SIST-TP CEN/CLC/TR 17603-31-08:2021

SLOVENSKI STANDARD
01-oktober-2021
Vesoljska tehnika - Priročnik o toplotni zasnovi - 8. del: Toplotne cevi
Space Engineering - Thermal design handbook - Part 8: Heat Pipes
Raumfahrttechnik - Handbuch für thermisches Design - Teil 8: Wärmerohre
Ingénierie spatiale - Manuel de conception thermique - Partie 8: Caloducs
Ta slovenski standard je istoveten z: CEN/CLC/TR 17603-31-08:2021
ICS:
49.140 Vesoljski sistemi in operacije Space systems and
operations
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

TECHNICAL REPORT
CEN/CLC/TR 17603-31-
RAPPORT TECHNIQUE
TECHNISCHER BERICHT
August 2021
ICS 49.140
English version
Space Engineering - Thermal design handbook - Part 8:
Heat Pipes
Ingénierie spatiale - Manuel de conception thermique - Raumfahrttechnik - Handbuch für thermisches Design -
Partie 8 : Caloducs Teil 8: Wärmerohre

This Technical Report was approved by CEN on 21 June 2021. It has been drawn up by the Technical Committee CEN/CLC/JTC 5.

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© 2021 CEN/CENELEC All rights of exploitation in any form and by any means Ref. No. CEN/CLC/TR 17603-31-08:2021 E
reserved worldwide for CEN national Members and for
CENELEC Members.
Table of contents
European Foreword . 10
1 Scope . 11
2 References . 12
3 Terms, definitions and symbols . 13
3.1 Terms and definitions . 13
3.2 Symbols . 13
4 General introduction . 17
5 Heat pipe wicks . 19
5.1 General . 19
5.2 Basic properties . 20
5.2.1 Equilibrium capillary height . 20
5.2.2 Permeability . 20
5.2.3 Effective thermal conductivity of the wick . 20
5.3 Low resistance wicks . 22
6 Heat pipe working fluids . 28
6.1 General . 28
6.2 Empirical correlations . 29
6.3 Physical properties . 31
6.4 Compatibility with wicks . 47
7 Simple heat pipe . 48
7.1 General . 48
7.2 Operating limits . 48
7.2.1 Capillary heat transfer limit . 49
7.2.2 Sonic limit (choking) . 54
7.2.3 Entrainment limit . 56
7.2.4 Boiling limit . 56
7.3 Performance . 57
8 Variable conductance heat pipes . 70
8.1 General . 70
8.2 Design considerations . 72
8.2.1 Diffusion of the working fluid . 72
8.2.2 Working fluid selection . 73
8.2.3 Reservoir sizing . 74
9 Existing System . 78
9.1 Eads Astrium . 78
9.2 Euro Heat Pipes . 91
9.2.1 Aluminium Heat Pipes . 91
9.2.2 STAINLESS STEEL HEAT PIPES. This part deals with the products
from Technical Data Sheet n° 1B: EHP Stainless Steel . 101
9.3 Iberespacio . 106
9.3.1 Axial Grooved Heat Pipes . 106
9.3.2 Arterial Heat Pipes . 109
9.4 Thales Alenia Space . 111
9.4.1 Technical Description . 111
9.4.2 External Geometries . 113
10 Cryogenic heat pipes . 116
10.1 General . 116
10.2 Working fluids . 116
10.3 Wicks . 118
10.3.1 Lab wicks . 120
10.3.2 Tunnel artery . 120
10.3.3 Graded-porosity wicks . 120
10.4 Operating limits . 121
10.4.1 Capillary heat transfer limit . 121
10.5 Transient operating characteristics . 127
10.5.1 Mathematical modelling of static transient . 127
10.5.2 Mathematical modelling of fluid dynamic transient. 128
10.6 Reduced gravity testing of cryogenic heat pipes . 129
10.7 Thermal diode cryogenic heat pipes . 131
10.7.2 Reversal requirements . 132
10.8 Superfluid heat pipes . 134
10.9 Existing systems . 138
Bibliography . 146

