hea
t Tra
nspo
rt L
imit
(Wat
ts)
320 330 340 350 360 370 380 390 400
Fig. D.6 Boiling heat transport limit
Appendix D: Different Heat Pipe Design Examples 487
be the performance-limiting condition for the tested heat pipe. This is based on the
boiling limit having the lowest heat transport capability over the expected operating
temperature range.
Design Example 2
This example is given by Larry W. Swanson [4].
Heat Transfer Research Institute College Station, TexasDesign a water heat pipe to transport 80 W of waste heat from an electronic
package to cooling water. The heat pipe specifications are:
1. Axial orientation—Complete gravity-assisted operation (condenser above the
evaporator; Ψ ¼ 180�).2. Maximum heat transfer rate—80 W.
3. Nominal operating temperature—40 �C.4. Inner pipe diameter—3 cm.
5. Pipe length—25-cm evaporator length, 50-cm adiabatic section, and 25-cm
condenser length.
The simplest type of wick structure to use is the single-layer wire mesh screen
wick shown in the table below. The geometric and thermophysical properties of the
wick have been selected as (this takes some forethought):
• d ¼ 2:0� 10�5 m
• w ¼ 6:0� 10�5 m
• 12N ¼ rc ¼ 1=2 2:0� 10�5 þ 6� 10�5
� � ¼ 4:0� 10�5 m
• ε ¼ 1
• keff ¼ k1 ¼ 0:630 W=m K
• tw ¼ 1:0� 10�3 m
• K ¼ t2w12¼ 1�10�3ð Þ2
12¼ 8:33� 10�8 m2
The other heat pipe geometric properties are:
• rv ¼ ri � tw ¼ 0:015� 0:001 ¼ 0:014 m
• leff ¼ 0:25þ0:252
þ 0:5 ¼ 0:75 m
• Lt ¼ 0:25þ 0:50þ 0:25 ¼ 1:0 m
• Aw ¼ π r2i � r2v� � ¼ π 0:015ð Þ2 � 0:014ð Þ2
h i¼ 9:11� 10�15 m2
• Av ¼ πr2v ¼ π 0:014ð Þ2 ¼ 6:16� 10�4 m2
The thermophysical properties of water at 40 �C are (see Table D.3):
• ρl ¼ 992:1 kg=m3
• ρv ¼ 0:05 kg=m3
• σl ¼ 2:402� 106 J=kg
488 Appendix D: Different Heat Pipe Design Examples
Table
D.3
Physicalproperties
ofwickstructure
Wicktypea
Thermal
conductivity
Porosity
Minim
um
capillary
radius
Permeability
Single-layer
wiremeshscreens
(heatpipeaxisin
theplaneofthe
paper
inthissketch)
Scr
een
Ann
ular
d
w
k eff¼
k eε¼
1r c
¼1=2N
ðÞ
K¼
t2 w=12
1/N
¼d+w
N¼number
ofaperturesper
unitlength
t wMultiplewiremeshscreens,
bplain
orsintered(screen
dim
ensionsas
forsingle
layersillustratedabove)
k eff¼
k ek e
þk s
�1�ε
ðÞk
e�k s
ðÞ
½�
k eþk s
þ1�ε
ðÞk
e�k s
ðÞ
Estim
ated
from
ε¼
1�
πNd
ðÞ=4
r c¼
1=2N
ðÞ
k¼
d2ε2
1221�ε
ðÞ2
(continued)
Table
D.3
(continued)
Wicktypea
Thermal
conductivity
Porosity
Minim
um
capillary
radius
Permeability
Unconsolidated
packed
spherical
particles
(d¼average
particle
diameter)
Plain
Sintered
k eff¼
k e2k e
þk s
�21�ε
ðÞk
e�k s
ðÞ
½�
2k e
þk s
þ1�ε
ðÞ k
e�k s
ðÞ
k eff¼
k e2k s
þk e
�2εk s
�k e
ðÞ
½�
2k s
þk e
þεk s
�k e
ðÞ
Estim
ated
from
(assumingcubic
packing)ε¼0.48
r c¼
0:21d
k¼
d2ε2
1501�ε
ðÞ2
k¼
C1
y2�1
y2�1
where
Sinteredmetal
fibers(d
¼fiber
diameter)
k eff¼
ε2k e
1�ε
ðÞ2 k
sþ4ε1�ε
ðÞk e
k sk e
þk s
Use
manufac-
turers
data
r c¼
d
21�ε
ðÞ
y¼
1þ
C2d2ε3
1�ε
ðÞ2
C1¼
6:0�10�1
0m
2
C2¼
3:3�107l=m
2
Revised
from
Peterson,G.P.,AnIntrod
uction
toHeatPipes:Mod
eling,
Testing
,an
dApp
lication
s,JohnWiley
&Sons,New
York,1994
aTheaxisofthepipeanddirectionoffluid
flow
arenorm
alto
thepaper
bThesewicksarepositioned
sothat
thelayersfollow
thecontours
oftheinner
surfaceofthepipewall
• μl ¼ 6:5� 10�3 kg=m s
• μv ¼ 1:04� 10�4 kg=m s• Pv ¼ 7000 Pa
• hfg ¼ 2:402� 106 is the latent heat of vaporization for water at the range of�40
to +40 �C.
