SIST-TP CEN/CLC/TR 17603-31-04:2021

Space Engineering - Thermal design handbook - Part 4: Conductive Heat Transfer

This Part 4 of the spacecraft thermal control and design data handbooks, provides information on calculating the conductive heat transfer rate for a variety of two and three-dimensional configurations.
Calculations for the conductance of the interface between two surfaces (joints) require special consideration and are included as a separate clause.
The Thermal design handbook is published in 16 Parts
TR 17603-31-01 Part 1
Thermal design handbook – Part 1: View factors
TR 17603-31-01 Part 2
Thermal design handbook – Part 2: Holes, Grooves and Cavities
TR 17603-31-01 Part 3
Thermal design handbook – Part 3: Spacecraft Surface Temperature
TR 17603-31-01 Part 4
Thermal design handbook – Part 4: Conductive Heat Transfer
TR 17603-31-01 Part 5
Thermal design handbook – Part 5: Structural Materials: Metallic and Composite
TR 17603-31-01 Part 6
Thermal design handbook – Part 6: Thermal Control Surfaces
TR 17603-31-01 Part 7
Thermal design handbook – Part 7: Insulations
TR 17603-31-01 Part 8
Thermal design handbook – Part 8: Heat Pipes
TR 17603-31-01 Part 9
Thermal design handbook – Part 9: Radiators
TR 17603-31-01 Part 10
Thermal design handbook – Part 10: Phase – Change Capacitors
TR 17603-31-01 Part 11
Thermal design handbook – Part 11: Electrical Heating
TR 17603-31-01 Part 12
Thermal design handbook – Part 12: Louvers
TR 17603-31-01 Part 13
Thermal design handbook – Part 13: Fluid Loops
TR 17603-31-01 Part 14
Thermal design handbook – Part 14: Cryogenic Cooling
TR 17603-31-01 Part 15
Thermal design handbook – Part 15: Existing Satellites
TR 17603-31-01 Part 16
Thermal design handbook – Part 16: Thermal Protection System

Raumfahrttechnik - Handbuch für thermisches Design - Teil 4: Konduktive Wärmeübertragung

Ingénierie spatiale - Manuel de conception thermique - Partie 4: Transfert de chaleur par conduction thermique

Vesoljska tehnika - Priročnik o toplotni zasnovi - 4. del: Konduktivni prenos toplote

General Information

• Status: Published
• Public Enquiry End Date: 12-May-2021
• Publication Date: 19-Aug-2021
• ICS: 49.140 - Space systems and operations
• Technical Committee: I13 - Imaginarni 13
• Current Stage: 6060 - National Implementation/Publication (Adopted Project)
• Start Date: 16-Aug-2021
• Due Date: 21-Oct-2021
• Completion Date: 20-Aug-2021
• Mandate: M/496 - Mandate addressed to CEN, CENELEC and ETSI to develop standardisation regarding space industry (Phase 3 of the process)
• Ref Project: CEN/CLC/TR 17603-31-04:2021 - Space Engineering - Thermal design handbook - Part 4: Conductive Heat Transfer

Standards Content (Sample)

SLOVENSKI STANDARD
SIST-TP CEN/CLC/TR 17603-31-04:2021
01-oktober-2021
Vesoljska tehnika - Priročnik o toplotni zasnovi - 4. del: Konduktivni prenos toplote
Space Engineering - Thermal design handbook - Part 4: Conductive Heat Transfer
Raumfahrttechnik - Handbuch für thermisches Design - Teil 4: Konduktive
Wärmeübertragung
Ingénierie spatiale - Manuel de conception thermique - Partie 4: Transfert de chaleur par
conduction thermique
Ta slovenski standard je istoveten z: CEN/CLC/TR 17603-31-04:2021
ICS:
49.140 Vesoljski sistemi in operacije Space systems and
operations
SIST-TP CEN/CLC/TR 17603-31-04:2021 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST-TP CEN/CLC/TR 17603-31-04:2021

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SIST-TP CEN/CLC/TR 17603-31-04:2021


TECHNICAL REPORT
CEN/CLC/TR 17603-31-
04
RAPPORT TECHNIQUE

TECHNISCHER BERICHT

August 2021
ICS 49.140

English version

Space Engineering - Thermal design handbook - Part 4:
Conductive Heat Transfer
Ingénierie spatiale - Manuel de conception thermique - Raumfahrttechnik - Handbuch für thermisches Design -
Partie 4 : Transfert de chaleur par conduction Teil 4: Leitender Wärmeübertragung


This Technical Report was approved by CEN on 14 June 2021. It has been drawn up by the Technical Committee CEN/CLC/JTC 5.

CEN and CENELEC members are the national standards bodies and national electrotechnical committees of Austria, Belgium,
Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy,
Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of North Macedonia, Romania, Serbia,
Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom.
























CEN-CENELEC Management Centre:
Rue de la Science 23, B-1040 Brussels
© 2021 CEN/CENELEC All rights of exploitation in any form and by any means Ref. No. CEN/CLC/TR 17603-31-04:2021 E
reserved worldwide for CEN national Members and for
CENELEC Members.

