contact conductance in common cubesat stacks

49th International Conference on Environmental Systems ICES-2019-335 7-11 July 2019, Boston, Massachusetts

Copyright © 2019 European Space Agency

Contact Conductance in Common CubeSat Stacks

Philipp B. Hager1, Tobias Flecht2, Katja Janzer3

European Space Agency, European Research and Technology Centre, Noordwijk, 2200 AG, The Netherlands

Hugo Brouwer4, Martin Jonsson5

Innovative Solutions in Space BV, Delft, 2623 CR, The Netherlands

and

Laura Léon Pérez6

GomSpace A/S, Aarlborg, 9220, Denmark

CubeSat thermal design, analysis and test is still in its infancy although the CubeSat

standard was christened 20 years ago. In the past, most CubeSat teams did either not face,

realize or acknowledge the need for thermal engineering and in-depth thermal analysis. With

deployable solar arrays, three axis stabilization, increasing power density, stringent thermal

requirements of payloads, more challenging orbits and mission destinations beyond Earth

orbit - thermal design, analysis and test become a natural necessity. In order to support this

demand, contact conductances tests in typical CubeSat printed circuit board (PCB) stacks

were performed at ESA.

Eight different configurations were tested in vacuum, varying spacer length (10, 12, 20

mm) spacer material (aluminium, brass), number of spacers (1, 2, 3), use of stainless steel

washers, and bolt torque (0.5 and 1 Nm). The test results were supported by material

characterization tests. The measurement errors were investigated intensively, such as heat

losses through MLI and harness, knowledge of applied heating power, thermocouple

calibration, and differences in material properties, such as thermal conductivity and optical

surface properties.

The results show contact conductances ranging from 6,500 to 20,000 W/m²K for

aluminium or brass spacer with stainless steel washers and conduct conductances from 33,500

to 107,000 W/m²K for aluminium spacers without washers. Reducing the torque from 1 Nm

to 0.5 Nm led to a decrease of contact conductance by approx. 20% between otherwise

identical test configurations. The error bars are large due to the associated uncertainties,

mainly regarding the exact material properties. The contact conductances are significantly

lower than values predicted by analytical models from literature, such as models by

Yovanovich, Tien, Mikic, Kumar or Yeh.

1 Thermal Engineer, Thermal Control Section (ESA-TEC-MTT), Keplerlaan 1, 2200 AG, Noordwijk, The

Netherlands, [email protected]. 2 German National Trainee, Thermal Control Section (ESA-TEC-MTT), same mail address as 1st author. 3 Young Graduate Trainee, Thermal Control Section (ESA-TEC-MTT), same mail address as 1st author. 4 Space Systems Engineer, Systems Engineering Group, Motorenweg 23, 2623 CR, Delft, The Netherlands,

[email protected]. 5 Mechanical Systems Engineer, Mechanical Engineering Group, Motorenweg 23, 2623 CR, Delft, The Netherlands,

[email protected]. 6 Senior Systems Engineer, Mission Systems Engineering Group, Langagervej 6, 9220, Aalborg East, Denmark,

[email protected]

International Conference on Environmental Systems

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Nomenclatur

AI = Interface area

AMLI = MLI surface area

AAWG = Heater harness crosssection area

Abar = Cross section area of threaded bar

a1 = Coefficient in plastic deformation

models

b1 = Coefficient in plastic deformation

models

C = Empirical constant for the computation

of contact conductances

D = Empirical constant for the computation

of contact conductances

d2 = Mean diameter

dS = Inner diameter of bolt head

dh = Outer diameter of bolt head

Fax = Axial force

GL = Linear conductance

GLharness = Conductance of harness

GLspacer = Conductance of a spacer stack

hc = Contact conductance

Hc = Micro hardness

I = Heater current

kS = Harmonic mean thermal conductivity

lharness = Length of harness

lbar = Length of threaded bar

m = Asperity slope

P = Pressure at interface

Pt = Thread pitch

Pdis = Heat dissipated in the heater harness

Pheater = Heater Power

Qbar = Heat conducted through the bar

Qharness = Heat conducted through the harness

QMLI = Heat radiated away from MLI

QSpacer,all = Heat transferred through four spacer

stacks

rm = Mean radius of the contact area

TMLI = Outer MLI temperature

Tshoud = Shroud temperature

Theater = Heater temperature

Tguard = Guard heater temperature

Tcoolplate = Coolplate temperature

Thot = Temperature at hot side of spacer stack

Tcold = Temperature at cold side of spacer stack

σ = Surface roughness

τtot = Total torque

µ = Coefficient of friction

εMLI = MLI emissivity

ϵshroud = Shroud emissivity

ρharness = Electrical resistivity of harness

λ = Thermal conductivity

CDR = Critical Design Review

CMY = Cooper, Mikic, Yovanovich

ECSS = European Cooperation for Space

Standardisation

ESA = European Space Agency

ESTEC = European Space Agency, European

Research and Technology Centre

LTAN = Local time of ascending node

MarCO = Mars Cube One

M-ARGO = Miniaturised – Asteroid Remote

Geophysical Observer

MLI = Multi-Layer-Insulation

NEO = Near Earth Objects

PCB = Printed Circuit Board

SDR = Software Defined Radio

SS = Stainless Steel

SSO = Sun Synchronous Orbit

VDA = Vapour Deposited Aluminium

I. Background and Motivation

hermal engineering for CubeSats is still in its infancy, even though the CubeSat standard has been around for 20

years. In the early CubeSat days, 1U CubeSat were standard and were mainly used by universities to educate

groups of students. The initial CubeSats were characterised by low power dissipation, body mounted solar cells, benign

low Earth orbits, no or restricted attitude control and very short lifetimes. Given those boundary conditions the

CubeSat teams did not encounter the need for thermal engineering. The CubeSat slogan of higher risk and shorter

development times along with the experimental or educational nature of the majority of the initial missions, allowed

to bypass common approaches to thermal engineering. System failures were seldom traced back to thermal problems1.

In a second wave, the 3U CubeSats became standard and besides universities, research institutes, as well as

commercial small to medium companies developed and used CubeSats. Thermal analysis was rarely done or was

restricted to low fidelity models with few thermal nodes, as well as rough estimations of material properties which

were often unknown. Even in cases when thermal analysis were performed, thermal model correlation was not done

in thermal balance tests or with in flight data, preventing the CubeSat community from improving their thermal

modelling.

