Thermal diffusivity of porous cordierite ceramic burners
E. Garcı
´
a, M. I. Osendi, and P. Miranzo
Instituto de Cera
´
mica y Vidrio, CSIC, 28500 Arganda del Rey, Madrid, Spain
共Received 22 January 2002; accepted for publication 28 May 2002兲
The applicability of the laser flash method for measuring the thermal diffusivity of highly porous
cordierite materials is investigated. Due to the surface roughness of the samples, some
indetermination in the sample thickness measurement is produced, which induces errors in the
thermal diffusivity calculation. This problem was partially overcome by attaching two thin Cu layers
to both surfaces of the samples. The thermal diffusivity and conductivity values of two porous
cordierite materials 共40 and 50 vol % of porosity兲 are reported using this procedure and results are
discussed comparing with data for three-layer models. © 2002 American Institute of Physics.
关DOI: 10.1063/1.1495071兴
I. INTRODUCTION
Infrared radiant burners seem to be an efficient and clean
way to obtain radiant energy from natural gas.
1
In typical
ceramic plate burners, the gas flows through multiple chan-
nels or pores
2
produced intentionally in the material and
combustion takes place on the top surface of the plate. When
working in radiant mode, the combustion occurs near to the
surface of the burner and a steep thermal gradient is usually
generated between top (⬃800 °C) and bottom surfaces
(⬃50°C).
3
Therefore, the thermal conductivity of the plate
material is a key parameter for this type of application. In
fact, low values are required to avoid problems of flashback
when the thickness of the plate is small. Cordierite-based
materials seem to be suitable for these purposes due to their
nominally low thermal conductivity.
4,5
Different techniques have been employed to measure
thermal diffusivity and conductivity of commercial cordierite
materials
4,5
with porosity levels ranging between 10 and 24
vol %. Deviations of 15% were found among the data ob-
tained with the different techniques, which were partly attrib-
uted to the testing method but also to the material reproduc-
ibility. In particular, the room temperature thermal
diffusivities measured by the laser flash method were 0.014
and 0.010 cm
2
/s for the 10 and 24 vol % porous cordierites,
respectively. These values gave thermal conductivities in the
range of 1.5–2.5 W/m K. There is no data in the literature for
thermal diffusivity /conductivity of highly porous 共more than
30 vol %兲 cordierite materials.
The laser flash method is a versatile and useful technique
to measure thermal diffusivity of materials.
6
This technique
is especially suitable for dense opaque materials, neverthe-
less, measurements are not totally reliable when materials are
transparent to infrared 共IR兲 radiation or have pores, which
allow laser radiation to penetrate into the sample. Some au-
thors have addressed this problem assuming a certain pen-
etration of the radiation and numerically correcting heat con-
duction equations.
7,8
Here, an alternative method is described
to avoid laser radiation penetration into the porous samples,
which was applied to samples of porous cordierite ceramic
burners. In this way, thin copper layers were attached to
cordierite samples and the thermal diffusivity of the Cu/
Cordierite/Cu sandwich structure was appraised using a
three-layer model.
9
The average pore size was an important
parameter that was used to correct the experimental data.
II. EXPERIMENT
Two different porous cordierite materials used in
honeycomb-type ceramic burners 共Morgan Matroc S.A.,
Spain兲 were studied. The main characteristics of both mate-
rials are shown in Table I. The crystalline phases in material
A were mainly cordierite and cristobalite, while in material
B, the main phase was cordierite. The density of cordierite B
is slightly higher than that of cordierite A. The average pore
diameter for both materials is ⬃100
m 共Fig. 1兲 and the
porosity of material A 共50 vol %兲 is higher than that of cordi-
erite B 共40 vol %兲.
Cylinders of 12.5-mm diameter and 1- and 2-mm thick
were machined from both materials using diamond core
drills. Two different sample thicknesses were used to verify
the reliability of the measurement. The Cu/cordierite/Cu
sandwich structures were assembled by placing two opaque–
to–light high-purity copper disks 共99.9% pure, Goodfellow
Ltd.兲 at both sides of the samples. These disks were 0.05-mm
thick and had the same diameter as the cordierite samples.