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CEN/CLC/TR 17603-31-04:2021 (E)
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 Abbreviated terms. 13
3.3 Symbols . 13
4 Conductive shape factors . 15
4.1 General . 15
4.2 Planar-planar surfaces . 16
4.2.1 Two-dimensional configurations . 16
4.3 Planar surface-cylindrical surface . 18
4.3.1 Two-dimensional configurations . 18
4.3.2 Axisymmetrical configuration . 21
4.4 Planar surface-spherical surface . 23
4.4.1 Plane and sphere . 23
4.5 Cylindrical-cylindrical surfaces . 25
4.5.1 Two-dimensional configurations . 25
4.6 Spherical-spherical surfaces . 41
4.6.1 Two concentric spheres . 41
5 Thermal joint conductance . 43
5.1 General . 43
5.1.1 Empirical correlations . 44
5.1.2 Thermal interface materials . 48
5.1.3 Joint geometries . 50
5.2 Bare metallic joints . 51
5.2.1 Metal-metal joints . 62
5.2.2 Metal-composite joints . 94
5.2.3 Composite-composite joints . 96
2

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5.3 Interfacial materials between metals . 98
5.3.1 Metallic foils between metals . 98
5.3.2 Metallic oxide powders between similar metals . 109
5.3.3 Porous metallic materials between similar metals. . 109
5.3.4 Insulating spacers between similar metals . 119
5.3.5 Fluids between metals . 133
5.3.6 Elastomeric spacers between similar metals . 142
5.4 Outgassing data . 151
Bibliography . 153

Figures
Figure 4-1: Values of the conductive shape factor per unit length, S/L, vs. the
dimensionless width of the strip, X. Calculated by the compiler. . 17
Figure 4-2: Values of the conductive shape factor per unit length, S/L, vs. X for different
values of Y. Calculated by the compiler. . 19
Figure 4-3: Values of the conductive shape factor per unit length, S/L, vs.
dimensionless diameter of the cylinder cross section. Calculated by the
compiler. . 20
Figure 4-4: Values of the dimensionless conductive shape factor, S/L, vs. cylinder
diameter to length ratio, D/L. Calculated by the compiler. . 22
Figure 4-5: Values of the dimensionless conductive shape factor, S/D, vs. the
dimensionless diameter of the sphere, Z. Calculated by the compiler. . 24
Figure 4-6: Values of the conductive shape factor per unit length, S/L, vs. radius ratio,
ρ; for different values of the dimensionless distance between cylinder axes,
ε. Calculated by the compiler. . 26
Figure 4-7: Values of the dimensionless conductive shape factors per unit length, S /L,
ij
vs. the eccentricity of one of the holes X , for different values of the relevant
2
geometrical parameters. From Faulkner & Andrews (1955) [13]. . 28
Figure 4-8: Values of the conductive shape factors per unit length, S /L, vs. the
ij
diameter ratio d , for different values of the relevant geometric parameters.
3
From Faulkner & Andrews (1955) [13]. . 30
Figure 4-9: Values of the conductive shape factor per unit length, S/L, vs. the
dimensionless characteristic length of the holes, X. Calculated by the
compiler. . 32
Figure 4-10: Values of the conductive shape factor per unit length, S/L, vs. the
dimensionless diameter of the hole, X, for several values of the aspect
ratio, Y, of the rectangular bar cross-section. Calculated by the compiler. . 34
Figure 4-11: Values of the conductive shape factor per unit length, S/L, vs. the
dimensionless diameter of the hole, X, for different values of the aspect
ratio, Y, of the rectangular bar cross section. After Griggs, Pitts & Goyal
(1973) [25]. . 36
Figure 4-12: Values of the conductive shape factor per unit length, S/L, vs. the
dimensionless diameter of the hole, X, for several values of the aspect
3

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CEN/CLC/TR 17603-31-04:2021 (E)
ratio, Y, of the rectangular bar cross section. After Griggs, Pitts & Goyal
(1973) [25]. . 38
Figure 4-13: Values of the conductive shape factor per unit length, S/L, vs. the
dimensionless hole radius, ρ, for several values of n. Calculated by the
compiler. . 40
Figure 4-14: Values of the dimensionless conductive shape factor, S/r , vs. radius ratio,
1
ρ. Calculated by the compiler. . 42
Figure 5-1: Estimation of the temperature drop at the interface. . 43
Figure 5-2: Variation of gap thickness parameter, δ , with contact surface parameter, d.
ο
After Fletcher & Gyorog (1970) [17]. . 45
Figure 5-3: Variation of contact conductance with apparent interface pressure. After
Fletcher & Gyorog (1970) [17]. . 46
Figure 5-4: Dimensionless conductance vs. dimensionless load. Stainless steel under
vacuum conditions. From Thomas & Probert (1972) [47]. . 47
Figure 5-5: Dimensionless conductance vs. dimensionless load. Stainless steel under
vacuum conditions. From Thomas & Probert (1972) [47]. . 48
Figure 5-6: Schematic representation of two surfaces in contact and heat flow across
the interface. . 48
Figure 5-7: Interface material compressed between two contacting surfaces. . 49
Figure 5-8: Plots of contact conductance vs. contact pressure for two different surface
finishes. From Fried & Kelley (1966) [24]. . 51
Figure 5-9: Plot of contact conductance vs. contact pressure for two different surface
finishes. From Fried & Atkins (1965) [23]. . 52
Figure 5-10: Plots of contact conductance vs. contact pressure for two different surface
finishes. From Fried (1966) [22] quoted by Scollon & Carpitella (1970) [43]. . 53
Figure 5-11: Plot of contact conductance vs. contact pressure for different ambient
pressures. From Fried & Kelley (1966) [24]. . 54
Figure 5-12: Plots of contact conductance vs. contact pressure for different surface
finishes and ambient pressures. Circle: From Fried & Atkins (1965) [23].
Square: From Fried (1966) [21] quoted by Scollon & Carpitella (1970) [43]. . 55
Figure 5-13: Plot of contact conductance vs. contact pressure for different surface
finishes. From Clausing & Chao (1965) [7]. . 56
Figure 5-14: Plot of contact conductance vs. contact pressure for different surface
finishes. From Fried & Atkins (1965) [23]. . 57
Figure 5-15: Plot of contact conductance vs. contact pressure for various surface
finishes, mean temperatures and ambient pressures. Circle, square and
rhombus: from Clausing & Chao (1965) [7]. Triangle: from Fried (1966) [21]
quoted by Scollon & Carpitella (1970) [43]. . 58
Figure 5-16: Plot of contact conductance vs. contact pressure. Notice the directional
effect on contact conductance. From Fried & Kelley (1966) [24]. . 59
Figure 5-17: Plot of contact conductance vs. contact pressure for different surface
finishes. Circle and square: from Fried (1965) [21]. Rhombus and triangle:
from Fried & Atkins (1965) [23]. Inverted triangle and right-oriented triangle:
from Fried & Kelley (1966) [24]. . 60
4