T


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Beside ISS orbits which are still used for the deployment of mainly educational CubeSats, deployment of CubeSats

in Sun-Synchronous Orbits (SSO) has become wide spread. The bandwitdth of local-time-of-ascending-nodes

(LTANs) can stretch the entire range with subsequent implications on the thermal design, although LTANs in the

range of 9:30 to 10:30 are most frequent. Besides, there is also a number of missions under development targeting

equatorial orbits. Recently the two 6U CubeSats Mars Cube One (MarCO) accompanied the NASA Insight lander to

Mars. Many studies have been conducted for CubeSats to Moon, Mars or Near Earth Objects (NEOs), as for example

the ESA M-ARGO2 or Sysnova Luce CubeSat studies3. There is also an increasing interest in using CubeSat

constellations for providing commercial services for example for telecommunication or radar-based earth observation,

which in turn will lead to more powerful payloads and in consequence dissipated heat4.

With the introduction of deployable solar arrays more and more power became available which consequently lead

to more heat being dissipated inside the CubeSat volume. At the same time the overall surface area of the CubeSats

did not increase equivalently. As a result, the power density of CubeSats increases. Also the attitude control of

CubeSats has significantly changed since the first wave of CubeSats. CubeSat attitude controlled moved from

uncontrolled spinning to 3-axis stabilised. The un-controlled or semi-controlled chaotic tumbling mode equilibrated

the incident heat fluxes and hence also temperatures across the CubeSat outer surfaces. Three-axis stabilisation and

fixed orientation with respect to the Earth or Sun now allow more applications on the CubeSats but also introduce

more challenges regarding the distribution of heat inside the CubeSat. Not all faces of CubeSats can partake in the

thermal control as the scarce surface area is either covered with solar cells, occupied with antenna patches, removed

to allow star trackers a view to space or payloads a view to wherever they are supposed to look at. Thus, real estate

for thermal control surfaces is a rare good in CubeSats. In parallel to this development the subsystems, instruments

and payloads embarking on CubeSats became more and more sophisticated, leading to more stringent thermal

requirements. Additionally, the application of software defined radios for CubeSats is driving high dissipation power

in the antennae front-ends, which requires thermal design solutions to stabilize the components within their respective

temperature limits. An example are butane gas thruster systems for limited in-orbit manoeuvres, a nanocom Software

Defined Radio (SDR) for S-band communications, or a hyper-spectral imager, devices tested in-orbit during the ESA

GOMX-4B mission5. The components were tested with limited duty cycles to minimize the thermal impact of these

high dissipated power equipments on the platform and amongst each other.

Sensitivity analysis in accordance with ECSS6, performed in one of the ESA CubeSat missions, revealed modelling

uncertainties for CubeSats of about 15 K even at CDR level. The parameters with the largest impact on the outcome

of the analysis were the unknown conductive interfaces in the stack of washers, spacers, and threaded bars apart from

the usual contributors such as external optical surface properties. Figure 1a shows the image of GOMX-3 and as such

Figure 1: Left: an image of the ESA GOMX-3B satellite with solar panels removed; and right:

Geometrical mathematical model of a generic 1U CubeSat stack.


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a typical CubeSat PCB stack of a 3U Cubesat. Figure 1b shows a generic geometric mathematical model of a 1U

CubeSat stack. The geometrical representation of the spacer stacks are shown in grey.

A survey among 20 ESA ran or supported CubeSat projects sized from 1U to 12U showed a range of used contact

conductance values from hc = 20 W/m²K to 100,000 W/m²K, or linear conductor values of GL = 0.007 W/K to 3.5

W/K for spacer stacks. Sensitivity analysis revealed further large contributors to the modelling uncertainty in CubeSat

specific stacks are the washer/spacer-PCB interfaces, the PCB in-plane and out-of-plane thermal conductivity, the

electrical connectors between PCBs, and the conductive heat links from the exterior (e.g. solar cells) to the interior

via the CubeSat structure. In this paper we focus on the contact conductance in common CubeSat stack configurations

in order to provide the CubeSat community a more refined range of values to be readily usable in CubeSat thermal

analysis before model correlation.

II. Background of Contact Conductance

Contact conductance has been intensively studied by numerous authors and published for more than six decades.

It goes beyond the scope of this paper to discuss and compare them all in detail. The interested reader is referred to

the very complete review article by Yovanovich7 and all the references therein, as well as other summaries such as in

Ref. 8 to 11. More recent work was published in Ref. 12&13.

The list of theoretical models of contact conductance is rather long. There are different model types distinguished

to explain heat transfer, gap and joint resistance. The main three deformation models distinguish between elastic,

plastic and elasto-plastic models. The CubeSat stacks are characterised by small surface areas and high contact

pressures. Consequently in this paper we focus solely on plastic models for comparison with our test results. Most

plastic models lead to an empirical equation in the form7:

(1)

In this equation hc is the contact conductance [W/m²K], σ is the surface roughness [μm], ks the harmonic mean

thermal conductivity of both adjacent materials [W/mK], and m is the mean asperity slope of the surface [μm]. P is

the pressure at the interface [MPa] and Hc is the micro hardness at the interface [MPa]. The coefficients a1 and b1 were

derived experimentally by different

researches and some combinations are listed

in Table 1.

The harmonic mean thermal

conductivity ks [W/mK], the mean surface

roughness σ [μm] and the asperity slope m

[μm] are defined by the properties of

adjacent parts with subscripts 1 and 27:

(2)

(3)

(4)

Whereas the surface roughness can be

derived by11:

(5)

Table 1. Coefficients for the empirical equation in plastic

deformation models.

Authors Year a1 b1

Cooper, Mikic, Yovanovich (CMY) 1969 1.45 0.985

Yovanovich 1982 1.25 0.95

Tien 1968 0.55 0.85

Mikic 1974 1.13 0.94

Kumar & Ramamurthi 2004 0.12 0.68

Table 2. Correlation for the asperity slope mi of Gaussian surfaces,

reproduced from Ref. 14.

Origin Correlation

Tanner and Fahoum

[6]

Antonetti et al.