Figures
−1
Figure 5-1: Measured values of the inverse permeability, K , vs. mass flow rate per
unit area, m .> From Phillips & Hinderman (1969) [67]. . 27
−1
Figure 5-2: Measured values of the inverse permeability, K , vs. mass flow rate per
unit area, m .> From Phillips & Hinderman (1969) [67]. . 27
Figure 6-1: Relevant physical properties of Ammonia as a function of temperature, T,
The labels correspond to experimental points. The expressions used to
calculate the tabulated values are given below. Calculated by the compiler. . 32
Figure 6-2: Relevant physical properties of Ethanol as a function of temperature, T, The
labels correspond to experimental points. The expressions used to
calculate the tabulated values are given below. Calculated by the compiler. . 34
Figure 6-3: Relevant physical properties of Freon 11 as a function of temperature, T,
The labels correspond to experimental points. The expressions used to
calculate the tabulated values are given below. Calculated by the compiler. . 36
Figure 6-4: Formulae Used for Calculating the Values of the Physical Properties. . 38
Figure 6-5: Relevant physical properties of Nitrogen as a function of temperature, T,
The labels correspond to experimental points. The expressions used to
calculate the tabulated values are given below. Calculated by the compiler. . 40
Figure 6-6: Relevant physical properties of Propane as a function of temperature, T,
The labels correspond to experimental points. The expressions used to
calculate the tabulated values are given below. Calculated by the compiler. . 42
Figure 6-7: Relevant physical properties of Water as a function of temperature, T, The
labels have been drawn to guide in the selection of the appropriate curve,
and do not correspond to experimental values. After Schmidt (1969) [82]. . 44
Figure 6-8: Figure of Merit, N, as a function of temperature, T, for several heat pipe
working fluids. For each curve, the range of temperature variation is
bounded between the largest and smallest operating pressures. Calculated
by the compiler. . 46
Figure 7-1: Sketch illustrating design variables in grooved heat pipes. From Frank et al.
(1967) [27], quoted by Winter & Barsch (1971) [96]. . 51
Figure 7-2: Relation between the dimensionless parameter 16/β(ν /ν )F and the
v l
geometrical parameter, ψ. From Frank et al. (1967) [27], quoted by Winter
& Barsch (1971) [96]. . 52
Figure 7-3: Optimum value of the dimensionless maximum heat transfer, Q /Γr , vs.
max w
the geometrical parameter, ψ. From Frank et al. (1967) [27], quoted by
Winter & Barsch (1971) [96]. . 53
Figure 7-4: Graph for determining F. From Frank et al. (1967) [27], quoted by Winter &
Barsch (1971) [96]. . 53
Figure 7-5: Optimum value of the aspect ratio of the grooves, α, vs. the geometrical
parameter, ψ. From Frank et al. (1967) [27], quoted by Winter & Barsch
(1971) [96]. . 54
Figure 7-6: Maximum heat transfer, Q , based on sonic limit, vs. evaporator
max
temperature, TE, for several values of the shear streets, τ, and of the
convective heat transfer, Q . Sodium heat pipe. A: τ = 0 and Q = 0; B:
conv conv
τ ≠ 0 and Qconv≠ 0; C: τ≠ 0 and Qconv = 0; D: τ≠ 0 and Qconv ≠ 0. In this case
the heat pipe had an adiabatic length. In curves A, B, and C choking is
reached at the evaporator, while in curve D choking is reached at the
adiabatic length end. From Levy (1972) [49]. . 55
Figure 7-7: Heat Transfer, Q , and Integral Heat Transport Factor, [Q.l ] , vs. wick
max eff max
thickness, δ, for several mesh sizes and two heat pipe diameters, D .
o
Circumferential screen wick. Solid lines: vapour laminar flow; dotted lines:
vapour turbulent flow. From Skrabek (1972) [88]. . 58
Figure 7-8: Heat Transfer, Q , and Integral Heat Transport Factor, [Q.l ] , vs. wick
max eff max
thickness, δ, for several mesh sizes and two heat pipe diameters, D .
o
Circumferential screen wick. Solid lines: vapour laminar flow; dotted lines:
vapour turbulent flow. From Skrabek (1972) [88]. . 59
Figure 7-9: Heat Transfer, Q , and Integral Heat Transport Factor, [Q.l ] , vs. wick
max eff max
thickness, δ, for several mesh sizes and two heat pipe diameters, D .
o
Circumferential screen wick. Solid lines: vapour laminar flow; dotted lines:
vapour turbulent flow. From Skrabek (1972) [88]. . 60
Figure 7-10: Heat Transfer, Q , and Integral Heat Transport Factor, [Q.l ] , vs. wick
max eff max
thickness, δ, for several mesh sizes and two heat pipe diameters, D .
o
Porous slab wick. Solid lines: vapour laminar flow; dotted lines: vapour
turbulent flow. From Skrabek (1972) [88]. . 61
Figure 7-11: Heat Transfer, Q , and Integral Heat Transport Factor, [Q.l ] , vs. wick
max eff max
thickness, δ, for several mesh sizes and two heat pipe diameters, D .
