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International Review of Mechanical Engineering (I.RE.M.E.), Vol. 8, N. 2
ISSN 1970  8734 March 2014
Manuscript received and revised February 2014, accepted March 2014 Copyright © 2014 Praise Worthy Prize S.r.l.  All rights reserved
344
Experimental and Numerical Investigation of Transverse
Thermal Conductivity of an Aluminum Honeycomb Panel
Silva D. F.1, Garcia E. C.2
Abstract – Transverse thermal conductivity of an aluminum honeycomb panel is evaluated by
experimental, analytical and computational approaches. The main objective of this work is to
investigate the best thermal modeling of a honeycomb panel for a satellite. The test was conducted
in a thermal vacuum chamber and the numerical results were obtained by Thermal Desktop®,
RadCAD® and SINDA/FLUINT thermal analyzer. Numerical results and analytical models were
compared to experimental data, in order to validate the numerical model and evaluate the more
appropriated analytical model. The panel was modeled as an element with effective thermal
conductivities in each direction, and two nodal division approaches were investigated: centered
nodes and edge nodes configurations. Analytical models have shown a good agreement with
experimental data. The analytical model (of the transverse thermal conductivity of the aluminum
honeycomb panel) based on the density and thermal conductivity of core’s material presents just a
slight deviation compared to experimental results. Regarding to numerical analyses, the results
have shown that the analysis method as well as nodal breakdown are extremely important to reach
acceptable results, and the edge nodes configuration has presented low computational cost, since
a smaller amount of nodes is required to achieve temperature convergence, compared to centered
nodes configuration. Copyright © 2014 Praise Worthy Prize S.r.l.  All rights reserved.
Keywords: Honeycomb Thermal Analysis, Thermal Conductivity Measurement, Heat Transfer
Nomenclature
A Panel area
e Core foil thickness
h Panel height
k
c
Al. 50560 thermal conductivity
k
cx
Core’s thermal conductivity in x direction
k
cy
Core’s thermal conductivity in y direction
k
cz
Core’s transverse thermal conductivity
k Panel’s effective thermal conductivity in
tangential directions
k
f
Al. 2024T3 thermal conductivity
kx Panel’s effective thermal conductivity in x
direction
ky Panel’s effective thermal conductivity in y
direction
k Core’s thermal conductivity in tangential
directions
K
t
Honeycomb transverse conductance
l Panel width
Q
1

2
Heat flux across honeycomb
S Core cell size
T
1
Surface 1 average temperature
T
2
Surface 2 average temperature
T
w
Shroud temperature
Panel thickness
c
Core thickness
f
Face sheet thickness
1
Surface 1 infrared emissivity
2
Surface 2 infrared emissivity
StefanBoltzmann constant
I. Introduction
The demand for composite materials has increased
due to the need for advanced performance in various
industries [1].
Also, the utilization of metal matrix composite
materials are increased enormously in many engineering
fields because of many beneficial properties [2], as well
as honeycomb sandwich panels. Honeycomb sandwich
panel, one kind of composite material, has come to be
used in many lightweight structures, such as satellites,
aircraft and highspeed trains [3]. The main benefits of
using the sandwich concept in structural components are
the high stiffness, good fatigue resistance and low weight
ratios [4]. Honeycomb panels offer great advantages in
weight and strength, but their ability to transport heat by
conduction is limited by the large ratio of void to solid
material. On occasion, the thickness and material of core
and face sheets are selected to enhance heat transfer, but,
generally, the design of honeycomb panels follow mainly
from structural and weight considerations [5].
Usually, a honeycomb panel is composed by two face
sheets bonded to a core. Due to the nonhomogeneous
character of the panel, it is necessary to understand its
properties [11].
D. F. Silva, E. C. Garcia
Copyright © 2014 Praise Worthy Prize S.r.l.  All rights reserved International Review of Mechanical Engineering, Vol. 8, N. 2
345
In vacuum environment the heat transfer process is
limited, since only heat conduction and radiation are
present. To investigate the honeycomb panel transverse
thermal conductivity, a test was conducted in a 0.25 m³
Thermal Vacuum Chamber (TVC) of the Integration and
Testing Laboratory (LIT) at Brazilian National Institute
for Space Research (INPE).