[7]

Lambert and Fletcher

[8]

Table 3. Coefficients for Thomas & Probert correlation8

Coefficient Material Value Tolerance

C Stainless Steel 0.743 ± 0.067

C Aluminium 0.072 ± 0.044

D Stainless Steel 2.260 ± 0.880

D Aluminium 0.660 ± 0.620


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The asperity slope m can be derived from the surface roughness based on empirical equations for Gaussian surfaces

as presented in Table 214.

Other models are those of Yeh et al 13 which solely bases on the tightening torque τ [Nm] or the approach by

Thomas & Probert [1972]8. The Thomas and Probert correlation is based on the same parameters as the plastic

deformation model but uses two additional empirical constants C and D for the computation of contact conductances.

Table 3 shows the coefficients C and D for stainless steel and aluminium.

The Thomas and Probert equation is given with8:

(9)

Common to the plastic deformation models in shape similar to the CMY model, and the Thomas and Probert

correlation are the need for the contact pressure. The contact pressure P [MPa] of a bolted interface depends on the

axial force Fax [N] and the interface area AI to which it is applied. In the case of the washer/spacer stacks we investigate

in this paper the assumption is valid that all the axial force has to be lead through the interface area and hence P =

Fax/AI. Whereas the axial force Fax can be determined by the following equation from common engineering text

books11:

(10)

To determine the axial force it is necessary to know the total torque τtot [Nm], the thread pitch Pt, the coefficient

of friction in the threads μ, the mean diameter d2, the coefficient of friction between bolt head and the surface of the

component and the mean radius of the contact area rm. The value rm [m] is defined by the inner diameter ds [m] and

outer diameters of the bolt head dh [m]:

(11)

III. Methods

A. Contact conductance test

An indirect measurement method was used to determine the linear contact conductance and conductive couplings

in CubeSat stacks. Measurement of contact conductances always requires the determination of temperature gradients

in an interface. In a Cubesat stack with small contact areas between washer and spacers there is almost no space to

place temperature sensors. The sensors themselves impact the local heat flux and as such the measured temperatures.

Hence, the selected approach was to place the temperature sensors at the top and bottom of a spacer/washer stack and

to measure the overall temperature gradient. This allows to directly derive the linear conductors (GL) which can be

applied in CubeSat thermal models. The disadvantage of the selected approach is that is does not allow to directly

quantify the temperature gradient in each individual interface. Without the knowledge of the temperature gradient in

the individual interface the contact conductance hc cannot be determined directly. Yet, by knowing the material

properties of the washers and spacers it is possible to derive the contact conductance hc, averaged over all interfaces

along a washer/spacer stack.

The test set-up reassembles a configuration similar to a CubeSat PCB stack. Figure 2 shows the four identical heat

paths at the corners of a square aluminium plate (6). The aluminium plate was selected over a PCB to have isotropic

material properties and allow for a unilateral heat distribution from the foil heater (5) to the four corners. The four

heat paths are a combination of washers (2, 4) and spacers (3), held in place by a threaded bar (8) and torqued by a

PEEK nut (7). The configuration is symmetric. All for corner stacks are identical. The aluminium plate has the same

dimensions as a typical CubeSat PCB. Not only is this approach similar to a PCB stack but also allows four

measurement points in one test run which increases the statistics. A copper plate (1) is used as a thermally controlled

cold sink at the bottom of the stack. A controlled tightening torque was applied to the PEEK nuts to have identical and

reproducible contact pressures in each stack. The test set-up is wrapped with MLI (9) and equipped with a total of 24

calibrated thermocouples of type-T. The thermocouples were placed at relevant locations along the four stack heat


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paths as well as to monitor the housing, TVac chamber shroud and cold plate temperature. Thermocouples were also

placed on the inner- and outermost layer of the MLI, and at the ends of the threaded bars. The measurement points on

MLI and threaded bar were used to determine heat losses and thus as input for the error calculations. The entire test

assembly is enclosed with a copper housing with a high IR emissivity surface finish. A guard heater was placed on

the heater harness. In order to reduce heat losses the guard heater was controlled to a temperature slightly below the

temperature of the aluminium plate.

Figure 3 shows a photograph of the

test set-up. The MLI covers of the

four threaded bars are visible, as

well as the MLI around the

aluminium heating plate. At the

lower side the copper base plate is

visible. Furthermore the

thermocouple harness in the

foreground and the heater harness

(red cables) are visible in the

background.

Figure 4 shows the schematic

test set-up in its test environment.

The test set-up is placed in a

thermal vacuum chamber, with a

temperature controlled shroud and

cold plate with standard high IR

emissivity coating. The voltage and current is measured close to the foil heater with a voltmeter and an ampere meter.

A power source is connected to the foil heater and to the guard heater.

In this test set-up, power dissipated by the foil heater is assumed to be evenly distributed and conducted to and via

the four identical washer/spacer stacks at the corners of the test assembly. Eight different configurations were tested

in vacuum, varying spacer length (10mm, 12mm, 20mm) spacer material (aluminium, brass), number of spacers (1,

2, 3), use of washers, and bolt torque (0.5Nm and 1Nm). In each test set-up three different heater power levels were

studied (approx. 2W, 4W and 6W). Table 4 shows the test matrix,

summarising all test configurations reported in this paper. The

temperatures were gathered during steady-state phases.

The test results were supported by material characterization tests

and error investigation. The considered errors are heat losses through

the MLI and the harness, the knowledge of applied heating power,

thermocouple calibration, and uncertainties in material properties,

such as thermal conductivity and optical surface properties.

From the measured temperature readings the second step requires

the computation of the contact conductance. In the following the main

equations behind this computation are listed. The heat dissipated by

the foil heater will follow four different paths between heater and cold

plate:

Radiated away from the MLI to the housing (QMLI),

Conducted through the harness (Qharness),

Figure 2. Test set-up schematic.

Figure 3. Test set-up with instrumentation

and MLI


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Conducted though the threaded bar (Qbar),

Conducted through the four spacer stack

(QSpacer,all).

Based on the main assumption that the test

set-up is symmetrical, the heat will distribute

evenly over all for stacks, the heat through one

washer/spacer stack QSpacer hence can be

computed with:

(12)

Heat lost though the MLI is computed with:

(13)

With the MLI outer surface area AMLI [m²], the

emissivity of the outer layer of the MLI ϵMLI [-],

the emissivity of the housing ϵshroud [-], the

Stefan-Boltzmann-constant σ [W/m²K], as well

as the measured temperatures on the MLI TMLI

[K] and the housing Tshroud [K]. Inner and outer

temperature of the MLI are measured with thermocouples and a mean temperature is computed. For the computation

of the heat losses via the MLI, only the measurement of the outermost MLI layer was used. It was assumed that the

MLI outer layer temperature was homogenous over the entire blanket.