o
Porous slab wick. Solid lines: vapour laminar flow; dotted lines: vapour
turbulent flow. From Skrabek (1972) [88]. . 62
Figure 7-12: Heat Transfer, Q , and Integral Heat Transport Factor, [Q.l ] , vs. wick
max eff max
thickness, δ, for several mesh sizes and two heat pipe diameters, D .
o
Porous slab wick. Solid lines: vapour laminar flow; dotted lines: vapour
turbulent flow. From Skrabek (1972) [88]. . 63
Figure 7-13: Heat pipe conductance, C, vs. wick thickness, δ, for several wick
conductivities, k , and two heat pipe diameters, D . Circumferential screen
eff o
wick. From Skrabek (1972) [88]. . 64
Figure 7-14: Heat pipe conductance, C, vs. wick thickness, δ, for several wick
conductivities, k , and two heat pipe diameters, D . Circumferential screen
eff o
wick. From Skrabek (1972) [88]. . 65
Figure 7-15: Heat pipe conductance, C, vs. wick thickness, δ, for several wick
conductivities, k , and two heat pipe diameters, D . Circumferential screen
eff o
wick. From Skrabek (1972) [88]. . 66
Figure 7-16: Heat pipe conductance, C, vs. wick thickness, δ, for several values of the
heat transfer coefficient of the wick, h, and heat pipe diameters, D . Porous
o
slab wick. From Skrabek (1972) [88]. . 67
Figure 7-17: Heat pipe conductance, C, vs. wick thickness, δ, for several values of the
heat transfer coefficient of the wick, h, and heat pipe diameters, D . Porous
o
slab wick. From Skrabek (1972) [88]. . 68
Figure 7-18: Heat pipe conductance, C, vs. wick thickness, δ, for several values of the
heat transfer coefficient of the wick, h, and heat pipe diameters, D . Porous
o
slab wick. From Skrabek (1972) [88]. . 69
Figure 8-1: VCHP with cold reservoir. . 71
Figure 8-2: VCHP with hot reservoir. (a) Internal hot reservoir. (b) External hot
reservoir. . 72
Figure 8-3: Vapor concentration at the reservoir, n(t), over its steady-state value, n(∞),
and control temperature range, ∆T, as functions of time, t. From
Hinderman. Waters & Kaser (1972) [35]. . 73
Figure 8-4: Dimensionless pressure ratio, π , vs. control temperature range, T −T ,
r Emax Emin
for several working fluids. From Hinderman, Waters & Kaser (1972) [35]. . 74
Figure 8-5: Sketch of a variable conductance heat pipe. 1: Evaporator. 2: Adiabatic
Section. 3: Condenser. 4: Adiabatic Section. 5: Reservoir. . 75
Figure 8-6: Dimensionless reservoir to condenser volume ratio, V /V , vs. evaporator
R C
temperature variation, (T −T ), for two different working fluids, and a
Emax Emin
given reservoir temperature variation, (T −T ) = 28 K. From Edelstein
Rmax Rmin
& Hembach (1972) [23]. . 75
Figure 8-7: Dimensionless reservoir to condenser volume ratio, V /V , vs. reservoir
R C
temperature variation, (T −T ), with fixed evaporator control
Rmax Rmin
temperature variation, (T −T ) = 6 K. From Edelstein & Hembach
Emax Emin
(1972) [23]. . 76
Figure 8-8: Dimensionless reservoir to condenser volume ratio, V /V , vs. evaporator
R C
temperature variation, (T −T ), for ammonia working fluid. From
Emax Emin
Edelstein & Hembach (1972) [23]. . 76
Figure 8-9: Dimensionless reservoir to condenser volume ratio, V /V , vs. evaporator
R C
temperature variation, (T −T ). Solid lines: cold reservoir. Dashed
Emax Emin
lines: hot reservoir. (A) and (M) correspond to ammonia and methanol
respectively. T is the sink temperature; in one case the back of the radiator
s
is pained black (222 K < T < 254 K), and in the other it is aluminized (196 K
s
< T < 245 K). Evaporator temperature, T = (287 + (T −T )/2) K. From
s E Emax Emin
Kirkpatrick & Marcus (1972) [42]. . 77
Figure 9-1: WR7 Heat Pipe Profile (Cryogenic Application) . 83
Figure 9-2: WR12 Heat Pipe Profile. 84
Figure 9-3: WR18 Heat Pipe Profile. 84
Figure 9-4: WR19 Heat Pipe Profile. 85
Figure 9-5: WR20 Heat Pipe Profile. 85
Figure 9-6: WR22 Heat Pipe Profile. 86
Figure 9-7: WR24 Heat Pipe Profile. 86
Figure 9-8: WR25 Heat Pipe Profile. 87
Figure 9-9: WR26 Heat Pipe Profile. 87
Figure 9-10: WR27 Heat Pipe Profile . 88
Figure 9-11: WR28 Heat Pipe Profile . 88
Figure 9-12: WR29 Heat Pipe Profile . 89
Figure 9-13: WR7 Heat Pipe used for SCIAMACHY on ENVISAT . 89
Figure 9-14: EADS ASTRIUM HP experience . 90
Figure 9-15: EHP: typical Aluminium extruded HP . 91
Figure 9-16: Heat transport capability – NH3 (Note: AG110 = size 11 mm in tens of
millimetres.) . 94
Figure 9-17: HP Profile Tolerances. 97
Figure 9-18: HP Profile Tolerances (cont.). 98
Figure 9-19: HP Profile Tolerances (cont.). 99
Figure 9-20: ESA SMART 1 with HP . 100
Figure 9-21: ESA AEOLUS – ALADIN instrument with HP network . 100
Figure 9-22: Constant Conductance Heat Pipe . 101
Figure 9-23: Variable Conductance Heat Pipe . 101