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Figure 5-18: Plot of contact conductance vs. contact pressure for different surface
finishes. Circle: From Fried (1966) [22] quoted by Scollon & Carpitella
(1970) [43]. Square: From Gyorog (1970) [26]. 61
Figure 5-19: Plot of contact conductance vs. contact pressure for different surface
finishes. From Fried (1966) [21] quoted by Scollon & Carpitella (1970) [43]. . 62
Figure 5-20: Plot of contact conductance vs. contact pressure for different surface
finishes: smooth surfaces. White square: from Padgett & Fletcher (1982)
[35]. Black square: from Padgett & Fletcher (1982) [35]. Black triangle: from
Fletcher & Gygorg (1971) [17]. Circle: from Clausing & Chao (1963) [7]. . 63
Figure 5-21: Plot of contact conductance vs. contact pressure for different surface
finishes: medium surfaces. White square: from Padgett & Fletcher (1982)
[35]. Black square: from Padgett & Fletcher (1982) [35]. Black triangle: from
Fletcher & Gygorg (1971) [17]. Circle: from Clausing & Chao (1963) [7]. . 64
Figure 5-22: Experimental values of thermal contact conductance vs. contact pressure.
From Marchetti, Testa & Torrisi (1988) [31]. . 65
Figure 5-23: Experimental values of thermal contact conductance vs. contact pressure.
From Marchetti, Testa & Torrisi (1988) [31]. . 66
Figure 5-24: 0,1 µm brass sample pair applied force comparison. Dashed line: 112 N;
dashed-dotted line: 224 N; long-short dashed line: 336 N; long-double short
dashed line: 448 N; dashed-triple dotted line: 560 N; solid line: 670 N. . 67
Figure 5-25: 0,2 µm brass sample pair applied force comparison. . 67
Figure 5-26: 0,4 µm brass sample pair applied force comparison. . 68
Figure 5-27: 0,8 µm brass sample pair applied force comparison. . 68
Figure 5-28: 1,6 µm brass sample pair applied force comparison. . 69
Figure 5-29: Brass sample pairs, 4,2 K surface finish comparison. Short dashed line:
0,1 µm; long dashed line: 0,2 µm; dashed-dotted line: 0,4 µm; long-short
dashed line: 0,8 µm; long-double short dashed line: 1,6 µm. . 69
Figure 5-30: Brass sample pairs, 4,2 K surface finish comparison. Long-double short
dashed line: 112 N; short dashed line: 224 N; dashed-dotted line: 336 N;
dotted line: 448 N; long dashed line: 560 N; solid line: 670 N. . 70
Figure 5-31: γ copper sample pairs, 4,2 K surface finish comparison. Key as in Figure
5-30. . 71
Figure 5-32: Physical model of two rotating cylinders contacted to each other. . 71
Figure 5-33: Contact thermal resistance after applied high contact pressure vs. rotating
speed. . 72
Figure 5-34: Contact thermal resistance after applied high contact pressure vs. rotating
speed. . 73
Figure 5-35: Thermal contact conductance as a function of position for: (a) 4 x 6 load
array; (b) 5 x 7 load array; c) 6 x 8 load array. From Peterson and Fletcher
(1992) [37]. . 75
Figure 5-36: Integrated thermal contact conductance. From Table 5-2. . 76
Figure 5-37: Plot of contact conductance vs. contact pressure. Notice the directional
effect on contact conductance. From Fried & Kelley (1966) [24]. . 77
Figure 5-38: Thermal contact conductance vs. interfacial pressure for Al 2024-T4/SS
304 contacts: experimental data and theoretical results. . 78
5