The heater harness is assumed to consist of 1-D linear conductors GLharness [W/K] based on the harness cross

section Aharness [m²], the harness length lharness [m] between heater and guard heater, as well as the harness material

conductivity λcopper [W/mK].

(14)

The heat transferred via the threaded bar is also calculated by assuming a conductance GLbar [W/K] with a cross-

section Abar, a length lbar and a conductivity λsteel.

(15)

The linear conductor of one single stack can be computed by dividing the resulting heat per washer/spacer stack

by the measured temperature difference at the two ends of the stack.

(16)

The computed linear conductor of each stack is a serial connection of the linear conductors of the elements in the

stack, i.e. washers and spacers, and the contact conductances at the interfaces. The accuracy of the used material

properties but also dimensions directly impacts the resulting contact conductance values. Table 4 shows the material

properties and their respective uncertainties.

Figure 4. Schematic of test set-up in the thermal vacuum

chamber with chamber control and data acquisition systems.


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As mentioned above, the contact conductance is

determined in an indirect way. This method requires the

computation of thermal resistances or linear conductors

through the washers and spacers. To compute the thermal

resistance of washers and spacers their material properties

must be known accurately. Uncertainties in the thermal

conductivity values of the used material for the washers and

spacers consequently become a significant contributor to the

overall error of the results. Hence, the washers and spacers

were investigated in order to determine their composition. The

relevant bulk properties are included in Table 5.

Apart from the material property uncertainties shown in

Table 5 seven further error sources were identified in the test

set-up. One source of error is the temperature sensor

calibration. The other six errors contribute to a mismatch in

the measured heating power versus the heat actually flowing

through the four washer/spacer stacks of the test set-up. These

errors are the heat loss via radiation through the MLI, heat

conducted via the heater and thermistor harness, heat

dissipated in the heater harness, heat conducted through the

threaded bar, and the measurement error in the data acquisition

system.

24 thermocouples of type-T were used. Each was

calibrated in accordance with facility procedures, and in their test configuration, i.e. the test harness, feedthrough and

data acquisition system. The calibration was performed at approx. -80°C, 0°C, and +75°C. A polynomial curve was

fitted for each thermocouple and applied to the measurements after the test. The thermocouples were suspended from

the chamber ceiling in the test configuration in order to reduce heat losses. They touched the chamber at the

feedthrough. The length, material pair thermal conductivity, and temperature difference between test item and chamber

wall were used to compute a maximum possible heat loss of 0.4 mW per sensor cable.

A 10 layer MLI blanket was used to minimize the radiative heat losses between the test set-up and its housing. The

temperature difference between inner- and outermost layer of the MLI was measured. For the error computations it

was assumed that the surface area of the MLI AMLI [m²] is equal to the heater plate size, and the outer layer of the MLI

blanket has a view factor of 1 to the housing of the thermal vacuum chamber. An emissivity of ϵMLI = 0.07 -0.03/+0.05

was used for the VDA outer surface of the MLI, and an emissivity of ϵshroud = 0.8 -0.1/+0.1 was used for the black

coating of the shroud.

The heater harness can create an error on the measurement results in two different ways. Either heat is conducted

into or out of the test set-up through a temperature difference between the two ends of the harness. Furthermore heat

Table 4. Test matrix of contact conductance test.

#

Sp

ace

r H

eig

ht

[mm

]

Sp

ace

r

ma

teria

l

Nu

mb

er o

f

spa

cers

W

ash

er

To

rqu

e

[Nm

]

A 10 Aluminium 1 Steel 1

B 12 Aluminium 1 Steel 1

C 12 Aluminium 2 none 1

D 12 Aluminium 1 none 1

E 12 Aluminium 3 none 1

F 20 Brass (Munz

Metal)

1 Steel 1

G 10 Brass (Munz

Metal)

1 Steel 1

H 10 Brass (Munz

Metal)

1 Steel 0.5

Table 5. List of material properties used for the computation of the contact conductance.

Element Material Conductivity

[W/mK]

Area [mm2] Length [mm] GL [W/K]

Steel Washer 17-7PH† 16.2−0.1+0.1 24.03−1.60

+1.60 0.5−0.1+0.1 0.784−0.177

+0.268

20 Brass Spacer Muntz Metal† 123.0−13+12 18.65−1.40

+1.40 20.0−0.1+0.1 0.115−0.020

+0.022

10 Brass Spacer Muntz Metal† 123.0−13+12 18.65−1.40

+1.40 10.0−0.1+0.1 0.229−0.041

+0.046

12 Alu Spacer Alu 6061† 160.5−6.5+6.5 18.65−1.40

+1.40 12.0−0.1+0.1 0.256−0.031

+0.027

10 Alu Spacer Alu 6061† 160.5−6.5+6.5 18.65−1.40

+1.40 10.0−0.1+0.1 0.308−0.037

+0.040

Harness Copper 350−240+41 0.129−0.027

+0.033 150.0−10+10 0.0003−0.00023

+0.00015

Stainless Steel

Bar

430F‡ 20.0−5+5 7.07−0.91

+0.97 ls ±5 0.0050−0.0037+0.0023

Notes: †) Material composition analysed in ESTEC’s materials labs ‡) Data provided by Innovative Solutions in Space *) ls is the threaded bar length, here in [mm]


9

is dissipated in the harness leading to an error of the overall dissipation in the test set-up. The test set-up used a guard

heater to reduce the first error mode mentioned and used a heater wire with a low electrical resistance to decrease the

second error mode.

The heat Pdis [W] dissipated in the harness is calculated based on the number of cables, the length lharness [m] of the

wire between the main foil heater in the test set-up and guard heater, the electrical resistivity ρharness [kg/m³], the cross-

section of the wire AAWG28 and the current I. The dissipation in the wires is considered to contribute as a positive error

to the power in the test setup. Because the guard heater is controlled to maintain the same temperature as the foil heater

in the test set-up, Pdis is assumed to be distributed evenly between the two heaters.

The measurement error in the data acquisition system, i.e. of voltage and current was quantified as part of the

calibration of the used TVac chamber and the deviation of the resistance for the current measurement was also taken

into account. The error contribution is given in Table 6, in percent rather than an absolute value.