These sandwich structures were heated at 1000 °C for1hin
a vacuum of 1.6 10
⫺ 6
mbar while applying a small pressure,
which ensured good contact between the layers. In Fig. 1, a
cross-sectional view of this type of structure can be ob-
served.
Diffusivity measurements were carried out by the laser
flash method in both monolithic cordierites and the Cu/
cordierite/Cu sandwiches. Experiments were done in an Ar-
gon atmosphere up to 800 °C, using Thermaflash 2200
equipment 共Holometrix-Micromet Inc. Bedford, USA兲.To
prevent direct transmission of the laser radiation through the
samples, they were thermally evaporated with a thin gold
layer of approximately 0.1
m. The efficiency in radiation
absorption and heat emission was increased by coating the
sample surfaces with a layer of ⬇10
m of colloidal graph-
ite. The experimental data were analyzed by the Clark–
JOURNAL OF APPLIED PHYSICS VOLUME 92, NUMBER 5 1 SEPTEMBER 2002
23460021-8979/2002/92(5)/2346/4/$19.00 © 2002 American Institute of Physics
Downloaded 10 Feb 2010 to 161.111.180.191. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp
Taylor model and the Koski procedure,
10,11
both imple-
mented in the equipment software.
Thickness indetermination was estimated on optical mi-
crographs of polished cross sections and the error associated
to it was analyzed for type A cordierite using two different
thicknesses. This error was also considered for the sandwich
structures. The thermal diffusivities of both cordierites were
deduced from the effective diffusivity of the sandwich struc-
tures by applying a mathematical model implemented in the
software by Holometrix.
9
Data for each condition have been
comparatively discussed.
The specific heat (C
p
) as a function of temperature was
calculated using the polynomial fit proposed by Cabannes
and Minges within an international
CODATA program aimed
to qualify a cordierite-based ceramic as a standard reference
material
4
C
p
⫽ 0.7327⫹ 1.946⫻ 10
⫺ 3
⫻ T⫺ 4.261⫻ 10
⫺ 6
⫻ T
2
⫹ 5.889⫻ 10
⫺ 9
⫻ T
3
⫺ 3.459⫻ 10
⫺ 12
⫻ T
4
. 共1兲
The thermal conductivity at each temperature was calculated
by the expression
⫽
C
p
␣
, 共2兲
where ‘‘
’’ and ‘‘
␣
’’ are the density and the thermal diffusiv-
ity of the material, respectively.
III. RESULTS AND DISCUSSION
The thermal diffusivity results for the monolithic
samples of cordierite A are shown as a function of tempera-
ture in Fig. 2共a兲. Thermal diffusivity differed by more than
40% for the different thicknesses, which is well above the
accuracy of the technique 共5%兲 that approximately corre-
sponds to the size of the symbols in the plots 共Fig. 2兲. There-
fore, these differences in diffusivity may be attributed to pen-
etration of the laser radiation inside the porous sample,
which induces large experimental errors. As the measured
sample thickness is higher than the actual value, the diffusiv-
ity is overestimated because it depends on the square of the
power of the sample thickness.
12
This error should be higher
for the thinner sample because the penetration/thickness ratio
is larger, which explains the overestimated diffusivity value
measured in the thin sample compared with the thick one.
This error can be estimated by observing the microstructure
of Fig. 1. The larger pores in the sample have an average
diameter of ⬃100
m, therefore, the actual thickness must
be reduced in ⬃200
m, taking into consideration both sur-
faces. The values attained correcting for this effect are shown
in Fig. 2共a兲. We note that the values are very similar for the
two thicknesses, assuring a greater reliability in the measure-
ments.