Experimental data were compared to analytical
models and numerical results, in order to validate the
numerical model and evaluate the more appropriated
analytical model. The panel was modeled as a single
element with effective thermal conductivities in each
direction. Also, two nodal divisions approach were
investigated: centered nodes and edge nodes.
As presented in [6], an exact method was developed
for considering internal reflections of radiant heat and for
reducing the given problem to an equivalent problem
which may be solved by wellestablished blackbody
methods. Temperature distributions and effective thermal
conductivities were calculated for both honeycombcore
and corrugatedcore sandwich panels. In addition, the
model was experimentally validated based on results
presented in [7]. Contrasting with the pioneering works
presented in [6] and [7], in this paper, in order to simplify
the analyses, the effects of heat transfer by radiation
between the inner surfaces of the panel were no
considered, and only heat conduction was assumed.
II. Experimental Setup
Honeycomb conductance may be verified by tests
performed in cryogenic vacuum chambers, in an
arrangement similar to that shown in Fig. 1.
As indicated, the instrumentation is very simple
consisting of skin heaters and thermocouples.
Fig. 1. Test setup for determining honeycomb transverse conductance
On neglecting the heat radiation exchange between
face sheets, a heat balance in steady state on the small
central region shows that the heat flux, Q12 [W], across
the honeycomb, Eq. (1), must be equal the heat radiated
from surface 2 to the shroud, Eq. (2):
1 2 1 2
t
Q K A T T (1)
4 4
1 2 2 2 w
Q A T T (2)
Making Eq. (1) equal to Eq. (2), it is possible to
determinate the honeycomb transverse conductance,
Kt [W/m²K], as stated by Eq. (3) [5]:
4 4
2 2
1 2
w
t
T T
KT T (3)
where 2 is the infrared emissivity of surface 2,
[5.667×108 W/m²K4] is the StefanBoltzmann constant,
T1 [K] and T2 [K] are the average temperature of surfaces
1 and 2, respectively and Tw [K] is the temperature of
TVC’s shroud.
II.1. Specimen Details
One honeycomb specimen with hexagonal cells was
used in this study. The honeycomb was made of two
different aluminum alloys, Al 50560 for core and
Al 2024T3 for face sheets. The specification of
specimen is summarized in Table I, as well as, surface’s 1
and 2 infrared emissivity. Five TType thermocouples
were disposed on each surface (total of 10 sensors) and
an image of the specimen is shown in Fig. 2.
Two skin heaters have been positioned on surface 2
and covered by aluminum film. An Agilent N5771A
power supply system was used to provide the required
voltage level to the skin heaters (in order to generate the
specified heat dissipation) and, also, a digital multimeter
Agilent 34401A was employed to acquire temperatures
and voltage level.
TABLE I
SPECIMEN SPECIFICATION
Parameter Value
Face sheet thickness 
f
0.3 mm
Core thickness 
c
29.4 mm
Core cell size  S 6.35 mm
Core foil thickness  e 0.0254 mm
Panel thickness  30 ± 0.02 mm
Panel width  l 0.19 ± 0.0005 m
Panel height  h 0.19 ± 0.0005 m
Panel area  A 0.0361 ± 0.0001 m²
Al. 50560 thermal cond.  k
c
115.96 W/m K
Al. 2024T3 thermal cond.  k
f
121.15 W/m K
Surface 1 emissivity 
1
0.050 ± 0.004
Surface 2 emissivity 
2
0.813 ± 0.033
Fig. 2. Image of the testing specimen
Thermocouples
Honeycomb Panel
Heater Aluminum Film  1
Shroud  Tw
Kapton
®
Film 2
T1
T2
Q12
D. F. Silva, E. C. Garcia
Copyright © 2014 Praise Worthy Prize S.r.l.  All rights reserved International Review of Mechanical Engineering, Vol. 8, N. 2
346
The sample positioning within TVC is shown in Fig.
3. The pressure level reached 0.00013 Pa and
temperature of TVC’s shroud reached approximately
190 °C.