B. Theoretical Contact Conductance

Equation 1-10 gives the theoretical basis to compute

contact conductances. A number of parameters are

involved. Some can be determined based on textbooks

and standards. For others dedicated measurements are

necessary. Measurements were conducted for average

roughness Ra and micro hardness HV, and are shown in

Table 7.

Other values could not be measured in the scope of

this activity, such as the friction coefficients or the

thermal conductivity of the materials. In those cases

bounding values from literature were used. Based on

the average roughness, Ra shown in Table 7, the surface

roughness σ and asperity slope m can be computed (see

equation 3,4 & 5). The mean thermal conductivity can

be derived from the minimum and maximum thermal

conductivities of adjacent parts. The micro hardness is

given in Table 7. With this, only the contact pressure P

has to be determined to compute hc based on equation

1 and Table 2. For the computation of P standard values

for M3 screws based on ISO-4762 were used, such as

thread pitch Pt = 0.5 mm, mean diameter d2 = 2.755

mm, outer diameter of bolt head ds = 5.5 mm, and hole

diameter dh = 3.2 mm. The coefficient of friction μ

varies between 0.14 and 0.2 in literature, and the coefficient of friction under the bolt head μb varies from 0.15 to 0.3

for PEEK nuts. Together with the applied torque the resulting axial force can vary in a range of approx. 673 N to 1,587

N. Taking into account the very small contact area at the interface between washers and spacers this yields in contact

pressures from 36 MPa to as high as 85 MPa. Additional tests were performed with a piezoelectric force washer. With

the controlled tightening torque of 1 Nm, the resulting forces varied from 826 N to 1194 N. This yields in a contact

pressure range of approx.. 44 MPa to 64 MPa.

IV. Results

Table 8 shows the results of the test campaign. The eight test set-ups are labelled A to H. The subsequent 5 columns

contain the spacer height, number of spacer, spacer material, the use of washers as well as the applied torque. Main

differences between subsequent cases are marked in bold font weight. For each test, the resulting linear conductors

GL as well as the contact conductance hc are shown, including the respective error range. Furthermore, the thermal

resistance R as inverse of the linear conductor GL is included.

The GL values are also shown in a bar chart in Figure 5a. The GL values are the series conductances of a) spacer

solid body linear conductor b) washer solid body linear conductor (if applicable), and c) the contact conductance at

the interfaces. Hence, these values can be read as equivalent values to be used in a thermal model. Figure 5b shows

the resulting contact conductances hc in a bar chart. The contact conductances are the averaged values for all contacts

Table 6: Errors during power measurement

Error Source Error [%]

Current measurement (mV range) 0.0113

Voltage measurement (V range) 0.2778

Resistor deviation from nominal value for

voltage measurement

0.5938

Total error of measurement 0.8828

Table 7. Vicker’s micro hardness and surface roughness

Ra.

Material

Vicker’s micro-

hardness HV [-]

Surface

Roughness Ra

[μm] Min Max Mean

Al 6061 spacer 104 120 113.6 0.514

Al 6061 plate 105 115 110.9 0.392

Brass spacer

(Muntz Metal) 177 226 197.2

-

Copper plate 93.8 105 100.9 0.307

SS 304 washer - - - 0.665 – 1.04


10

in the respective washer / spacer stack. With the used measurement method it was not possible to distinguish between

the individual interfaces. A further explanation and discussion is given in section V. The table in the appendix contains

all power measurements and calibrated temperature readings from all four stacks in each test case. For each of the

eight test cases A to H, three heater power steady states are reported which yields in a total of 24 data sets.

Figure 6 shows the comparison between theoretical computation of contact conductance and measurement values.

Only the theoretical results for cases B and C are shown here. Case B and C represent a combination of stainless steel

washers and aluminium spacers which is common for CubeSat. Furthermore, case B and C yielded in similar contact

conductance values, and the material properties, micro hardness, and surface roughness of the used washers and

spacers were well characterized. With that, case B and C were the best candidates with the largest data base to be used

for the theoretical computation of the contact conductance. The contact conductance hc was computed based on

equations 1-10. Figure 6a shows the comparison between the plastic deformation models discussed in section III. The

black full horizontal line marks a test result contact conductance of 15,000 W/m²K, averaged for case B and C. The

grey area indicates the measured contact pressure range of 44 MPa to 64 MPa. The theoretical contact conductance hc

was computed with equation 1 using the coefficients from Table 1. A combination of assumptions and measurement

values was used in order to derive minimum, maximum and mean values. The factors of Yovanovich et al., Kumar et

al., Tien et al., end Mikic et al. were used for the comparison in Figure 6a. ‘Maximum’ plots indicate a combination

of high surface roughness Ra, high thermal conductivity λ, and low micro hardness HC. The ‘minimum’ plots represent

a combination of low Ra, low λ and high HC. The mean plots utilise the measured values of Ra, HC and a mean value

of λ. The test results are in all cases far below the calculated theoretical values. Only the Mikic ’74 and Kumar ‘04

empirical coefficients yield in theoretical contact conductance values similar to the test results, but only if the

minimum assumptions are assumed and not if the measured values for HC, Ra, λ are used. Figure 6b shows the correlation between equation 9 from Thomas & Probert, and the test results. Also in this case

minimum, maximum and mean values have the same meaning as described for the previous figure and the horizontal

full black line marks the test results. Also here the grey area marks the measured contact pressure range. For the

theoretical results of the Thomas & Probert equation in Figure 6b, the empirical coefficients for aluminium are used.

V. Discussion

From Figure 5a it can be seen that the equivalent GL values are all in a similar range, 0.032 W/K to 0.062 W/K

and on average lower than the values used in the reviewed CubeSat projects. There is one outlier which is case D with

GL = 0.168 -0.0115/+0.0070 W/K. Case D is the configuration without stainless steel washers and with one 12 mm

Table 8. Result table. L

abel

Sp

acer

Hei

gh

t [m

m]

Nu

mb

er o

f S

pac

er [

-]

Sp

acer

Mat

eria

l

Was

her

To

rqu

e [N

m]

Lin

ear

Co

nd

uct

or

GL

to

tal

[W/K

]

Err

or

neg

.

[W/K

]

Err

or

po

s.