The various heat transfer limitations can now be determined to ensure that the
heat pipe meets the 80 W heat transfer rate specification. The vapor pressure
(viscous limitation) limitation is:
Qvpmax¼ πr4vhfgρvePve
12μveleff
Qvpmax¼ π 0:014ð Þ4 2:402� 106
� �0:05ð Þ 7000ð Þ
12 1:04� 10�4� �
0:75ð Þ¼ 1:08� 105 W
The sonic limitation is
Qsmax¼ 0:474Avhfg ρvPvð Þ1=2
Qsmax¼ 0:474 6:16� 10�4
� �2:402� 106� �
0:05ð Þ 7000ð Þ½ �1=2¼ 1:31� 104 W
The entrainment limitation is:
Qemax¼ Avhfg
ρvσl2rcave
� �1=2
Qemax¼ 6:16� 10�4� �
2:402� 106� �
0:05ð Þ 0:07ð Þ2 4:0�10�5ð Þ� �1=2
¼ 9:979� 103 W
Noting that cosΨ ¼ 1, the capillary limitation is:
Qcmax¼ ρlσlhfg
μl
� �AwK
leff
� �2
rc, e� ρl
σl
� �gLt cosΨ
�
Qcmax¼ 992:1ð Þ 0:07ð Þ 2:402� 106
� �6:5� 10�3
" #9:11� 10�5� �
8:33� 10�8� �
0:75
" #
� 2
4:0� 10�5þ 992:1
0:079:8 1:0ð Þ
� �
492 Appendix D: Different Heat Pipe Design Examples
Finally the boiling limitation is:
Qbmax¼ 4πleffTvσv
hfgρlln ri=rvð Þ1
rn� 1
rc, e
�
Qbmax¼ 4π 0:75ð Þ 0:63ð Þ 313ð Þ 0:07ð Þ
2:402� 106� �
992:1ð Þln 0:015
0:014
� 1
2:0� 10�6� 1
4:0� 10�5
� �
¼ 0:376 W
All of the heat transfer limitations, with the exception of the boiling limitation,
exceed the specified heat transfer rate of 80 W. The low value of 0.376 for the
boiling limitation strongly suggests that the liquid will boil in the evaporator and
possibly cause local dry spots to develop. The reason the liquid boils is that the
effective thermal conductivity of the wick is equal to the conductivity of the liquid,
which is very low in this case. Because the liquid is saturated at the vapor–liquid
interface, a low-effective thermal conductivity requires a large amount of wall
superheat, which, in turn, causes the liquid to boil. This problem can be
circumvented by using a high-conductivity wire mesh or sintered metal wick,
which greatly increases the effective conductivity. It should be noted, however,
that because porous wicks have lower permeabilities, the capillary limitation should
be lower as well. Let us try a sintered particle wick made of copper with the
following properties (see Table D.3):
• d ¼ 1:91� 10�4 m
• rc ¼ 0:21d ¼ 4:0� 10�5 m
• ε ¼ 0:48
• K ¼ 1:91�10�4ð Þ 0:48ð Þ150 1�0:48ð Þ2 ¼ 2:07� 10�10 m2
• K1 ¼ 400 W=m K Copperð Þ• K1 ¼ 0:630 W=m K Waterð Þ• keff ¼ 400 2
�400þ0:63�2 0:48ð Þ 400�0:63ð Þ
�2 400ð Þþ0:63þ0:48 400�0:63ð Þ ¼ 168 W=m K
All other geometric and thermophysical properties are the same. The heat
transfer limitations affected by the change in wick structure are the capillary and
boiling limitations. The sintered metal wick produces a capillary limitation of
Qcmax¼ 992:1ð Þ 0:07ð Þ 2:402� 106
� �6:5� 10�3
" #9:1� 110�5 2:07� 10�10
� �0:75
" #
� 2
4:0� 10�5þ 992:1
0:079:8 1:0ð Þð Þ
� �¼ 122 W
Appendix D: Different Heat Pipe Design Examples 493
The boiling limitation for the sintered wick is
Qbmax¼ 4π 0:75ð Þ 168ð Þ 313ð Þ 0:07ð Þ
2:402� 106� �
992:1ð Þln 0:015
0:014
� 1
2:0� 10�6� 1
4:0� 10�5
� �¼ 100 W
This design now meets all the specifications defined in the problem statement. More
points can be calculated to reveal that for the anticipated operating temperature
range of �40 to +40 �C, the boiling limit was expected to constrain the maximum
heat transport of the test article since it has the lowest heat transport value for the
entire operating range. This will allow one to plot all the limiting operation of this
heat in order to come up with best optimum design and envelope of operating range
where under that the heat up pipe operates according to its spec. See Example 1.
Design Example 3
This example is given by G. P. Peterson [5].
G. P. Peterson: An Introduction to Heat Pipes—Modeling, Testing, and Appli-
cations, John Wiley & Sons, Inc., 1994.