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Figure 5-39: Thermal contact conductance vs. interfacial pressure for Al 2024-
T4/Zircaloy-2 contacts: experimental data and theoretical results. 79
Figure 5-40: Thermal contact conductance vs. interfacial pressure for SS 304/Zircaloy-
2 contacts: experimental data and theoretical results. . 80
Figure 5-41: Thermal contact conductance vs. interfacial pressure for Mg
AZ31B/zircaloy-2 contacts: experimental data and theoretical results. . 81
Figure 5-42: Thermal contact conductance vs. interfacial pressure for Brass
271/Zircaloy-2 contacts: experimental data and theoretical results. . 82
Figure 5-43: Variation of contact conductance with apparent interface pressure for Al
2024-T4/SS 304 metal surfaces at different mean junction temperatures. . 83
Figure 5-44: Thermal contact conductance vs. contact pressure. Theoretical curve: h =
c
0,93 -11 -11
KP . (1) SS-Al, K = 3,27 x 10 . (2) SS-Cu, K = 1,84 x 10 . 84
Figure 5-45: Comparison between experimental and theoretical values for SS/Al
-9 0,66
interface. Theoretical curve: h = 3,65 x 10 P . 84
c
Figure 5-46: Comparison between experimental and theoretical values for SS/Cu
interface. . 85
Figure 5-47: Comparison between experimental and theoretical values for SS/Al
interface. . 85
Figure 5-48: Thermal contact resistance vs. applied pressure for SS to Cu specimens
(RMS roughness values as indicated). . 86
Figure 5-49: Thermal contact resistance vs. applied pressure for Cu to SS (RMS
roughness values as indicated). . 87
Figure 5-50: Dimensionless correlation of contact resistances between machined SS
specimens pressed against copper optical-flats (surface finishes of the SS
specimens as indicated). . 88
Figure 5-51: Dimensionless correlation as for Figure 5-50 but for different surface
finishes of the SS specimens. . 89
Figure 5-52: Overall thermal conductance as a function of apparent contact pressure
and mean junction temperature. . 91
Figure 5-53: Joint Configuration. . 92
Figure 5-54: Thermal contact conductance as a function of distance from center of bolt.
From Peterson, Stanks & Fletcher (1991) [39]. 92
Figure 5-55: Integrated thermal contact conductance. From Table 5-4. . 93
Figure 5-56: Stainless-steel and Graphite-epoxi-laminate. . 94
Figure 5-57: Stainless-steel and glass-epoxi-laminate. . 95
Figure 5-58: Experimental values of thermal transverse conductivity a) Graphite-epoxi-
laminate. b) Glass-epoxi-laminate. . 96
Figure 5-59: Graphite-epoxi-laminate and graphite-epoxi-laminate. 97
Figure 5-60: Glass-epoxi-laminate and glass-epoxi-laminate. 97
Figure 5-61: Plot of contact conductance vs. contact pressure. From Cunnington (1964)
[9]. . 98
Figure 5-62: Loading resistance with tin. . 99
Figure 5-63: Unloading resistance with tin. . 99
6

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Figure 5-64: Loading resistance with lead. . 100
Figure 5-65: Unloading resistance with lead. . 100
Figure 5-66: Loading resistance with aluminium. . 101
Figure 5-67: Unloading resistance with aluminium. . 101
Figure 5-68: Loading resistance with copper. . 102
Figure 5-69: Unloading resistance with copper. . 102
Figure 5-70: Dimensionless minimum resistance to bare joint resistance. . 103
Figure 5-71: Dimensionless thermal contact conductance for specimen sets 1, 2 and 3
3
as a function of the distance from a load point. P = 689,5 x 10 Pa.
contact
Values for h from Table 5-1 (clause 5.2.1.1). From Peterson and
uncoated
Fletcher (1992) [37]. . 104
Figure 5-72: Thermal contact conductance variation: a) 0,79 N.m; b) 1,92 N.m; c) 3,04
N.m. From Peterson & Fletcher (1991) [37]. . 107
Figure 5-73: Integrated thermal contact conductance. From Table 5-6. . 108
Figure 5-74: Plot of contact conductance vs. contact pressure for different surface
finishes and mean temperatures. From Miller & Fletcher (1973) [32]. . 110
Figure 5-75: Plot of contact conductance vs. contact pressure for different surface
finishes and mean temperatures. From Miller & Fletcher (1973) [32]. . 111
Figure 5-76: Plot of contact conductance vs. contact pressure for different porosities.
From Miller & Fletcher (1973) [32]. . 112
Figure 5-77: Plot of contact conductance vs. contact pressure. From Gyorog (1970)
[26]. . 113
Figure 5-78: Plot of contact conductance vs. contact pressure. From Gyorog (1970)
[26]. . 114
Figure 5-79: Comparison of thermal conductance of fiber metals with aluminium bare
junction conductance, T = 307 K. . 116
m
Figure 5-80: Comparison of thermal conductance of powder metals with aluminium
bare junction conductance, T = 342 K. . 116
m
Figure 5-81: Effect of surface finish on thermal conductance with a porous copper
interstitial material. . 117
Figure 5-82: Effect of mean junction temperature on thermal conductance with a
porous copper interstitial material. . 117
Figure 5-83: Dimensionless effectiveness parameter for porous metals and selected
thermal control materials. . 118
Figure 5-84: Effects of surface finish and temperature conductance with a porous nickel
interstitial material. . 118
Figure 5-85: Effects of mean junction temperature on thermal conductance with a
porous copper interstitial material. . 119
Figure 5-86: Plot of contact conductance vs. contact pressure. From Fletcher, Smuda &
Gyorog (1969) [20]. . 120
Figure 5-87: Plot of contact conductance vs. contact pressure. From Fletcher, Smuda &
Gyorog (1969) [20]. . 121
7