[W/K

]

Th

erm

al R

esis

tan

ce

[K/W

]

Co

nta

ct C

on

du

ctan

ce

[W/m

²K]

Err

or

neg

.

[W/m

²K]

Err

or

po

s.

[W/m

²K]

A 10 1 Alu Yes 1.0 0.041 0.0017 0.0016 24.46 10,257 1,531 2,054

B 12 1 Alu Yes 1.0 0.053 0.0023 0.0021 18.77 15,590 2,809 4,130

C 12 2 Alu Yes 1.0 0.037 0.0032 0.0029 27.30 14,605 3,532 5,494

D 12 1 Alu No 1.0 0.168 0.0115 0.0070 5.96 55,197 19,534 42,266

E 12 3 Alu No 1.0 0.062 0.0022 0.0017 16.14 52,156 18,619 55,083

F 20 1 Brass Yes 1.0 0.038 0.0015 0.0012 26.33 12,648 2,663 4,525

G 10 1 Brass Yes 1.0 0.038 0.0019 0.0013 26.22 9,865 1,680 2,220

H 10 1 Brass Yes 0.5 0.032 0.0017 0.0015 31.26 7,822 1,243 1,700


11

aluminium spacer. Figure 5b also shows that the contact conductance is very high in case D. This was traced back to

the low micro hardness of aluminium and the relatively high contact pressure at the interface. The good thermal

conductivity of aluminium in that case leads to a very high overall linear conductor. The subsequent case (E) is a

similar configuration, i.e. without stainless steel washers but a combination of three 12 mm aluminium spacers on top

of each other. Here the number of spacers paired with the high contact conductance yields in a GL value of 0.062 -

0.0022/+0.0017 W/K, which is comparable to the other cases.

Two more resulting values are worth mentioning. Case A and case B yield counter intuitive results. In both cases

aluminium washers and stainless steel spacers are used. In case A it is a 10 mm spacer and in case B a 12 mm spacer.

Case A results in a GL = 0.041 -0.0017/+0.0016 W/K and case B in a GL = 0.053 -0.0023/+0.0021 W/K. It should be

expected that the linear conductor of case A is higher, i.e. the heat flow through this stack is less impacted than for

case B. The reason for this deviation could be that the aluminium spacers were from different lots with different

material properties or they were subjected to difference annealing processes. The type of aluminium was defined and

variations of thermal conductivity within this type of aluminium are accounted for in the error bars, yet the annealing

was not known nor determined and hence is not reflected in the error bars. Different annealing processes of the same

aluminium type can lead to a wide variety in thermal conductivity. The second noteworthy finding is that case F and

G yield in almost identical linear conductor values, GL = 0.038 -0.0015/+0.0012 W/K and 0.038 -0.0019/+0.0013

Figure 5. a) Resulting linear conductors; blue bars refer to tests with aluminium spacers and green bars

refer to tests with brass spacers. b) Resulting contact conductance values; blue bars refer to tests with

aluminium spacers and green bars refer to tests with brass spacers.

Figure 6. a) Theoretical contact conductances in a configuration such as B and C. Computed with the

coefficients a1 and b1 from Yovanovich ’69, Tien ’68, Mikic ‘74, Kumar ’04.; subscripts min., mean, and max.

refer to the assumptions for surface roughness Ra, thermal conductivity λ, and micro hardness Hc;

b) Theoretical contact conductance based on the Thomas & Probert equation for an average contact pressure

for test case B and C. The grey shaded area indicated the measured pressure range.

a) b)

a) b)


12

W/K respectively. Yet, case F had one 20 mm brass spacer and case G had one 10 mm brass spacer. In both cases

stainless steel washers were used. It should be expected that the 20mm brass spacer yields in a lower GL than the 10

mm spacer. Similar to the previous case, differences in the material properties of the brass spacers or the stainless steel

washers could be the reason for the unexpected results.

Figure 5b shows the contact conductance values. They are in the range of 10,257 W/m²K to 15590 W/m²K for

configurations including stainless steel washers and with 1 Nm torque applied (case A, B, C, F, G). The contact

conductance is significantly higher, i.e. h = 52,156 W/m²K to 55,197 W/m²K in the case with aluminium spacers

without stainless steel washers (case D & E). The contact conductance decreased from 9,865 W/m²K to 7,822 W/m²K

when reducing the torque from 1 Nm to 0.5 Nm in an otherwise identical test set-up (case G & H). The reduction in

contact conductance was apparent but in its magnitude smaller than expected. The error bars are especially large for

the cases with aluminium spacers and without stainless steel washers. This large error bar can be associated with the

uncertainties in thermal conductivity of the spacer bulk material.

The resulting contact conductances from the test campaign were compared with the equations presented in

literature. Figure 6a shows the comparison between plastic deformation models with different empirical coefficients

and the test results of case B & C, which is the configuration composed of aluminium spacer with stainless steel

washers. Figure 6b shows the comparison between the Thomas & Probert empirical equation and cases B & C. The

plastic deformation models on average yield far higher theoretical contact conductance than the ones measured in the

presented test campaign. Only the coefficients derived by Mikic et al. and those by Kumar et al. as well as the

correlation from Thomas & Probst result in contact conductances which are close to the test results. The measurement

of the contact pressure allowed to narrow down the possible solution space. Even so, the unknown coefficients of

friction, as well as uncertainties in micro hardness, surface roughness and thermal conductivity does not allow the

conclusion that the Mikic or Kumar coefficients or the Thomas and Probst correlation will predict reliably contact

conductances in other CubeSat joints or in other CubeSat stacks with different spacer / washer combinations. The

correlation in Figure 6 is restricted to a stainless steel washer / aluminium spacer combination such as in case B & C.

VI. Conclusions

The presented work is focusing on a representative and typical configuration of washers and spacers, to investigate

the heat flow in and through common CubeSat PCB stacks. A set of 8 washer/spacer configurations with a total of 24

measurement points were investigated. Different spacer materials, torques, and stack combinations were tested in a

vacuum environment. Linear conductors ranged mostly from 0.037 W/K to 0.062 W/K and the derived contact

conductance between components in the stacks was in the order of 9,800 W/m²K to 15,600 W/m²K. It was also shown

that common empirical equations for the determination of contact conductances are ill suited for the specifics of

CubeSat stacks. In general, the empirical equations led to far higher contact conductance values. The correlation with

empirical equations is challenging as it requires the knowledge of numerous properties such as friction coefficients in

the bolted connection, surface roughness, micro hardness, and the thermal conductivity of the individual components.