Fig. 3. Sample positioning inside thermal vacuum chamber
The specimen was suspended by a PTFE string, in
order to reduce the heat conduction between specimen
and thermal vacuum chamber.
II.2. Testing Results
A steadystate condition is required to characterize the
thermal behavior of the panel, and it was assumed to
have been reached when none of the measured
temperatures in test specimen varied by more than
±0.2°C over a 1hour period. The temperatures, as well
as heating dissipation profile (curve Q) measured during
all testing execution, are shown in Fig. 4.
0 3 6 9 12 15
200
100
0
100
TC01 TC02 TC03 TC04 TC05
TC06 TC07 TC08 TC09 TC10
Q Tw
Time  hours
0
40
Fig. 4. Temperatures and heat rate profiles during test
After stabilization of the imposed boundary conditions
the steadystate was reached, and two shroud’s
temperature levels were analyzed: one hot and another
cold. The hot case consists on maximum heat dissipation
(37.56 ± 0.46 W) and higher temperature on shroud,
while the cold case is characterized by lower temperature
on shroud and moderated heat dissipation (9.32 ±
0.45 W).
Surface’s 1 temperature, T1, is achieved by the
arithmetic mean of TC1, TC2, TC3, TC4 and TC5, and
the temperature of surface 2, T2, is the arithmetic mean of
TC6, TC7, TC8, TC9 and TC10. The average
temperatures of both surfaces 1 and 2, as well as shroud
average temperature, Tw, are summarized in Table II, for
hot and cold cases.
Also in Table II, honeycomb’s effective transverse
thermal conductivity is presented (kz). The value of the
effective transverse thermal conductivity is the product
between panel transverse conductance (Kt, obtained by
applying Eq. (3)) and thickness ( ).
It should be noted that all uncertainties presented in
this work were calculated for a 95 % confidence level.
TABLE II
AVERAGE TEMPERATURES AND EFFECTIVE TRANSVERSE
THERMAL CONDUCTIVITY
Parameter Hot Case Cold Case
T
1
[°C] 106.88 ± 1.21 8.47 ± 1.31
T
2
[°C] 91.82 ± 0.91 12.7 ± 1.22
T
w
[°C] 157.14 ± 1.20 186.85 ± 1.20
k
z
[W/m K] 1.611 ± 0.17 1.586 ± 0.15
III. Analytical Approach
A comparison between two analytical models and
experimental results was accomplished in order to
evaluate which model fits better the experimental results.
Based on [5], the transverse thermal conductivity of
the panel can be obtained by applying Eq. (4):
c
z c
m
k k (4)
where c is the core’s density [36.84 kg/m³] and m is the
density of core’s material [2769 kg/m³, Al. 50560].
According to [8] the transverse thermal conductivity
of the core, kcz [W/m K], is calculated through Eq. (5):
8
3
c
cz
k e
kS (5)
And the effective transversal thermal conductivity is
achieved by Eq. (6) [9]:
2
1 1 f
c
z cz f
k k k (6)
The values obtained by applying Eq. (4) and Eq. (6),
as well as the deviation regarding to experimental results,
based on available analytical models, are disposed on
Table III.
TABLE III
ANALYTICAL RESULTS AND DEVIATIONS
Analytical Model
Parameter Ref. [5] Ref. [8]
k
z
[W/m K] 1.543 1.262
Deviation: Hot Case 4.41 % 30.23 %
Deviation: Cold Case 2.79 % 28.21 %
D. F. Silva, E. C. Garcia
Copyright © 2014 Praise Worthy Prize S.r.l.  All rights reserved International Review of Mechanical Engineering, Vol. 8, N. 2
347
IV. Numerical Approach
In order to analyze the experimental results, numerical
simulations were performed with two separate
approaches on panel’s nodal distribution. In the first
approach the panel was modeled by using centered nodes
and, in the second one, it was modeled with edge nodes.
The panel was modeled as a single element with
effective thermal properties, and the TVC was
considered with boundary temperature, equals to the
average temperature of shroud during the test. Also, two
elements were positioned on the panel to represent the
skin heaters, ten elements were added representing
thermocouples. It should be noted that all numerical
results were obtained employing C&R Technologies
software, Thermal Desktop®, RadCAD® and
SINDA/FLUINT thermal analyzer, and only hot
conditions were simulated.