Figure 2共b兲 represents the effective thermal diffusivity
for three-layer structures considered as homogenous speci-
mens; data in the plot correspond to two thicknesses of the
middle cordierite 共type A兲 layer. Although effective diffusiv-
ity in layered structures should depend on the relative thick-
ness of each layer,
9
this was not observed in our data as they
were very similar for the 1- and 2-mm thick cordierite layer
specimens. This divergence indicates that the thermal diffu-
sivity data are not representative and that an error in the
thickness measurement may still occur. In fact, a bending of
the Cu layer into the pores can be observed in Fig. 1. This
deflection was estimated in ⬃44
m and a total decrease in
thickness of 88
m should be considered to correct errors in
the thickness determination of the sandwich structures. As
can be seen from Fig. 2共b兲, the corrected values were slightly
lower than the noncorrected ones and, as expected, depend
on the cordierite layer thickness.
In a first attempt, it can be assumed that the Cu layer
does not affect the thermal diffusivity of porous samples, but
FIG. 1. Optical micrograph of the polished cross section of a Cu/
cordierite/Cu multilayer structure. P indicates pores, C indicates cordierite,
and Cu indicates copper layer.
FIG. 2. Thermal diffusivity from room temperature to 800 °C for cordierite
A: 共a兲 monolithic specimens and 共b兲 three-layer structures. Full symbols
correspond to the values obtained from the optically corrected thickness.
TABLE I. Characteristics of the cordierite materials
Cordierite
A
Cordierite
B
Chemical SiO
2
65 52
Composition Al
2
O
3
20 35
共wt %兲 MgO 15 13
Density (g/cm
3
) 0.92 1.04
Open Porosity 50 40
共vol %兲
Pore size range 10–300 10–300
共
m兲
2347J. Appl. Phys., Vol. 92, No. 5, 1 September 2002 Garcı
´
a, Osendi, and Miranzo
Downloaded 10 Feb 2010 to 161.111.180.191. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp
would only prevent the laser-beam penetration.
13
This as-
sumption can be made when the diffusivity of the first and
the third layers are very high compared to the middle layer,
their thickness is thin compared to the middle layer thickness
and when their contribution to the total structure mass is
small. In the present case, the first and second assumptions
are true but not the third one, due to the low density of both
A and B cordierites compared to the density of Cu 共8.96
g/cm
3
). Therefore, a thermal diffusivity model for three-
layer configurations
9
should be considered to analyze the ef-
fect of the Cu layers. In this way, the thermal diffusivity of
the middle cordierite layer was calculated from the measured
effective thermal diffusivity, and data are plotted in Fig. 3.
Diffusivity values for cordierite A were similar for the two
thicknesses and close to the values for the monolithic
samples after applying the thickness correction. Comparing
data of Figs. 2 and 3, it can be said that the porosity and
surface roughness effects are less critical for the thicker
samples.
The three-layer configuration can be used to measure the
thermal diffusivity of highly porous samples, ⭓40 vol %, by
the laser flash method using the procedure described above.
In the case of samples with high roughness associated with a
coarse porosity, a less ductile metal that does not bend into
the pores may be used to avoid thickness corrections.
Thermal diffusivity results for cordierite B using the pre-
cedent three-layer procedure are also depicted in Fig. 3. The
higher diffusivity of this material compared to cordierite A is
consistent with its lower porosity 共Table I兲, although its dif-
ferent phase composition should also be taken into account.
For both materials, the thermal diffusivity decreased with
temperature up to 500 °C while showing a steady increase at
higher temperatures. This increase at higher temperatures
may be due to the high porosity of these samples 共⭓40
vol %兲, which leads to heat transfer by gas convection and
radiation at high temperatures.
14
This affect was more pro-
nounced for the thicker samples because heat losses also in-
creased by a ‘‘flash-by‘‘ effect. In this case, the background
temperature of the back surface increased because heat flew
by the sides of the sample instead of through it. Experimen-
tally, this effect was demonstrated by an initial step in the
temperature-time curves that distorted the diffusivity value.
The thermal conductivities calculated from expression
共2兲 using the thermal diffusivity data of Fig. 3 are plotted in
Fig. 4. Thermal conductivity of cordierite A 共⬃0.4 W/m K兲
was 33% lower than that of cordierite B 共⬃0.6 W/m K兲. The
difference between both cordierites in porosity alone 共⬇10
vol %兲 cannot justify this difference in the thermal conduc-
tivity values and therefore, the difference in composition
共Table I兲 may be important. To get an idea of the effect of the
cristobalite in the composition we can assume that cordierite
B is pure and that cordierite A has a 33 vol % of cristobalite.