A simple horizontal copper–water heat pipe is to be constructed from a 1.5-cm
internal diameter, 0.75-m-long tube to cool an enclosed electrical cabinet as shown
in Fig. D.7. The evaporator and condenser lengths of the heat pipe are 0.25 m each,
Cabinet
Evaporator (0.25 m)
Adiabatic Region(0.25 m) Condenser (0.25 m)
Cool Air
Fins
A
A
Warm AirCopperTube
100 MeshCopper Screen(2 Layers)
2.75
cm
Fig. D.7 Sketch of copper–water heat pipe of Example 3 [5]
494 Appendix D: Different Heat Pipe Design Examples
and the wicking structure consists of two layers of 100-mesh copper screen. The
maximum heat transport capacity of the heat pipe is estimated to be 20 W and to
occur at an adiabatic vapor temperature of 30 �C:
1. If the working fluid is water and is assumed to fully wet the wicking structure,
will this heat pipe be adequate?
2. What happens to the maximum transport capacity if the wetting angle is
increased to 45 �C due to poor cleaning?
Solutions
First it is necessary to summarize the physical parameters and known information
for this application:
Wick geometry
N ¼ 100 in:�1 ¼ 3937 m�1 (Mesh number)
dw ¼ 0:0045 in: ¼ 1:143� 10�4 m (Wire diameter)
Spacing ¼ dw ¼ 1:143� 10�4 m (Assume)
Fluid properties at 30 �C
λ ¼ 2425� 10 3 J=kg (Latent heat of vaporization)
ρ‘ ¼ 995:3 kg=m 3 (Working liquid density)
ρv ¼ 0:035 kg= m 3 (Vapor density)
μ‘ ¼ 769� 10�6 N s=m2 (Working liquid absolute viscosity)
μv ¼ 70:9� 10�6 N s=m2 (Vapor absolute viscosity)
σ ¼ 70:9� 10�3 N=m
Next, calculate the vapor diameter:
dv ¼ d � 2 Two Layersþ Two Spaceð Þ¼ 00:015� 2 4 1:143� 10�4
� � �¼ 0:0141 m
To evaluate the maximum heat transport capacity, the capillary limit must be
evaluated. This is represented by Eq. (2.8):
ΔPcð Þm �ðLeff
∂Pv
∂xdxþ
ðLeff
∂Pl
∂xdxþ ΔPephase þ ΔPcphase þ ΔP⊥ þ ΔPk
where
(ΔPc)m¼Maximum capillary pressure difference generated within capillary
wicking structure between wet and dry points.
Appendix D: Different Heat Pipe Design Examples 495
ðLeff
dPv
dxdx¼Vapor pressure drop (Eq. 2.55).ð
Leff
dPl
dxdx¼Liquid pressure drop (Eq. 2.38).
ΔPephase ¼ Pressure gradient across phase transition in evaporator.
ΔP⊥ ¼ ρlgdv cosψ Normal hydrostatic pressure (Eq. 2.8a)
ΔPk ¼ ρlgL sinψ Axial hydrostatic pressure (Eq. 2.8b).
Assuming that one-dimensional flow and the wet point are at the end of the
condenser yields,ðLeff
dPv
dxdx ¼ ΔPv ¼ C f vRevð Þμv
2 rhvð Þ2Avρvλ
!Leffq (Eqs. 2.55 and 2.55a)ð
Leff
dPl
dxdx ¼ ΔPl ¼ μl
KAwρlλ
� �Leffq (Eqs. 2.38 and 2.38a)
ΔP⊥ ¼ ρlgdv cosψ ¼ ρlgdvΔPk ¼ 0
�.
For horizontal heat pipe where ψ ¼ 0, then sinψ ¼ 0.
ψ is the inclination angle of heat pipe in respect to horizontal frame of reference.
Utilizing Eq. (2.7a) and (2.7b), we can write:
ΔPcð Þm ¼ 2σ cos θ
rcwhere rc ¼ 1
2N
Thus Eqs. (2.8a and 2.8b) takes the form of
2σ cos θ
rc¼ C f vRevð Þμv
2 rhvð Þ2Avρvλ
!Leffqþ μl
KAwρlλ
� Leffqþ ρlgdv
Next it is necessary to find the capillary radius rc from Table 2.1.