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Figure 5-88: Plot of contact conductance vs. contact pressure. From Fletcher, Smuda &
Gyorog (1969) [20]. . 122
Figure 5-89: Plot of contact conductance vs. contact pressure. From Fletcher, Smuda &
Gyorog (1969) [20]. . 123
Figure 5-90: Plot of contact conductance vs. contact pressure. From Fletcher, Smuda &
Gyorog (1969) [20]. . 124
Figure 5-91: Plot of contact conductance vs. contact pressure. From Fletcher, Smuda &
Gyorog (1969) [20]. . 126
Figure 5-92: Plot of contact conductance vs. contact pressure. From Gyorog (1970)
[26]. . 127
Figure 5-93: Plot of contact conductance vs. contact pressure. From Fletcher, Smuda &
Gyorog (1969) [20]. . 128
Figure 5-94: Plot of contact conductance vs. contact pressure. From Fletcher, Smuda &
Gyorog (1969) [20]. . 129
Figure 5-95: Plot of contact conductance vs. contact pressure. From Fletcher, Smuda &
Gyorog (1969) [20]. . 130
Figure 5-96: Plot of contact conductance vs. contact pressure. From Fletcher, Smuda &
Gyorog (1969) [20]. . 131
Figure 5-97: Plot of contact conductance vs. contact pressure. From Gyorog (1970)
[26]. . 132
Figure 5-98: Plot of contact conductance vs. contact pressure. From Fletcher, Smuda &
Gyorog (1969) [20]. . 133
Figure 5-99: Plot of contact conductance vs. contact pressure. From Cunnington (1964)
[9]. . 134
Figure 5-100: Plot of contact conductance vs. contact pressure. From Cunnington
(1964) [9]. . 135
Figure 5-101: Photograph of segmented surface test specimen. . 135
Figure 5-102: Thermal contact resistance values for Al 6061-T6 with and without
segmented surfac
...

SLOVENSKI STANDARD
kSIST-TP FprCEN/CLC/TR 17603-31-04:2021
01-maj-2021
Vesoljska tehnika - Priročnik za toplotno zasnovo - 4. del: Konduktivni prenos
toplote
Space Engineering - Thermal design handbook - Part 4: Conductive Heat Transfer
Raumfahrttechnik - Handbuch für thermisches Design - Teil 4: Konduktive
Wärmeübertragung
Ingénierie spatiale - Manuel de conception thermique - Partie 4: Transfert de chaleur par
conduction thermique
Ta slovenski standard je istoveten z: FprCEN/CLC/TR 17603-31-04
ICS:
49.140 Vesoljski sistemi in operacije Space systems and
operations
kSIST-TP FprCEN/CLC/TR 17603-31- en,fr,de
04:2021
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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kSIST-TP FprCEN/CLC/TR 17603-31-04:2021

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kSIST-TP FprCEN/CLC/TR 17603-31-04:2021


TECHNICAL REPORT
FINAL DRAFT
FprCEN/CLC/TR 17603-
RAPPORT TECHNIQUE
31-04
TECHNISCHER BERICHT


February 2021
ICS 49.140

English version

Space Engineering - Thermal design handbook - Part 4:
Conductive Heat Transfer
Ingénierie spatiale - Manuel de conception thermique - Raumfahrttechnik - Handbuch für thermisches Design -
Partie 4: Transfert de chaleur par conduction Teil 4: Konduktive Wärmeübertragung
thermique


This draft Technical Report is submitted to CEN members for Vote. It has been drawn up by the Technical Committee
CEN/CLC/JTC 5.

CEN and CENELEC members are the national standards bodies and national electrotechnical committees of Austria, Belgium,
Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy,
Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of North Macedonia, Romania, Serbia,
Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom.

Recipients of this draft are invited to submit, with their comments, notification of any relevant patent rights of which they are
aware and to provide supporting documentation.

Warning : This document is not a Technical Report. It is distributed for review and comments. It is subject to change without
notice and shall not be referred to as a Technical Report.



















CEN-CENELEC Management Centre:
Rue de la Science 23, B-1040 Brussels
© 2021 CEN/CENELEC All rights of exploitation in any form and by any means Ref. No. FprCEN/CLC/TR 17603-31-04:2021 E
reserved worldwide for CEN national Members and for
CENELEC Members.

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kSIST-TP FprCEN/CLC/TR 17603-31-04:2021
FprCEN/CLC/TR 17603-31-04:2021 (E)
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 Abbreviated terms. 13
3.3 Symbols . 13
4 Conductive shape factors . 15
4.1 General . 15
4.2 Planar-planar surfaces . 16
4.2.1 Two-dimensional configurations . 16
4.3 Planar surface-cylindrical surface . 18
4.3.1 Two-dimensional configurations . 18
4.3.2 Axisymmetrical configuration . 21
4.4 Planar surface-spherical surface . 23
4.4.1 Plane and sphere . 23
4.5 Cylindrical-cylindrical surfaces . 25
4.5.1 Two-dimensional configurations . 25
4.6 Spherical-spherical surfaces . 41
4.6.1 Two concentric spheres . 41
5 Thermal joint conductance . 43
5.1 General . 43
5.1.1 Empirical correlations . 44
5.1.2 Thermal interface materials . 48
5.1.3 Joint geometries . 50
5.2 Bare metallic joints . 51
5.2.1 Metal-metal joints . 62
5.2.2 Metal-composite joints . 94
5.2.3 Composite-composite joints . 96
2

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5.3 Interfacial materials between metals . 98
5.3.1 Metallic foils between metals . 98
5.3.2 Metallic oxide powders between similar metals . 109
5.3.3 Porous metallic materials between similar metals. . 109
5.3.4 Insulating spacers between similar metals . 119
5.3.5 Fluids between metals . 133
5.3.6 Elastomeric spacers between similar metals . 142
5.4 Outgassing data . 151
Bibliography . 153