IV.1. Panel’s Configuration Parameters
As elucidated previously the panel was modeled as a
single element (parallelepiped), with effective thermal
properties in each direction, in order to simplify the
development process. The value of thermal conductivity
in transverse direction was equal to the obtained by test.
The values of thermal conductivities in core’s
tangential (x and y ones) directions, were determined by
applying Eqs. (7) and (8) [8]:
c
cx
k e
kS (7)
3
2
c
cy
k e
k
S
(8)
where kcx, and kcy [W/m K] are core’s thermal
conductivity in x and y direction, respectively.
Once core’s thermal conductivities have been reached,
it is necessary to obtain panel’s effective thermal
conductivities. The tangential effective thermal
conductivity, in each direction, is calculated in function
of honeycomb’s and face sheet’s conductivities, applying
thickness as weighting factor and, Eq. (9) [9] presents an
expression to calculate these properties:
2
c f f
ef
k k
k (9)
where k [W/m K] is the panel’s effective thermal
conductivity in tangential directions, and k [W/m K] is
core’s thermal conductivity in tangential directions (kcx or
kcy). By replacing in Eq. (4) the value of thickness
presented in Table I, in combination with results obtained
by Eqs. (7) and (8), the values of effective thermal
conductivities in tangential directions are reached.
These ones are shown in Table IV, as well as core’s
thermal conductivities values.
TABLE IV
EFFECTIVE THERMAL CONDUCTIVITIES OF PANEL AND CORE
IN TANGENTIAL DIRECTIONS
Thermal
Conductivity Direction
[W/m K] x y
Core kcx = 0.464 kcy = 0.696
Panel (Effective) k
x
= 2.878 k
y
= 3.105
IV.2. Simulations Results
Regarding the methods of nodal location, there are
two available options: centered and edge nodes. Centered
nodes option places the nodes at the node center.
The Edge nodes option also places the nodes at the
center of the nodal area, but will make the nodes span the
entire surface by adding “half” nodes on the edges and
“quarter” nodes at the corners [10].
In order to achieve the temperature obtained during
the test, an analysis of the nodal distribution on the panel
was performed. Fig. 5 shows the average temperatures T1
and T2, for centered nodes configuration in hot case
condition, depending on the amount of nodes in the
model, while the lines represent the temperatures
obtained in the test.
The results shown in Fig. 5 were obtained by varying
the number of nodes in the three directions of the panel.
The amount of nodes in each direction was always the
same, starting with 2 (total of 8 nodes) to 20 (total of
8000 nodes).
0 2000 4000 6000 8000
92
94
96
98
100
102
104
106
T1
T2
Amount of Nodes
Fig. 5. Temperatures for centered nodes configuration
As shown in Fig. 5, T1 gradually increases until
reaching the amount of approximately 500 nodes.
Between 500 and 1000 nodes a slight elevation occurs,
and after this point it begins to ascend until reaching
convergence. The average temperature T2 undergoes
small variations throughout the period, starting to
stabilize with 4000 nodes.
For edge nodes configuration, Fig. 6 shows the
variation of T1 and T2, as a function of amount of nodes.
As presented in Fig. 6, the temperatures T1 and T2
present small variations regarding to the amount of
nodes, and less nodes than centered nodes configuration
is required to achieve convergence.
D. F. Silva, E. C. Garcia
Copyright © 2014 Praise Worthy Prize S.r.l.  All rights reserved International Review of Mechanical Engineering, Vol. 8, N. 2
348
0 2000 4000 6000 8000
90
92
94
96
98
100
102
104
106
108
Amount of Nodes
T1
T2
Fig. 6. Temperatures for edge nodes configuration
In order to achieve a regular behavior of nodal
directional distribution for centered nodes configuration,
since it requires more nodes to convergence than edge
nodes configuration, an analysis of T1 as a function of the
number of nodes in transverse (z) and tangential (x and y)
directions was performed. The results of this analysis are
shown in Fig. 7.