rc ¼ 1
2N¼ 1
2 3937ð Þ ¼ 1:27� 10�4 m
The vapor space area of Av is then given by the following relationship:
Av ¼ 1
4π dvð Þ2 ¼ 1
4π 0:0141 mð Þ2 ¼ 1:56� 10�4 m2
The liquid flow area Al is given by the following relationship:
Al ¼ 1
4π d2 � dv� �2 ¼ 1
4π 0:015 mð Þ2 � 0:014 mð Þ2h i
¼ 1:057� 10�5 m2
496 Appendix D: Different Heat Pipe Design Examples
And the wick permeability K can be calculated from Table 2.2 as follows;
K ¼ d2l ε3
122 1� εð Þ2 where ε ¼ 1� 1:05πNdl4
ε ¼ 1� 1:05πNdl4
¼ 1� 1:05π 3937ð Þ 1:143� 10�4� �4
¼ 0:629
And as a result for permeability K, we have
K ¼ d2l ε3
122 1� εð Þ2 ¼1:143� 10�4� �2
0:629ð Þ3122 1� 0:629ð Þ2 ¼ 1:94� 10�10 m2
Because, at this point, it is not known if the vapor flow is laminar or turbulent or
compressible or even incompressible; it is necessary to, as a first approximation,
assume laminar, incompressible flow situations, which means f vRev ¼ 16 and
C¼ 1:0 in Eq. (2.55a). Substituting these and the other values from above into
modified Eqs. (2.8a and 2.8b) that is shown above, we have:
2 70:9� 10�3� �
cos θ�
1:27� 10�4¼ 1:0 16ð Þ 9:29� 10�6
� �0:50ð Þq
2 0:00705ð Þ2 1:56� 10�4� �
0:035ð Þ 2425� 103� �
þ 769� 10�6� �
0:50ð Þq1:94� 10�10� �
2:057� 10�5� �
2425� 103� �
995:3ð Þþ 995:3 9:81ð Þ 0:0141ð Þ
or
1116:5 ¼ 0:0565qþ 25:1qþ 137:7
Solving for q yields,
q ¼ 1116:5� 137:7
0:0565þ 39:9
or the value which represents the maximum axial heat transfer that heat pipe can
transport prior to reaching the capillary limit is given by
qm ¼ 24:5 W
Next, the assumption of laminar, incompressible flow must be verified. This can be
done by evaluating the Reynolds number:
Appendix D: Different Heat Pipe Design Examples 497
Re ¼ 4m�
πdvμ¼ 4q
πdvμλ¼ 4 24:5ð Þ
π 0:0141ð Þ 2:29� 10�6� �
2425� 103� �
) Re ¼ 97:9
This value of Reynolds number validates the laminar flow assumption. For uniform
mass addition (vaporization) and uniform mass removal (condensation), the Leff isgiven by
Leff ¼ 0:5Le þ La þ 0:5Lc
Finally, the Mach number must be calculated to verify the assumption of incom-
pressible flow as follows:
Mach ¼ vmc
¼ m�=AvffiffiffiffiffiffiffiffiffiffiγRTv
p ¼ 4q= λπd2v� �ffiffiffiffiffiffiffiffiffiffiγRTv
p
¼4 38:91ð Þ= 2425� 103
� �π 0:0141ð Þ2
� �1:22ð Þ 461:89 30þ 273ð Þð �1=2
¼ 0:1028
431:4¼ 2:38� 10�4 ¼ 0:3 ) Incompressible flow
Because the original assumptions are valid, the maximum heat transport capacity is
equal approximately to 24.5 W.
If θ approaches to 45� due to poor cleaning, then the maximum capillary
pressure becomes
ΔPcð Þm ¼ 2σ cos θ
rc¼ 2 70:9� 10�3� �
cos 45�
1:27� 10�4¼ 789:5 Pa
and qm ¼ 15:98 W or 66% of qm with θ ¼ 0�
The preceding example illustrates the procedure for finding and estimating the
maximum transport capacity as determined by the capillary limit and assumption
was that the heat pipe is horizontal, which may not always be the case of somebody
application.
Design Example 4
This example is given by G. P. Peterson [5].
G. P. Peterson: An Introduction to Heat Pipes—Modeling, Testing, and Appli-
cations, John Wiley & Sons, Inc., 1994.
For the heat pipe of Design Example 3, determine the effects of tilt angle
(evaporator elevated above the condenser) on the heat pipe performance. What is
the maximum tilt angle at which heat pipe will still operate?
498 Appendix D: Different Heat Pipe Design Examples
Solutions
IfΔPk is no longer equal to zero, then the capillary limit is represented by (Fig. D.8
and Table D.4)
ΔPcð Þm �ðLeff
∂Pv
∂xdxþ
ðLeff
∂Pl
∂xdxþ ΔP⊥ þ ΔPk
At 30 �C, these terms are equal to
1116:5 ¼ 0:0565qþ 39:9qþ 137:7þ ρlgL sinψ
or
0
0
5
10
15
20
25
10 20 30 40 50Evaporator Elevation (mm)
Hea
t Tra
nspo
rt C
apac
ity (
Wat
ts)
60 70 80 90 100
Fig. D.8 Evaporator
elevation vs. heat transport
capacity of Example 4 [5]
Table D.4 Heat pipe data for
different inclined angles of
Example 4 [5]
ψ (�) h ¼ L sin ψ cmð Þ qm(W)
0 0 24.5
1 1.31 21.28
2 2.62 18.18
3 3.92 14.89
4 5.23 11.70
5 6.54 8.52
6 7.83 5.33
7 9.14 2.16
8 10.43 –
Appendix D: Different Heat Pipe Design Examples 499
978:8 ¼ 39:96qþ 995:3 9:81ð Þ 0:75ð Þ sinψ
) qm ¼ 978:8� 7323 sinψ
39:96
The maximum angle at which the heat pipe will still operate occurs when qm ¼ 0 or
ψ ¼ 7:68� h ¼ 10:02 cmð Þ. However, to still transfer the required thermal load of
20 W, the tilt angle must be less than approximately 1.4�.
Note: ΔP⊥ will not change for small angles of ψ since cos θ ’ 1:0 (e.g. cos 7�
¼ 0:993).In addition to determine the effect of tilt angle on the transport capacity,
variations in the mean operating temperature may also have a significant impact
on the transport capacity. While in practice, it is difficult to estimate what this value
will be, the capillary transport limit can be estimated for a reasonable temperature
range, allowing the designer to determine if the design is appropriate.