Figure 9-24: Heat Pipe Profiles examples Table 9.2-3. Stainless Steel Heat Pipes
types. . 102
Figure 9-25: “Thank to 40 state-of-the art variable conductance heat pipes located in
the avionics bay the ATV is able to carry away the heat and release the
energy directly into space or, otherwise, to warm up other parts in a very
economic fashion” Astrium – ESA “Jules Verne goes hot and cold” –
Successful achievement of the Qualification Thermal Test campaign – 14
Dec 2006. . 104
Figure 9-26: Stainless Steel HP Performance curves . 105
Figure 9-27: Stainless Steel HP Performance curves (cont.) . 105
Figure 9-28: Axial Grooved HP profiles . 106
Figure 9-29: Axial Grooved HP profiles drawings . 107
Figure 9-30: Dependence of AGHP Heat Transfer Capacity on Working Fluid
(Ammonia) . 108
Figure 9-31: Influence of tilt angle on AGHP maximum Heat Transfer Capacity at 20°C . 108
Figure 9-32: Thermal performance of Arterial HP with different working fluids . 109
Figure 9-33: Experimental data for Arterial HP with ammonia . 109
Figure 9-34: Arterial HP profile schematics . 110
Figure 9-35: Arterial HP typical configurations . 110
Figure 9-36: Arterial HP for rotator application. Length 2400 mm. Power 150 W. . 111
Figure 9-37: 0g guaranteed heat transport capability for ThalesAlenia Space Heat
Pipes . 112
Figure 9-38: Mono-core heat pipe profile . 113
Figure 9-39: Dual-core heat pipe profiles . 114
Figure 9-40: Minimal dimensions of straight parts for Ø 12.2 bent heat pipe . 115
Figure 10-1: Operating temperature range for cryogenic working fluids. Data from
ECSS-E-HB-31-01 Part 14, Table 8-1, clause 8.1.1. For fluorine: melting
point, T = 53,5 K, critical point, T = 144 K. . 117
Figure 10-2: Figure of Merit, N, as a function of temperature, T, for several cryogenic
working fluids. Compare with Figure 6-8, clause 6.3. Replotted after Chi &
Cygnarowicz (1970) [15]. . 118
Figure 10-3: Axial distribution of porosity, Φ, and cross section of a graded-porosity
slab wick. From Groll, Pittman & Eninger (1976) [30]. . 121
Figure 10-4: Maximum heat transport factor, (Q.l ), for a homogeneous wick heat pipe
eff
as a function of inner diameter, D, for different gravity levels. a) Working
i
fluid is Nitrogen at 77 K. b) Oxygen at 77 K. From Joy (1970) [38]. . 124
Figure 10-5: Maximum heat transport factor, (Q.l ), for an axially grooved heat pipe
eff
and for a homogeneous wick heat pipe vs. inner diameter of the pipe, D , for
i
different gravity levels. Working fluid is Oxygen at 77 K. From Joy (1970)
[38]. . 125
Figure 10-6: Axial temperature drop, ∆T, for Oxygen heat pipes at 77 K vs. inner
diameter of the pipe, D. Also shown are data for an axially grooved heat
i
pipe and for aluminium rods of the same diameter. From Joy (1970) [38].
Calculation procedure is outlined in the text. . 126
Figure 10-7: Nodal points in the static transient model of a heat pipe. From Smirnov,
Barsookov & Mishchenko (1976) [89]. . 127
Figure 10-8: Schematic of the heat pipe considered by Chang & Colwell (1985) [13]. . 128
Figure 10-9: ERTS-C (Landsat III) cryogenic heat pipe experiment configuration. From
Brennan & Kroliczek (1975) [45]. . 130
Figure 10-10: Schematic of a blocking orifice thermal diode heat pipe. From Kosson,
Quadrini & Kirckpatrick (1974) [44] . 131
Figure 10-11: a) Axial temperature profiles during reverse mode tests of a cryogenic
heat pipe diode. No tilt. Tests performed in an insulated LN cooled
enclosure. At time 0 power (3 W) is removed from the evaporator, and the
reservoir heater is on. T is the ambient temperature within the enclosure.
o
b) Shut-down temperature response of evaporator and upstream end of
blocked transport section. From Quadrini & McCreight (1977) [66]. . 133
Figure 10-12: Axial temperature profiles during reverse mode tests. Tests performed as
in Figure 10-11a except 1 W heat load on the evaporator continuously fed
during the run. T is the ambient temperature within the enclosure. From
o
Quadrini & McCreight (1977) [66]. . 134
Figure 10-13: Cross section of Heat Pipe 2. From Murakami & Kaido (1980) [61]. All
the dimensions are in mm. . 135
Figure 10-14: Temperature, T, vs. heat transfer rate, Q, in Heat Pipe 3. T is the
-3
evaporator temperature, T and T are in the adiabatic clause 88 x 10 m
2 3
-3
and 78 x 10 m from the evaporator end. The sink temperature is T = 1,9
s
K. From Murakami (1982) [60]. . 136
Figure 10-15: Critical heat transfer rate, Q , and l-transition heat transfer rate, Q , for
c λ
the three heat pipes as a function of sink temperature, T . From Murakami
s
(1982) [60]. Key is given below. . 137
Figure 10-16: Integral heat transport factor, (Q.l ) , vs. operating temperature, T, of
eff max
the cryogenic heat pipes tabulated in Table 10-4. . 145