0 20 40 60 80 100
92
94
96
98
100
102
104
106
108
Amount of Nodes in Tangential Plane
Z1
Z2
Z3
Z4
Z5
Z6
Z7
Z8
Z9
Z10
Exp.
Fig. 7. Temperatures on surface 1 as a function of nodal breakdown
In Fig. 7 the abscissa presents the amount of nodes in
tangential (x and y) direction, starting with 2 nodes in
each direction (total of 4) up to 10 nodes (totalizing 100
nodes in the plane). Also, the labels indicate the amount
of nodes in transverse (z) direction, starting with 1 node
(curve Z1) reaching 10 nodes (curve Z10). Thus, by
analyzing the results in Fig. 7, it should be pointed out
that T1 is more influenced by transverse direction nodal
breakdown relative to tangential direction.
Temperature variations on tangential plane is quite
small, since in any curve the temperature difference
between 4 nodes or 100 nodes is less than 2.0%.
However, the variation in the transverse direction is very
significant, reaching 13% between configurations with 1
(Z1) and 10 (Z10) nodes.
This analysis was performed only to T1 once, as
shown in Fig. 5, T2 undergoes small variations in the
convergence period.
V. Conclusion
The experimental setup has been presented simple and
easy to drive, and the results obtained in the experimental
analysis have proved to be valid and are within the
expected range. The analytical model based on the
densities and thermal conductivity of core’s material fits
better the experimental results than those one based on
dimensional parameters and thermal conductivity of
core’s material, presenting a very small deviation. The
influences of face sheets and adhesive have shown to be
negligible and, therefore, they shall not be considered in
analytical models.
Regarding to numerical analyses the configuration
with edge nodes have converged quickly, compared to
centered nodes configuration, and also requires less
nodes to achieve the expected results. Besides, when the
centered nodes configuration is used, at least 3 nodes in
transversal direction should be used, in order to reduce
errors.
Thus, based on all results presented in this work, the
best strategy to model a honeycomb panel in a satellite is
to consider it as a single element with transverse thermal
conductivity, based on the analytical model which
considers density of core and its material, with edge
nodes configuration.
Acknowledgements
We acknowledge support and infrastructure provided
for this work by Integration and Testing Laboratory and
CNPQBrazilian Foundation (research program
n°560065/20108 Ed. MCT/CNPQ/AEB nº 33/2010).
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Copyright © 2014 Praise Worthy Prize S.r.l.  All rights reserved International Review of Mechanical Engineering, Vol. 8, N. 2
349
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Authors’ information
1Instituto Nacional de Pesquisas Espaciais, Divisão de Engenharia e
Tecnologias Espaciais, Av. Dos Astronautas, 1758, Jardim da Granja,
CEP 12.227010, São José dos CamposSP, Brazil.
2Instituto Tecnológico de Aeronáutica, Divisão de Engenharia
Mecânica, Praça Marechal Eduardo Gomes, 50, Vila das Acácias,
CEP 12.228900, São José dos CamposSP, Brazil.
Douglas F. Silva is a D.Sc. student at Brazilian
Aeronautical Technological Institute (ITA),
focused on satellite thermal control. His M.Sc.
degree was obtained at the same school (2009)
in mechanical and aeronautical engineering, and
his bachelor in mechanical engineering was
obtained at University of Taubaté (UNITAU), in
2005. Currently works as thermal engineer at
Brazilian National Institute for Space Research (INPE), developing the
Amazonia1 satellite thermal control project.
Ezio C. Garcia is graduated in mechanical
engineering from the Federal University of
Uberlândia (UFU, 1983), M.Sc. degree in
aeronautical and mechanical engineering at
Brazilian Aeronautical Technological Institute
(ITA) in 1987, and also D.Sc. by the same
Institute, in 1996. Currently works as associate
professor and deputy head of the
aeronautics/mechanical engineering division at ITA, with experience in
mechanical and aerospace engineering, thermodynamics, heat transfer
and satellite thermal control, teaching courses on these areas. Also,
coordinates the thermal control subsystem of the ITASAT satellite
program.