Design Example 5
This example is given by G. P. Peterson [5].
G. P. Peterson: An Introduction to Heat Pipes—Modeling, Testing, and Appli-
cations, John Wiley & Sons, Inc., 1994.
For the heat pipe described in Design Example 3, determine the effects of the
capillary limit of varying the adiabatic vapor temperature over a range of
10–120 �C.
Solutions
Variations in the adiabatic vapor temperature will cause corresponding changes in
the properties of the working fluid. This in turn will affect the performance and the
capillary limit. The basic equation is
2σ cos θ
rc¼ C f vRevð Þμv
2 rhvð Þ2Avρvλ
!Leffqþ μl
KAwρlλ
� Leffqþ ρlgdv
which in terms of the fluid properties reduces to
500 Appendix D: Different Heat Pipe Design Examples
2σ
1:27� 10�4¼ 1 16ð Þμv 0:5ð Þq
2 0:0075ð Þ2 1:56� 10�4� �
ρvλ
þ μl 0:50ð Þ1:94� 10�10� �
2:057� 10�5� �
ρlλ
þ ρl 9:81ð Þ 0:0141ð Þ
or
1:575� 104σ ¼ 4:546� 108μvρvλ
þ 1:25� 1014μlρlλ
� qþ ρl 0:138ð Þ
Simplifying yields
q ¼ 1:575� 104� �
σ � 0:138ð Þρl4:56� 108� �
μv=ρvλð Þ þ 1:25� 1014� �
μl=ρlλð Þ
The results as a function of temperature can be calculated and tabulated as follows.
Appendix D: Different Heat Pipe Design Examples 501
Tλ(kJ/kg)
σ(N
/m)
ρ v(kg/m
3)
ρ l(kg/m
3)
μ v(N
s/m
2)
μ l(N
s/m
2)
ΔPe(Pa)
ΔPl/q(Pa/w)
ΔPv/q
(Pa/w)
ΔP+
(Pa)
q(W
)
10
2478.0
0.075
0.006
1000.0
82.9�10�7
14.2�10�4
1181.3
71.6
0.191
138.0
14.5
20
2453.8
0.073
0.0173
999.0
88.5�10�7
10.0�10�4
1149.8
51.0
0.095
137.86
19.8
40
2406.5
0.069
0.051
993.1
96.6�10�7
6.51�10�4
1086.8
34.1
0.036
137.05
27.8
60
2358.4
0.066
0.130
983.3
105.0�10�7
4.63�10�4
1039.5
25.0
0.016
135.7
36.0
80
2308.9
0.063
0.293
971.8
113.0�10�7
3.51�10�4
992.3
19.55
0.008
134.1
43.9
100
2251.2
0.059
0.597
958.8
121.0�10�7
2.79�10�4
929.3
16.2
0.004
132.3
49.2
120
2202.2
0.055
1.121
943.4
128.0�10�7
2.3�10�4
866.3
13.8
0.002
130.2
53.3
502 Appendix D: Different Heat Pipe Design Examples
or shown graphically (Fig. D.9).
The preceding examples illustrate the effects the gravitational environment and
operating temperature can have on the capillary limit of heat pipes, but as men-
tioned previously, this is only one of the several limits encountered during the
design and operation of heat pipes. The following example illustrates the modeling
procedures for finding the other limitations outlined in Chap. 2.
Design Example 6
This example is given by G. P. Peterson [5].
G. P. Peterson: An Introduction to Heat Pipes—Modeling, Testing and Appli-
cations, John Wiley & Sons, Inc., 1994.
In addition to the capillary limit, it is also necessary in many applications to
determine the capillary, sonic, boiling, and entrainment limits as function of mean
operating temperature and the tilt angle of the heat pipe described in Design
Example 3. Assume a round copper–water heat pipe with an overall length of
25.4 mm; a finned condenser section 9.39 mm long; an evaporator section
11.81 mm long, constructed from 3.2-mm diameter copper tubing with a wall
thickness of 0.9 mm; a wicking structure constructed from phosphor bronze wire
mesh (No. 325) with a wire diameter of 0.0355 mm; and a condenser section with a
series of ten fins approximately 6-mm square, 0.2 mm thick, at a spacing of 1 mm.
These limits can be found as follows.
100
10
20
30
40
50
60
20 30 40 50 60Adiabatic Temperature (�C)
Hea
t Tra
nspo
rt C
apac
ity (
W)
70 80 90 100 110 120
Fig. D.9 Plot of heat
transport capacity versus
adiabatic temperature
Appendix D: Different Heat Pipe Design Examples 503
Solutions
The thermophysical properties of the working fluid are summarized below.