Tables
Table 5-1: Empirical Correlations for the Determination of Wick Properties . 21
Table 5-2: Properties of Wick Materials . 23
Table 6-1: Chemical Compatibility between Typical Wick Materials and Working Fluids. . 47
Table 7-1: Combinations of Temperatures, Working Fluids, Wick and Container
Materials, and Heat Pipe Outer Diameters. . 57
Table 9-1: Selected Aluminium Heat Pipe Profiles. . 79
Table 9-2: Aluminium Heat Pipe Profiles (cont.) . 80
Table 9-3: Aluminium Heat Pipe Profiles (cont.) . 81
Table 9-4: Aluminium Heat Pipe Profiles (cont.) . 82
Table 9-5: Aluminium Heat Pipe Profiles (cont.) . 83
Table 9-6: EHP Aluminium Heat Pipes Performance . 92
Table 9-7: Available HP Profiles . 95
Table 9-8: Stainless Steel Heat Pipes types . 102
Table 9-9: Geometrical Parameters . 107
Table 9-10: Thermal Performances of ThalesAlenia Space Heat Pipes (*): QL 6mm
max
guaranteed . 112
Table 9-11: Mass of ThalesAlenia Space Heat Pipes . 113
Table 9-12: External geometries of ThalesAlenia Space Heat Pipes . 114
Table 10-1: Main Features of Cryogenic Fluids in Heat Pipes, Consequences . 116
Table 10-2: Wicking Structures. Current Technology . 118
Table 10-3: Evolution of Vapor to Liquid Kinematic Viscosity Ratio over Working
a
Temperature Range . 123
Table 10-4: Characteristics of Tested Cryogenic Heat Pipes . 138
Table 10-5: Characteristics of Tested Cryogenic Heat Pipes, Materials . 140
Table 10-6: Characteristics of Tested Cryogenic Heat Pipes, Operating Conditions . 142