Figures
Figure 4-1: Values of the conductive shape factor per unit length, S/L, vs. the
dimensionless width of the strip, X. Calculated by the compiler. . 17
Figure 4-2: Values of the conductive shape factor per unit length, S/L, vs. X for different
values of Y. Calculated by the compiler. . 19
Figure 4-3: Values of the conductive shape factor per unit length, S/L, vs.
dimensionless diameter of the cylinder cross section. Calculated by the
compiler. . 20
Figure 4-4: Values of the dimensionless conductive shape factor, S/L, vs. cylinder
diameter to length ratio, D/L. Calculated by the compiler. . 22
Figure 4-5: Values of the dimensionless conductive shape factor, S/D, vs. the
dimensionless diameter of the sphere, Z. Calculated by the compiler. . 24
Figure 4-6: Values of the conductive shape factor per unit length, S/L, vs. radius ratio,
; for different values of the dimensionless distance between cylinder axes,
. Calculated by the compiler. . 26
Figure 4-7: Values of the dimensionless conductive shape factors per unit length, S /L,
ij
vs. the eccentricity of one of the holes X , for different values of the relevant
2
geometrical parameters. From Faulkner & Andrews (1955) [13]. . 28
Figure 4-8: Values of the conductive shape factors per unit length, S /L, vs. the
ij
diameter ratio d , for different values of the relevant geometric parameters.
3
From Faulkner & Andrews (1955) [13]. . 30
Figure 4-9: Values of the conductive shape factor per unit length, S/L, vs. the
dimensionless characteristic length of the holes, X. Calculated by the
compiler. . 32
Figure 4-10: Values of the conductive shape factor per unit length, S/L, vs. the
dimensionless diameter of the hole, X, for several values of the aspect
ratio, Y, of the rectangular bar cross-section. Calculated by the compiler. . 34
Figure 4-11: Values of the conductive shape factor per unit length, S/L, vs. the
dimensionless diameter of the hole, X, for different values of the aspect
ratio, Y, of the rectangular bar cross section. After Griggs, Pitts & Goyal
(1973) [25]. . 36
Figure 4-12: Values of the conductive shape factor per unit length, S/L, vs. the
dimensionless diameter of the hole, X, for several values of the aspect
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ratio, Y, of the rectangular bar cross section. After Griggs, Pitts & Goyal
(1973) [25]. . 38
Figure 4-13: Values of the conductive shape factor per unit length, S/L, vs. the
dimensionless hole radius, , for several values of n. Calculated by the
compiler. . 40
Figure 4-14: Values of the dimensionless conductive shape factor, S/r , vs. radius ratio,
1
. Calculated by the compiler. . 42
Figure 5-1: Estimation of the temperature drop at the interface. . 43
Figure 5-2: Variation of gap thickness parameter,  , with contact surface parameter, d.