Operating
temperature (K) ρl ρv μl μv keff σ λ
298.15 996.92 0.024 9.47� 10�4 1.03� 10�5 0.605 7.29� 10�2 2.347
323.15 996.92 0.083 5.5� 10�4 1.116� 10�5 0.640 6.93� 10�2 2.324
348.15 974.50 0.247 3.93� 10�4 1.119� 10�5 0.657 6.20� 10�2 2.254
373.15 960.72 0.580 2.82� 10�5 1.28� 10�5 0.680 5.84� 10�2 2.1
where
ρl¼Liquid density (kg/m 3)
ρv¼Vapor density (kg/m 3)
μl¼Liquid viscosity (kg/m s)
μv¼Vapor viscosity (kg/m s)
σ¼ Surface tension (N/m)
keff¼Thermal conductivity (W/m K)
For screen mesh, the capillary radius can be found in Table 2.1 as follows:
rc ¼ 1
2N¼ 1
2 12; 795:25ð Þ ¼ 3:91� 10�5 m
The maximum capillary pressure can be found in Eq. (2.10) as follows:
PCapillarymax¼ 2σ
rcN=m2� �
The normal hydrostatic pressure can be found in Eq. (2.8a) as follows:
ΔP⊥ ¼ ρlgdv cosψ N=m2� �
The axial hydrostatic pressure can be found in Eq. (2.28b) as follows:
ΔPk ¼ ρlgL sinψ N=m2� �
And the maximum effective pumping pressure can be expressed as
Pp,m ¼ Pc,m � ΔP⊥ � ΔPk
Using these expressions, the contributions of each of the pressure terms can be
summarized in tabular form as shown below.
504 Appendix D: Different Heat Pipe Design Examples
Operating temperature (K) σ Pc,m ΔP+ ΔP|| Pp,m
298.15 7.29� 10�2 3728.90 12.21 0 3716.70
232.15 6.93� 10�2 3544.76 12.10 0 3532.66
348.15 6.20� 10�2 3171.35 11.94 0 3159.41
373.15 5.84� 10�2 2987.21 11.77 0 2975.44
Other intermediate values that must be evaluated are as follows:
Wick cross-sectional area: Aw ¼ 14π d2i � d2v� � ¼ 2:9� 10�7 m2
Wick porosity, ε ¼ 1� 14πSNd ¼ 0:625 (Table 2.2, Eq. (2.53), where a wick
crimping factor S ¼ 1:05 is used).
Wick permeability, K ¼ d2 t3=122 1� tð Þ2h i
¼ 2� 10�11 m2 (Table 2.2,
Eq. (2.52)).
Liquid frictional coefficient, Fl ¼ μlKAwλρl
(Eq. 2.44).
Vapor core cross-sectional area, Av ¼ 14πd2v ¼ 1:277� 10�6 m2.
Vapor core hydraulic radius, rhv ¼ 12dv ¼ 0:000625 m.
Drag coefficient, f vRevð Þ ¼ 16 (circular vapor flow passage).
Vapor frictional coefficient, Fv ¼ f vRevð Þμv2r2
hvAvρvλ
(Eq. 2.59).
Assuming that phase transition pressure is almost 0, then, we have
ΔPPh � 0
The governing equation becomes
Pc ¼ FlLeffqþ FvLeffqþ ΔP⊥ þ ΔPk þ ΔPPh
The friction factors can be summarized as follows:
Temperature (K) Fe Fv (qL)c,m qc,m
298.15 69,782.83 3052.10 0.0510 3.45
323.15 41,287.91 965.68 0.0836 5.65
348.15 30,848.13 335.50 0.1013 6.85
373.15 23,182.43 168.66 0.1275 8.61
Computing the effective length as
Leff ¼ 0:5Lc þ La þ 0:5Le ¼ 0:0148 m
The transport capacity can be found as a function of length or in terms of the total
power:
qc,mL� � ¼ Pp,m
Fl þ Fv
W mð Þ or qc,mL� � ¼ qc,mL
Leff
Using a similar approach, the individual pressure terms and transport capacities can
be determined for tilt angles of 15� as follows.
Appendix D: Different Heat Pipe Design Examples 505
Temperature (K) Pc,m ΔP⊥ ΔPk Pp,m
298.15 3728.90 11.79 63.26 3653.85
323.15 3544.76 11.69 62.71 3470.36
348.15 3171.35 11.53 31.84 3097.98
373.15 2987.21 11.38 60.96 2914.87
Temperature (K) qc,mL qc,m
298.15 0.0502 3.39
323.15 0.0821 5.55
348.15 0.0993 6.71
373.15 0.1249 8.44
And for tilt angles of 45� can be determined as follows.