European Foreword
This document (CEN/CLC/TR 17603-31-08:2021) has been prepared by Technical Committee
CEN/CLC/JTC 5 “Space”, the secretariat of which is held by DIN.
It is highlighted that this technical report does not contain any requirement but only collection of data
or descriptions and guidelines about how to organize and perform the work in support of EN 16603-
31.
This Technical report (TR 17603-31-08:2021) originates from ECSS-E-HB-31-01 Part 8A.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such
patent rights.
This document has been prepared under a mandate given to CEN by the European Commission and
the European Free Trade Association.
This document has been developed to cover specifically space systems and has therefore precedence
over any TR covering the same scope but with a wider domain of applicability (e.g.: aerospace).
Scope
Heat pipes are a solution to many thermal dissipation problems encountered in space systems.
The types of heat pipes that can be used in spacecrafts are described. Details on design and
construction, usability, compatibility and the limitations of each type are given.

The Thermal design handbook is published in 16 Parts
TR 17603-31-01 Thermal design handbook – Part 1: View factors
TR 17603-31-02 Thermal design handbook – Part 2: Holes, Grooves and Cavities
TR 17603-31-03 Thermal design handbook – Part 3: Spacecraft Surface Temperature
TR 17603-31-04 Thermal design handbook – Part 4: Conductive Heat Transfer
TR 17603-31-05 Thermal design handbook – Part 5: Structural Materials: Metallic and
Composite
TR 17603-31-06 Thermal design handbook – Part 6: Thermal Control Surfaces
TR 17603-31-07 Thermal design handbook – Part 7: Insulations
TR 17603-31-08 Thermal design handbook – Part 8: Heat Pipes
TR 17603-31-09 Thermal design handbook – Part 9: Radiators
TR 17603-31-10 Thermal design handbook – Part 10: Phase – Change Capacitors
TR 17603-31-11 Thermal design handbook – Part 11: Electrical Heating
TR 17603-31-12 Thermal design handbook – Part 12: Louvers
TR 17603-31-13 Thermal design handbook – Part 13: Fluid Loops
TR 17603-31-14 Thermal design handbook – Part 14: Cryogenic Cooling
TR 17603-31-15 Thermal design handbook – Part 15: Existing Satellites
TR 17603-31-16 Thermal design handbook – Part 16: Thermal Protection System