As a consequence, it was not possible to identify one single empirical equation, neither was it possible in the scope of

this activity, to derive such an empirical equation suitable for CubeSat stacks.

Yet, the presented measurements, especially of the common combination of stainless steel washers and aluminium

spacers will allow CubeSat thermal engineers to utilise reasonable assumptions for linear conductors and/or contact

conductance values when setting up a thermal model. In addition, the presented test results could support the CubeSat

community to optimize design and integration of systems through a better understanding of the impact of the stacks

layout. Finally the results are a contribution to growing efforts in the CubeSat community to tackle upcoming thermal

challenges.

Appendix

The following table shows the calibrate temperature reading and corrected heater power input as measured during

the 8 tests. Since each test case was repeasted at 3 different heater power levels a total of 24 temperature measurements

sets are included in the table. The cases A to H are detailed in Table 4.


13

10mm Alu + W

(A)

12mm Alu + W

(B)

2*12mm Alu + W

(C)

12mm Alu – W

(D)

3 * 12mm Alu –W

(E)

20mm Brass + W

(F)

10mm Brass + W

(G)

10mm Brass + W 0.5Nm

(H)

Power (total) [W] 1.980 3.945 5.949 1.979 3.961 5.366 1.987 3.973 5.386 1.980 3.942 5.371 1.976 3.957 5.361 1.970 3.975 5.417 1.987 3.975 5.376 1.981 3.953 5.386

Heater 1 [C] 12.40 25.08 39.05 13.20 26.68 36.23 14.53 29.69 41.56 4.81 10.02 13.80 9.24 18.89 25.78 15.89 31.88 40.90 14.50 29.07 38.98 17.09 33.96 45.49

Heater 2 [C] 9.20 18.59 27.74 11.91 24.17 32.50 13.60 27.48 36.88 2.84 6.22 8.71 7.81 16.09 21.98 12.72 25.82 35.08 12.88 25.78 34.65 15.40 30.67 41.06

Guard Heater Bottom [C] 9.01 18.93 26.95 8.89 21.87 31.33 11.00 26.38 34.05 2.09 9.90 13.58 8.33 14.00 18.78 9.35 19.49 26.78 11.00 25.21 33.08 12.87 26.12 39.88

Guard Heater Top [C] 8.73 18.42 26.23 8.68 21.39 30.65 10.80 25.87 33.35 2.01 9.63 13.20 8.12 13.65 18.35 9.18 19.17 26.32 10.77 24.70 32.47 12.58 25.55 38.98

Cool Plate Center [C] -0.42 -0.31 -0.17 -0.43 -0.37 -0.27 -0.47 -0.31 -0.26 -0.45 -0.29 -0.21 -0.43 -0.37 -0.27 -0.38 -0.37 -0.24 -0.47 -0.36 -0.27 -0.42 -0.36 -0.27

Housing Top [C] -0.47 -0.47 -0.43 -0.47 -0.47 -0.47 -0.50 -0.47 -0.47 -0.47 -0.47 -0.47 -0.47 -0.47 -0.47 -0.47 -0.47 -0.47 -0.47 -0.47 -0.47 -0.47 -0.47 -0.47

MLI Bottom [C] -0.57 -0.57 -0.57 0.53 1.13 1.60 0.73 1.43 1.92 0.13 0.33 0.43 0.64 1.05 1.37 0.73 1.32 1.72 0.53 1.22 1.68 0.63 1.42 2.01

MLI Top [C] 0.83 1.45 2.13 1.03 1.82 2.49 1.12 2.19 2.92 0.27 0.46 0.63 0.70 1.25 1.72 0.94 1.83 2.52 1.02 1.92 2.55 1.12 2.12 2.82

Stack 1

Cool Plate [C] -0.46 -0.32 -0.17 -0.50 -0.29 -0.17 -1.02 -0.31 -0.18 -0.47 -0.36 -0.24 -0.47 -0.37 -0.23 -0.47 -0.37 -0.27 -0.47 -0.33 -0.22 -0.47 -0.37 -0.25

Spacer [C] 3.92 7.97 11.95 5.33 11.20 15.29 5.37 11.10 15.19 1.03 2.32 3.27 3.61 7.51 10.30 5.56 11.45 15.68 5.71 11.52 15.63 7.11 14.38 19.39

Threaded Bar [C] 4.92 9.90 14.06 6.53 13.40 18.09 8.61 17.29 23.28 1.23 2.72 3.82 5.03 10.38 14.10 7.41 15.14 20.59 9.60 19.05 25.44 7.01 14.10 19.09

Heater Plate [C] 8.92 17.99 26.80 11.60 23.28 31.36 13.27 26.61 35.78 2.65 5.68 7.81 7.60 15.48 21.09 12.50 25.28 34.28 12.60 25.08 33.59 15.19 30.02 40.09

Stack 2

Cool Plate [C] -0.37 -0.17 -0.08 -0.37 -0.18 -0.16 -0.39 -0.22 -0.17 -0.35 -0.17 -0.13 -0.37 -0.22 -0.16 -0.37 -0.17 -0.16 -0.37 -0.17 -0.14 -0.37 -0.18 -0.14

Spacer [C] 3.92 8.31 12.49 6.32 12.80 17.19 5.02 10.80 14.80 0.93 2.32 3.32 3.52 7.49 10.30 5.71 11.90 16.31 6.81 14.00 18.95 8.26 16.49 22.18

Threaded Bar [C] 5.61 11.40 17.00 5.42 11.40 15.46 9.08 18.11 24.08 1.42 3.22 4.52 6.11 12.49 16.99 7.86 16.09 21.94 6.54 13.39 18.19 6.31 12.79 17.29

Heater Plate [C] 8.90 18.03 26.81 11.50 23.18 31.18 13.12 26.47 35.58 2.52 5.51 7.70 7.51 15.38 20.91 12.39 25.09 34.10 12.49 24.98 33.56 14.99 29.67 39.68

Stack 3

Cool Plate [C] -0.37 -0.21 -0.14 -0.37 -0.22 -0.17 -0.39 -0.20 -0.17 -0.37 -0.17 -0.13 -0.37 -0.25 -0.17 -0.37 -0.25 -0.17 -0.37 -0.26 -0.17 -0.37 -0.24 -0.17