Temperature (K) qc,mL ΔP⊥ ΔP⊥ Pp,m
298.15 3728.90 8.64 172.64 3547.62
323.15 3544.76 8.56 171.14 3365.06
348.15 3171.35 8.44 168.75 2994.16
378.15 2987.21 8.32 166.37 2812.52
Temperature (K) qc,mL qc,m
298.15 0.0487 3.29
323.15 0.0796 5.38
348.15 0.0960 6.48
373.15 0.1205 8.14
Sonic Limit
The sonic limit can be found in Eq. 2.20:
Qsmax¼ Avρ0λ
γ0RvT0
2 γ0 þ 1ð Þ� �1=2
Wð Þ
Vapor molecular weight M ¼ 18
Vapor specific heat ration γ0 ¼ 1:33
Universal gas constant eR ¼ 8:314� 103 J=kg mol K
Vapor constant Rv ¼ 8:314�103
18¼ 462 J=kg K
506 Appendix D: Different Heat Pipe Design Examples
Temperature (K) qs,m
298.15 13.70
323.15 48.85
348.15 146.36
373.15 344.76
Boiling Limit
The boiling limit can be found in Eq. 2.96;
Qbmax¼ 2πLekeffTv
λρvln ri=rvð Þ2σ
rn� Pc,m
� where Pc,m is the capillary pressure in the wicking structure or, if Pc < Pc,m the
maximum capillary pressure found earlier, and the nucleation radius rn is in the
range 2:54� 10�5 � 2:54� 10�7. The effective conductivity of the saturated wick,
keff can be found in
keff ¼ kl klþkw� 1�εð Þ kl�kwð Þð Þklþkw 1�εð Þ kl�kwð Þ
where Le ¼ 0:0118 m and rn ¼ 2:54� 10�7 m or
kw ¼ 402 W=m K.
Temperature (K) keff qb,m
298.15 1.327 2797.53
323.15 1.404 890.54
348.15 1.441 305.24
373.15 1.491 140.35
Entrainment Limit
The entrainment limit can be estimated using Eq. (2.34)
Qemax¼ Avλ
σρv2rh,w
� �1=2where the wick surface pore hydraulic radius is rh,w ¼ 1
2N � d2¼ 2:13� 10�5m
Appendix D: Different Heat Pipe Design Examples 507
Temperature (K) qc,m
298.15 18.45
323.15 33.13
348.15 52.44
373.15 75.56
Viscous Limit
Finally the viscous limit can be estimated using Eq. 2.109:
Qvapormax¼ πr4vhfgρvePve
12μve leff
where f vRevð Þ ¼ 16 and
Temperature (K) Pv(N/m2) qv,m
298.15 3293 42.93
323.15 12,349 219.25
348.15 37,290 760.72
373.15 101,350 2095.25
The five limits can be represented graphically as a function of the mean adiabatic
or operation temperature as shown below (Fig. D.10).
As shown above, this configuration is a capillary limit over the entire tempera-
ture range.
10
100
1000
20 30 40 50ADIABATIC VAPOR TEMPERATURE (�C)
HE
AT
TR
AN
SP
OR
T C
AP
AC
ITY
(W
atts
)
60 70
CAPILLARYSONICBOILINGENTRAINMENTVISCOUS
80 90 100 110
Fig. D.10 Heat transport capacity versus adiabatic vapor temperature
508 Appendix D: Different Heat Pipe Design Examples
Note: It is important to note that in order to determine the actual heat transport
capacity in the preceding Example 6 from Peterson [5], the mean operating
temperature or adiabatic vapor temperature must be known, a priori, which is not
usually the case.
There are many more examples following this one in Peterson’s book [5] that is
recommended for the reader to refer to it.
References
1. Berennan, P. J., & Kroliczek, E. J. (1979). Heat pipe design. From B & K Engineering Volume
I and II. NASA contract NAS5-23406.
2. Chi, S. W. (1976). Heat pipe theory and practice. New York: McGraw-Hill.
3. Silverstein, C. C. (1992). Design and technology of heat pipes for cooling and heat exchange.Washington, DC: Taylor and Francis.
4. Swanson, L. W. Heat Transfer Research Institute College Station, Texas. The CRC Handbookof Mechanical Engineering (2nd Ed., Handbook Series for Mechanical Engineering).