References
EN Reference Reference in text Title
EN 16603-00-01 ECSS-S-ST-00-01 ECSS System - Glossary of terms
TR 17603-31-10 ECSS-E-HB-31-01 Part 10 Thermal design handbook – Part 10: Phase-
Change Capacitors
TR 17603-31-13 ECSS-E-HB-31-01 Part 13 Thermal design handbook – Part 13: Fluid
Loops
TR 17603-31-14 ECSS-E-HB-31-01 Part 14 Thermal design handbook – Part 14: Cryogenic
Cooling
All other references made to publications in this Part are listed, alphabetically, in the Bibliography.

Terms, definitions and symbols
3.1 Terms and definitions
For the purpose of this Standard, the terms and definitions given in ECSS-S-ST-00-01 apply.
3.2 Symbols
vapour core cross-sectional area, [m ]
Av
wick cross-sectional area, [m ].
Aw
-1
heat pipe thermal conductance, [W.K ]
C
-1
heat capacity associated to node i, [J.K ]
Ci
inner wall diameter of the pipe, [m]
Di
outer wall diameter of the pipe, [m]
Do
diameter of particles, [m]
DP
diameter of the vapour space, [m]
Dv
equilibrium capillary height, [m]
H
-1
heat transfer coefficient between nodes i and j, [W.K ]
Hij
permeability, [m ]
K
-1
molar mass, [kg.mol ]
M
-2
figure of merit, [W.m ] N = ρ1hfgσ/µ1
N
heat transfer rate, [W]
Q
integral heat transport factor, [W.m]
(Q.leff)
-1 -1
universal gas constant, R = 8,3143 J.K .mol
R
-1 -1
gas constant of a particular gas, [J.K .kg ] Rg = R/M
Rg
Reynolds number, Re = ρVDi/µ
Re
temperature, [K]
T
sink temperature, [K]
Ts
Clause 5: radial temperature drop between vapour-liquid
∆T
interface and heat pipe wall, [K]
Clause 8: control temperature range of a VCHP, [K]

Clause 10: axial temperature drop, [K]

-1
Clause 7: velocity, [m.s ]
V
Clause 8: volume, [m ]
Weber number, We = ρv(Vv) l’/σ
We
-1
velocity of sound, [m.s ]
a
dimensionless constant of a capillary structure, see clause
b
7.2.1.1
-2
acceleration due to gravity, [m.s ]
g
-2 -1
heat transfer coefficient of the wick, [W.m .K ]
h
-1
latent heat of vaporization, [J.kg ]
hfg
-1 -1
thermal conductivity, [W.m .K ]
k
-1 -1
effective thermal conductivity of the wick, [W.m .K ]
keff
-1 -1
thermal conductivity of the wick material, [W.m .K ]
kw
length, [m]
l
characteristic length associated with the wick surface, [m]
l’
it is used to define the Weber number
effective heat pipe length, [m] leff = lA + (lC+lE)/2
leff
wick length, [m]
lw
-1
mass flow rate. [kg.s ]
m
-2 -1
mass flow rate per unit area, [kg.m .s ] it is also called

mass flux
number of moles
n
pressure, [Pa]
p
standard atmospheric pressure, pa = 1,01325x10 Pa
pa
pressure drop, [Pa]
∆p
capillary pumping pressure, [Pa]
∆pc
-2
radial heat flux, [W.m ]
q
radius, [m]
r
radius of bubble nucleus, [m]
rb
effective pore radius of the capillary structure, [m]
rc
Time, [h]
t
groove width, [m]
w
fin thickness, [m]
w’
coordinate along heat pipe, [m] it is measured from the
x
evaporator
Π wetted perimeter of a duct, [m]
wick porosity
Φ
γ vapor specific heat ratio
wick thickness or groove depth, [m]
δ
θ wetting angle, [angular degrees]
wetting angle in the evaporator, [angular degrees]
θE
µ dynamic viscosity, [Pa.s]
ν Clauses 5 and 7: liquid to wick material thermal
conductivity ratio
2 -1
Clause 10: kinematic viscosity, [m .s ]

dimensionless pressure ratio
πr
-3
density, [kg.m ]
ρ
-1
σ surface tension, [N.m ]
shear stress, [Pa]
τ
ϕ tilting angle, [angular degrees], positive when the
evaporator is up
ψ geometrical parameter, it is defined in clause 11.2.1.2