After Fletcher & Gyorog (1970) [17]. . 45
Figure 5-3: Variation of contact conductance with apparent interface pressure. After
Fletcher & Gyorog (1970) [17]. . 46
Figure 5-4: Dimensionless conductance vs. dimensionless load. Stainless steel under
vacuum conditions. From Thomas & Probert (1972) [47]. . 47
Figure 5-5: Dimensionless conductance vs. dimensionless load. Stainless steel under
vacuum conditions. From Thomas & Probert (1972) [47]. . 48
Figure 5-6: Schematic representation of two surfaces in contact and heat flow across
the interface. . 48
Figure 5-7: Interface material compressed between two contacting surfaces. . 49
Figure 5-8: Plots of contact conductance vs. contact pressure for two different surface
finishes. From Fried & Kelley (1966) [24]. . 51
Figure 5-9: Plot of contact conductance vs. contact pressure for two different surface
finishes. From Fried & Atkins (1965) [23]. . 52
Figure 5-10: Plots of contact conductance vs. contact pressure for two different surface
finishes. From Fried (1966) [22] quoted by Scollon & Carpitella (1970) [43]. . 53
Figure 5-11: Plot of contact conductance vs. contact pressure for different ambient
pressures. From Fried & Kelley (1966) [24]. . 54
Figure 5-12: Plots of contact conductance vs. contact pressure for different surface
finishes and ambient pressures. Circle: From Fried & Atkins (1965) [23].
Square: From Fried (1966) [21] quoted by Scollon & Carpitella (1970) [43]. . 55
Figure 5-13: Plot of contact conductance vs. contact pressure for different surface
finishes. From Clausing & Chao (1965) [7]. . 56
Figure 5-14: Plot of contact conductance vs. contact pressure for different surface
finishes. From Fried & Atkins (1965) [23]. . 57
Figure 5-15: Plot of contact conductance vs. contact pressure for various surface
finishes, mean temperatures and ambient pressures. Circle, square and
rhombus: from Clausing & Chao (1965) [7]. Triangle: from Fried (1966) [21]
quoted by Scollon & Carpitella (1970) [43]. . 58
Figure 5-16: Plot of contact conductance vs. contact pressure. Notice the directional
effect on contact conductance. From Fried & Kelley (1966) [24]. . 59
Figure 5-17: Plot of contact conductance vs. contact pressure for different surface
finishes. Circle and square: from Fried (1965) [21]. Rhombus and triangle:
from Fried & Atkins (1965) [23]. Inverted triangle and right-oriented triangle:
from Fried & Kelley (1966) [24]. . 60
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Figure 5-18: Plot of contact conductance vs. contact pressure for different surface
finishes. Circle: From Fried (1966) [22] quoted by Scollon & Carpitella
(1970) [43]. Square: From Gyorog (1970) [26]. 61
Figure 5-19: Plot of contact conductance vs. contact pressure for different surface
finishes. From Fried (1966) [21] quoted by Scollon & Carpitella (1970) [43]. . 62
Figure 5-20: Plot of contact conductance vs. contact pressure for different surface
finishes: smooth surfaces. White square: from Padgett & Fletcher (1982)
[35]. Black square: from Padgett & Fletcher (1982) [35]. Black triangle: from
Fletcher & Gygorg (1971) [17]. Circle: from Clausing & Chao (1963) [7]. . 63
Figure 5-21: Plot of contact conductance vs. contact pressure for different surface
finishes: medium surfaces. White square: from Padgett & Fletcher (1982)
[35]. Black square: from Padgett & Fletcher (1982) [35]. Black triangle: from
Fletcher & Gygorg (1971) [17]. Circle: from Clausing & Chao (1963) [7]. . 64
Figure 5-22: Experimental values of thermal contact conductance vs. contact pressure.
From Marchetti, Testa & Torrisi (1988) [31]. . 65
Figure 5-23: Experimental values of thermal contact conductance vs. contact pressure.
From Marchetti, Testa & Torrisi (1988) [31]. . 66
Figure 5-24: 0,1 µm brass sample pair applied force comparison. Dashed line: 112 N;
dashed-dotted line: 224 N; long-short dashed line: 336 N; long-double short
dashed line: 448 N; dashed-triple dotted line: 560 N; solid line: 670 N. . 67
Figure 5-25: 0,2 µm brass sample pair applied force comparison. . 67
Figure 5-26: 0,4 µm brass sample pair applied force comparison. . 68
Figure 5-27: 0,8 µm brass sample pair applied force comparison. . 68
Figure 5-28: 1,6 µm brass sample pair applied force comparison. . 69
Figure 5-29: Brass sample pairs, 4,2 K surface finish comparison. Short dashed line:
0,1 µm; long dashed line: 0,2 µm; dashed-dotted line: 0,4 µm; long-short
dashed line: 0,8 µm; long-double short dashed line: 1,6 µm. . 69
Figure 5-30: Brass sample pairs, 4,2 K surface finish comparison. Long-double short
dashed line: 112 N; short dashed line: 224 N; dashed-dotted line: 336 N;
dotted line: 448 N; long dashed line: 560 N; solid line: 670 N. . 70
Figure 5-31:  copper sample pairs, 4,2 K surface finish comparison. Key as in Figure
5-30. . 71
Figure 5-32: Physical model of two rotating cylinders contacted to each other. . 71
Figure 5-33: Contact thermal resistance after applied high contact pressure vs. rotating
speed. . 72
Figure 5-34: Contact thermal resistance after applied high contact pressure vs. rotating
speed. . 73
Figure 5-35: Thermal contact conductance as a function of position for: (a) 4 x 6 load
array; (b) 5 x 7 load array; c) 6 x 8 load array. From Peterson and Fletcher
(1992) [37]. . 75
Figure 5-36: Integrated thermal contact conductance. From Table 5-2. . 76
Figure 5-37: Plot of contact conductance vs. contact pressure. Notice the directional
effect on contact conductance. From Fried & Kelley (1966) [24]. . 77
Figure 5-38: Thermal contact conductance vs. interfacial pressure for Al 2024-T4/SS
304 contacts: experimental data and theoretical results. . 78
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Figure 5-39: Thermal contact conductance vs. interfacial pressure for Al 2024-
T4/Zircaloy-2 contacts: experimental data and theoretical results. 79
Figure 5-40: Thermal contact conductance vs. interfacial pressure for SS 304/Zircaloy-
2 contacts: experimental data and theoretical results. . 80
Figure 5-41: Thermal contact conductance vs. interfacial pressure for Mg
AZ31B/zircaloy-2 contacts: experimental data and theoretical results. . 81
Figure 5-42: Thermal contact conductance vs. interfacial pressure for Brass