5. Peterson, G. P. (1994). An introduction to heat pipes—Modeling, testing and applications.New York: John Wiley & Sons.
Appendix D: Different Heat Pipe Design Examples 509
Index
AAavid Engineering, 20
Advanced High Temperature Reactor
(AHTR), 342
Aligned Parallel Rectangles, 242
American Society of Mechanical
Engineering (AMSE), 189
Assembly of heat pipe parts, 408
ATS-6, 36
Axial Power Rating (APC), 20
Axial Reynolds Number, 67, 68
BBessel functions, 240
Biot (Bi) number, 238
Bouk fast reactor, 349
Butt joints, 397
CCapillary limit, 88, 139
Capillary pressure, 57
Capillary Pumped Loop (CPL), 10, 289
Charging heat pipe, 414
Cleaning techniques, 405
Closed Loop Pulsating Heat Pipes
(CLPHP), 434
Coaxial Cylinders, 242
Coaxial Parallel Disks, 242
Compressed Air Energy Storage (CAES), 369
Computer Aided Design (CAD), 288
Concentrated Solar Power (CSP), 369, 390
Condenser, 79
Constant Conductance Heat Pipe (CCHP),
12, 13, 431, 439
Cullimore & Ring Technologies (C&R), 287
DData Center Cooling, 343
Design Guidelines, 20
Designed Analysis of Heat-Pipe Wicks, 261
Diffusitivity, 220
Dirty envelope, 403
Dirty wick, 403
Dropwise Condensation, 75
EEddying motions, 66
Electro-Magnetic Interference (EMI), 357
End cap installation, 409
End closure design guidelines, 410
ERATO program, 351
ERIDAN 214, 36
ESRO (the IKE Institute in Stuttgart), 36
Evacuated Tube Heat Pipe Solar Collectors
(ETHPSC), 390
Evaporator, 79
FFirst Law of Thermodynamics, 71
Fixed Conductance, 185
Fixed Conductance Heat Pipe (FCHP), 12, 13
Fluid Integrator (FLUINT), 287
Forced convection, 73
Free convection, 73
© Springer International Publishing Switzerland 2016
B. Zohuri, Heat Pipe Design and Technology, DOI 10.1007/978-3-319-29841-2511
French National Center for Space Research, 36
Fully Inherent, 342
Furukawa Electric, 229
GGas gap, 78
General Purpose Heat Source (GPHS), 348
GFW (Dornier), 36
Goddard Space Flight Center (GSFC), 353
Graphics User Interface (GUI), 288
HHeat Pipe Assemblies, 20
Heat Pipe Heat Exchanger (HPHE), 364
Heat Pipe Operated Mars Exploration
Reactor (HOMER), 344
Heat Transfer Coefficient, 231
Heat Transfer Fluid (HTF), 375, 379,
382, 383
Heat Transfer Unit NTU, 272
High Power Electric Propulsion (HiPEP), 353
HOMER-15 - the Heat Pipe Operated Mars
Exploration Reactor, 351
Hughes (Hughes), 36
IInsulated Gate Bipolar Transistors
(IGBT’s), 358
KKinematic viscosity, 65
Kolmogorov length scale, 65
LLaminar flow, 64, 65, 96
Latent Heat Thermal Energy Storage
(LHTES), 370, 371, 374, 376,
379, 390
Levelized Cost of Energy (LCOE), 369
Liquid Controlled Heat Pipe (LCHP), 13
Liquid Metal Fast Breeder Reactors
(LMFBR), 342
Liquid Transport Factor, 30
Liquid-Vapor Interface, 219
Log Mean Temperature Difference, 231
Loop Heat Pipe (LHP), 10, 34, 121, 289
MMach number, 80
Manufacturing cycle, 401
Maximum capillary pressure, 61
Maximum Expected Operating Pressures
(MEOP), 31
Maximum heat transport rate, 81
Mesh screen, fiberglass, 261
Multi-Mission RTG (MMRTG), 348
NNaK coolant, 349
NASA/Ames (Hughes), 36
NASA/GSFC (Grumman and TRW), 36
Non-Condensable Gas (NCG), 23, 28, 49, 414
Non-Operating Thermal Environment, 258
Nuclear electric systems, 350
OOAO-III, 36
Ocean Reconnaissance Satellites
(RORSATs), 349
Ocean Thermal Energy Conversion
(OTEC), 233
PPartial Differential Equations (PDEs),
220, 326
Performance degradation, 405, 414
Perpendicular Rectangles with a Common
Edge, 242
Phase Change Materials (PCMs), 368,
370–372, 374–377, 379, 383, 385–387,
389, 390
Photovoltaics (PV), 368
Pipe blockage, 422
Prandtl number, 236
Pumped Hydro-Power storage (PHPS), 369
RRadioactive Heater Units (RHUs), 348
Radioisotope Thermoelectric Generators
(RTGs), 347
Reciprocity, 243
Reduced Basis (RB), 240
Reynolds Number, 65
Romashka reactors, 349
512 Index
SSABCA, 37
SAFE-400 space fission reactor, 350
Seamless and butt welded, 396
Sensible Thermal Energy Storage Systems
(STES), 370
Silicon Controlled Rectifiers (SCR’s), 358Skylab, 36
Small Business Innovation Research
(SBIR), 288
Sound structural design, 427
Spiral artery design, 396
Steady-State Design, 212
Steady-State mode, 209
Stirling Radioisotope Generator (SRG), 348
Surface tension, 52
TThermal Energy Storage (TES), 369,
371, 386
Timberwind pebble bed reactor, 349
Tokamak, 350
Topaz reactors, 349
Total thermal capacity, 217
Turbulent flow, 64
Two Phase Flow, 68
Two-Dimensional analyses, 233
UU.S. Department of energy SunShot, 385
VVapor pressure, 415
Vapor-pressure limitation, 133
Variable Conductance, 185
Variable Conductance Heat Pipe (VCHP),
12–14, 16, 28, 49, 431
Variable Cryogenic Heat Pipe, 213
Variable Specific Impulse Magneto plasma
Rocket (VASIMR), 350
Ventilating, and Air Conditioning (HVAC), 2
Viscous limitation, 82, 133
WWeber number, 86
Wick structure, 201, 255
Wicking limit, 88
Wick-liquid dynamics, 68
Working fluid, 399
YYoung-Laplace equation, 52, 57, 58
Index 513