Subscripts
adiabatic
A
condenser
C
evaporator
E
reservoir
R
normal boiling conditions
b
Clause 6: thermodynamic critical conditions
c
Clause 7: capillary
Clause 10: superfluid dynamics critical conditions

effective
eff
freezing conditions
f
inner wall
i
liquid phase
l
maximum
max
minimum
min
Clause 6: reference temperature conditions
o
Clauses 7, 8 and 10: outer wall

saturation conditions
sat
vapour phase
v
wick material
w
helium-4 conditions at the Lambda point
λ
Other symbols, mainly used to define the geometry of the configuration, are introduced when
required.
General introduction
The heat pipe is a thermal device which affords an efficient transport of thermal energy. It is
constituted by a closed structure containing a working fluid which transfers the thermal energy from
one part (evaporator) to another (condenser). The phenomena involved in the transfer process are the
following:
1. Vaporization in the evaporator;
2. vapor flow in the core region of the container;
3. condensation in the condenser, and
4. liquid return to the evaporator by capillary action in the wick.
The capillary pumping permits to the heat pipe to be operated in any orientation, in contrast to
evaporation cooling devices which can only work when the evaporator is placed at the lowest point of
the system.
The pressure variations in the vapor core are normally small and, therefore, the heat pipe temperature
is nearly uniform and close to the saturated vapor temperature corresponding to the vapor pressure.
The capability of transporting large amounts of thermal energy between two terminals (evaporator
and condenser) with a small temperature difference is the main characteristic of the heat pipe which
can be considered an extra-high thermal conductivity device in the Fourier’s law sense.
In addition to its superior heat transfer characteristics, the heat pipe is structurally simple, relatively
inexpensive, insensitive to the gravitational field, and silent and reliable in its operation. It can be
made into different shapes and, by using the working fluid best suited to the desired temperature
range, can operate at temperature ranging from the cryogenic regions up to high temperature levels
which are only limited by structural reasons.
Because the immense potential of heat pipes, they have been employed in many engineering
applications, spacecraft thermal control not being an exception.
Classical papers concerning heat pipes are those by Grover et al. (1964) [32] and Cotter (1965) [18]. A
presentation of the background required by those wishing to use or to design heat pipes has been
made by Dunn & Reay (1976) [21].
Several examples of application of heat pipes to spacecraft are given in the following:
1. It is well known that large temperature variations may occur in the surface of a spacecraft
because non-uniform heating. These temperature variations can cause a host of problems
including undesirable thermal stresses. Katzoff (1967) [39] has recommended the use of
long heat pipes wrapped around the outer surface of a spacecraft to accomplish the
necessary equalization of the temperature distribution.
2. Another application which has received considerable attention is the cooling of electronic
components of spacecraft systems. These components are often located in the interior of
the satellite, and the aim of the heat pipe is to transfer the waste heat over some distance
for ultimate rejection to outer space.
3. The use of radiators formed by heat pipes has been suggested several times. The heat
pipes produce nearly uniform temperatures on the radiator surface, and the redundancy
achieved when used in parallel arrangement provides some degree of increased meteor
protection to the radiator.
Intensive heat pipe research and development have resulted in rapid advancement in a variety of
directions: from the simple cylindrical shape to complex geometries; from a screen mesh to
multicomponent capillary-wick structures; from a passive variable-temperature conduction link to
self-controlled, variable-conductance, constant-temperature devices, and from the high conductance
function to a multitude of thermal control functions (such as switching, trans
...