271/Zircaloy-2 contacts: experimental data and theoretical results. . 82
Figure 5-43: Variation of contact conductance with apparent interface pressure for Al
2024-T4/SS 304 metal surfaces at different mean junction temperatures. . 83
Figure 5-44: Thermal contact conductance vs. contact pressure. Theoretical curve: h =
c
0,93 -11 -11
KP . (1) SS-Al, K = 3,27 x 10 . (2) SS-Cu, K = 1,84 x 10 . 84
Figure 5-45: Comparison between experimental and theoretical values for SS/Al
-9 0,66
interface. Theoretical curve: h = 3,65 x 10 P . 84
c
Figure 5-46: Comparison between experimental and theoretical values for SS/Cu
interface. . 85
Figure 5-47: Comparison between experimental and theoretical values for SS/Al
interface. . 85
Figure 5-48: Thermal contact resistance vs. applied pressure for SS to Cu specimens
(RMS roughness values as indicated). . 86
Figure 5-49: Thermal contact resistance vs. applied pressure for Cu to SS (RMS
roughness values as indicated). . 87
Figure 5-50: Dimensionless correlation of contact resistances between machined SS
specimens pressed against copper optical-flats (surface finishes of the SS
specimens as indicated). . 88
Figure 5-51: Dimensionless correlation as for Figure 5-50 but for different surface
finishes of the SS specimens. . 89
Figure 5-52: Overall thermal conductance as a function of apparent contact pressure
and mean junction temperature. . 91
Figure 5-53: Joint Configuration. . 92
Figure 5-54: Thermal contact conductance as a function of distance from center of bolt.
From Peterson, Stanks & Fletcher (1991) [39]. 92
Figure 5-55: Integrated thermal contact conductance. From Table 5-4. . 93
Figure 5-56: Stainless-steel and Graphite-epoxi-laminate. . 94
Figure 5-57: Stainless-steel and glass-epoxi-laminate. . 94
Figure 5-58: Experimental values of thermal transverse conductivity a) Graphite-epoxi-
laminate. b) Glass-epoxi-laminate. . 96
Figure 5-59: Graphite-epoxi-laminate and graphite-epoxi-laminate. 97
Figure 5-60: Glass-epoxi-laminate and glass-epoxi-laminate. 97
Figure 5-61: Plot of contact conductance vs. contact pressure. From Cunnington (1964)
[9]. . 98
Figure 5-62: Loading resistance with tin. . 99
Figure 5-63: Unloading resistance with tin. . 99
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Figure 5-64: Loading resistance with lead. . 100
Figure 5-65: Unloading resistance with lead. . 100
Figure 5-66: Loading resistance with aluminium. . 101
Figure 5-67: Unloading resistance with aluminium. . 101
Figure 5-68: Loading resistance with copper. . 102
Figure 5-69: Unloading resistance with copper. . 102
Figure 5-70: Dimensionless minimum resistance to bare joint resistance. . 103
Figure 5-71: Dimensionless thermal contact conductance for specimen sets 1, 2 and 3
3
as a function of the distance from a load point. P = 689,5 x 10 Pa.
contact
Values for h from Table 5-1 (clause 5.2.1.1). From Peterson and
uncoated
Fletcher (1992) [37]. . 104
Figure 5-72: Thermal contact conductance variation: a) 0,79 N.m; b) 1,92 N.m; c) 3,04
N.m. From Peterson & Fletcher (1991) [37]. . 107
Figure 5-73: Integrated thermal contact conductance. From Table 5-6. . 108
Figure 5-74: Plot of contact conductance vs. contact pressure for different surface
finishes and mean temperatures. From Miller & Fletcher (1973) [32]. . 110
Figure 5-75: Plot of contact conductance vs. contact pressure for different surface
finishes and mean temperatures. From Miller & Fletcher (1973) [32]. . 111
Figure 5-76: Plot of contact conductance vs. contact pressure for different porosities.
From Miller & Fletcher (1973) [32]. . 112
Figure 5-77: Plot of contact conductance vs. contact pressure. From Gyorog (1970)
[26]. . 113
Figure 5-78: Plot of contact conductance vs. contact pressure. From Gyorog (1970)
[26]. . 114
Figure 5-79: Comparison of thermal conductance of fiber metals with aluminium bare
junction conductance, T = 307 K. . 116
m
Figure 5-80: Comparison of thermal conductance of powder metals with aluminium
bare junction conductance, T = 342 K. . 116
m
Figure 5-81: Effect of surface finish on thermal conductance with a porous copper
interstitial material. . 117
Figure 5-82: Effect of mean junction temperature on thermal conductance with a
porous copper interstitial material. . 117
Figure 5-83: Dimensionless effectiveness parameter for porous metals and selected
thermal control materials. . 118
Figure 5-84: Effects of surface finish and temperature conductance with a porous nickel
interstitial material. . 118
Figure 5-85: Effects of mean junction temperature on thermal conductance with a
porous copper interstitial material. . 119
Figure 5-86: Plot of contact conductance vs. contact pressure. From Fletcher, Smuda &
Gyorog (1969) [20]. . 120
Figure 5-87: Plot of contact conductance vs. contact pressure. From Fletcher, Smuda &
Gyorog (1969) [20]. . 121
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Figure 5-88: Plot of contact conductance vs. contact pressure. From Fletcher, Smuda &
Gyorog (1969) [20]. . 122
Figure 5-89: Plot of contact conductance vs. contact pressure. From Fletcher, Smuda &
Gyorog (1969) [20]. . 123
Figure 5-90: Plot of contact conductance vs. contact pressure. From Fletcher, Smuda &
Gyorog (1969) [20]. . 124
Figure 5-91: Plot of contact conductance vs. contact pressure. From Fletcher, Smuda &
Gyorog (1969) [20]. . 126
Figure 5-92: Plot of contact conductance vs. contact pressure. From Gyorog (1970)
[26]. . 127
Figure 5-93: Plot of contact conductance vs. contact pressure. From Fletcher, Smuda &
Gyorog (1969) [20]. . 128
Figure 5-94: Plot of contact conductance vs. contact pressure. From Fletcher, Smuda &
Gyorog (1969) [20]. . 129
Figure 5-95: Plot of contact conductance vs. contact pressure. From Fletcher, Smuda &
Gyorog (1969) [20]. . 130
Figure 5-96: Plot of contact conductance vs. contact pressure. From Fletcher, Smuda &
Gyorog (1969) [20]. . 131
Figure 5-97: Plot of contact conductance vs. contact pressure. From Gyorog (1970)
[26]. . 132
Figure 5-98: Plot of contact conductance vs. contact pressure. From Fletcher, Smuda &
Gyorog (1969) [20]. . 133
Figure 5-99: Plot of contact conductance vs. contact pressure. From Cunnington (1964)
[9]. .
...