Spacer [C] 2.93 6.30 9.55 6.21 12.70 17.20 4.32 9.21 12.60 0.93 2.22 3.13 3.46 7.31 10.08 5.05 10.58 14.53 5.88 11.90 16.09 7.63 15.50 20.98

Threaded Bar [C] 6.32 12.83 19.09 4.90 7.81 8.61 5.71 11.70 16.09 1.82 3.91 5.41 5.71 11.67 15.99 9.29 18.85 25.48 3.37 7.41 11.11 3.72 7.60 10.30

Heater Plate [C] 8.90 17.89 26.59 11.72 23.68 31.79 12.58 25.18 33.76 2.63 5.65 7.81 7.61 15.53 21.10 12.48 25.19 34.25 12.62 25.26 33.87 15.29 30.19 40.33

Stack 4

Cool Plate [C] -0.40 -0.23 -0.13 -0.41 -0.23 -0.17 -0.60 -0.24 -0.17 -0.40 -0.24 -0.16 -0.40 -0.28 -0.19 -0.40 -0.26 -0.20 -0.40 -0.25 -0.18 -0.40 -0.26 -0.19

Spacer [C] 3.72 7.81 11.87 2.35 5.22 7.25 3.42 7.21 9.81 1.22 2.72 3.82 2.86 6.02 8.31 5.73 11.50 15.63 4.32 9.31 12.80 5.32 11.76 16.09

Threaded Bar [C] 6.02 11.69 16.79 3.42 7.21 9.79 8.03 16.17 21.72 1.28 2.82 3.92 5.48 11.15 15.19 9.42 18.89 25.58 9.41 18.77 25.19 3.73 7.60 10.30

Heater Plate [C] 8.97 17.99 26.78 11.82 23.78 31.90 13.23 26.58 35.68 2.62 5.52 7.62 7.57 15.39 20.89 12.48 25.18 34.08 12.58 24.98 33.38 15.22 30.08 40.18

Acknowledgments

The authors would like to acknowledge the German Aerospace Center (DLR) for the German Trainee program at

ESA ESTEC. Further the authors want to thank the companies Innovative Solutions in Space (ISIS) and GomSpace

for the in-kind contribution of common CubeSat components. In addition the authors would like to thank the TEC-

QEE lab at ESA ESTEC for providing support in characterising material properties of the tested components, as well

as the Material Science Lab at ESTEC for providing the test equipment and facilities for the contact conductance

measurements.

References 1Bouwmeester, J., Langer, M., Gill, E., “Survey on the implementation and reliability of CubeSat electrical bus

interfaces”, CEAS Space Journal, Volume 9, pp. 163-173, 2017. 2Walker, R., Binns, D., Bramanti, C., Casasco, M., Concari, P., Izzo, P., Feili, D., Fernandez, P., Gil Fernandez, J., Hager, P.,

Koschny, D., Pesquita, V., Wallace, N., Carnelli, I., Khan, M., Scoubeau, M., Taubert, D., “Deep-space CubeSats: thinking inside

the box,” Astronomy & Geophysics, Volume 59, Issue 5, pp. 5.24–5.30, 1 October 2018. 3Sundaramoorthy, P., Topputo, F., Massari, M., Biggs, J., Di Lizia, P., Dei Tos, D., Mani, K., Ceccherini, S.,

Franzese, V., Cervone, A., Speretta, S., Mestry, S., Noomen, R., Ivanov, A., Labate, D., Jochemsen, A., Furfaro, R.,

Reddy, V., Jacquinot, K, Walker, R., Vennekens, J., Cipriano, A., Pepper, S., van de Poel, M., “System design of

LUMIO: A CubeSat at Earth-Moon L2 for observing lunar meteoroid impacts”, Proceedings of the 69th International

Astronautical Congress, Bremen, Germany, 2018 4Bardoux, E., Belkouchi, B., Najjar, A., Lacombe, A., “Prospects for the small satellite market”, 4th edition, edited

by Puteaux, M., Euroconsult, 86 Blvd Sebastopol, 75003 Paris, France, August 2018 5Léon Pérez, L., Koch, P., Walter, R. “GOMX-4 – the twin European mission for IOD purposes,” 32nd Annual AIAA/USU

Conference on Small Satellites, Conference Proceedings, 2018. 6European Cooperation for Space Standardisation, “Space Engineering, Thermal Analysis Handbook,” ECSS-E-HB-31-03A,

ESA Requirements and Standards Division, 15 November 2016. 7Yovanovich, M.M. “Four Decades of Research on Thermal Contact, Gap, and Joint Resistance in Microeletronics,” IEEE

Transactions on Components and Packaging Technologies, Vol. 28, No. 2, Juen 2005. 8European Cooperation for Space Standardisation, “Space Engineering, Thermal Design Handbook – Part 4: Conductive Heat

Transfer,” ECSS-E-HB-31-01, ESA Requirements and Standards Division, 5 December 2011. 9Gluck, D.F., Baturkin, V., “8 Mounting and Interfaces,“ Spacecraft Thermal Control Handbook, 2nd edition, edited by

Gilmore, D.G., The Aerospace Press, El Segundo, California, 2002 10Mantelli, M.B.H, Yovanovich, M.M., “16 Thermal Contact Resistance,” Spacecraft Thermal Control Handbook, 2nd edition,

edited by Gilmore, D.G., The Aerospace Press, El Segundo, California, 2002 11Hasselstroem, A. J., Nilsson, U.E., “Thermal Contact Conductance in Bolted Joints,” Diploma Work. 85/2012, Chalmers

Reproservice Gothenburg, Sweden, 2012.


14

12Kumar, S.S., Ramamurthi, K., “Thermal contact conductance of pressed contacts at low temperatures,” Cryogenics, 44, pp.

727-734, 2004. 13Yeh, C.L., Wen, C.Y, Chen, Y.F. Yeh, S.H., Wu, C.H., “An experimental investigation of thermal contact conductance across

bolted joints,” Experimental Thermal and Fluid Science 25, pp. 349-357, 2001. 14Bahrami, M., Culham, J.R., Yovanovich, M.M., Schneider, G.E., “Review of Thermal Joint Resistance Models for

Nonconforming Rough Surfaces,”, Applied Mechanics Review, Vol 59/1, January 2006.

contact conductance in common cubesat stacks

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