Santos et al.
15
reported a room temperature thermal dif-
fusivity of 0.002 cm
2
/s for a 95% dense cristobalite material
that means a thermal conductivity of 0.34 W/m K consider-
ing a specific heat of 0.74 J/g °C.
16
On the other hand, Neuer
et al.
5
gave a room temperature thermal conductivity of
dense cordierite of 2.5 W/m K. Introducing both conductivity
data in the Maxwell equation,
17
the effective thermal conduc-
tivity of a dense material composed of 67 vol % of cordierite
and 33 vol % of cristobalite as dispersed phase should be
around 1.6 W/m K. Therefore, the thermal conductivity at
room temperature of dense cordierite-cristobalite composi-
tion would be reduced by 36% compared to a dense pure
cordierite. As we are dealing with cordierite-based materials
with porosities ⭓40 vol %, the solid phase is hardly continu-
ous and the reduction in thermal conductivity of 36% attrib-
uted to the difference in composition of the solid phase
should be dimmed. A rough estimation could be given by
applying the reduction to the percentage of solid phase 共50
vol %兲 which will give a 18% reduction in the thermal con-
ductivity of cordierite A compared to cordierite B.
The thermal conductivity values measured for both po-
rous cordierites are much lower, ⬃80%, than those reported
for denser cordierite materials 共porosity ⬍25 vol %兲
4,5
and,
furthermore, they are almost independent of temperature for
the typical working range in burner applications.
IV. CONCLUSIONS
The laser flash technique is adequate for measuring the
thermal diffusivity of materials with high porosity 共⬃50
vol %兲 and coarse pores 共⬎100
m兲 by applying the appro-
priate corrections and models. Three-layer structures formed
by two layers of a high-diffusivity material attached to both
sides of the porous specimen have been proved to give reli-
able values of thermal diffusivity for this type of material.
FIG. 3. Thermal diffusivity between room temperature and 800 °C for
cordierites A and B calculated from the three-layer effective thermal diffu-
sivity. Dashed lines correspond to thermal diffusivity data of monolithic
samples with the thickness correction due to the pore structure.
FIG. 4. Thermal conductivity as a function of temperature for cordierites A
and B in the range room-temperature 800 °C.
2348 J. Appl. Phys., Vol. 92, No. 5, 1 September 2002 Garcı
´
a, Osendi, and Miranzo
Downloaded 10 Feb 2010 to 161.111.180.191. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp
The thermal conductivity of highly porous 共⬎40 vol %兲
cordierite-based burners was almost constant and below 1
W/m K in the range of possible working temperatures.
ACKNOWLEDGMENTS
This project has been funded by the EC 共Brite-EURAM
III Program兲 under Contract No. BR-CT98-0743 共LIFE-
BURN Project兲 and by Mcyt 共ES兲 Project Nos. MAT99-
0168-CE and 2FD97-0345-C02-01. The partners to the
LIFEBURN Project are N.V. Acotech SA, CATIM, CSIC-
ICV, EcoCeramics BV, Eindhoven University of Technology,
Gaz de France, Ikerlan, INETI, Italgas, Kanthal AB, Morgan
Matroc SA, N.V. Nederlandse Gasunie, Politecnico di
Torino, Repsol Petroleo SA, and Worgas Bruciatori Srl.
1
L. Tico
´
, Global Ceramic Review 4Õ98,12共1998/99兲.
2
J. K. Kilham and E. P. Laningan, Gas Council Research Communication
GC167, Institution of Gas Engineers Journal, 10, 700 共1970兲.
3
P. H. Bouma, Ph.D. Thesis, Eindhoven University of Technology, 1997.
4
F. Cabannes and M. L. Minges, High Temp.-High Press. 21,69共1989兲.
5
G. Neuer, R. Brandt, K. D. Maglic, N. Milosevic, G. Groboth, and S.
Rudtsch, High Temp.-High Press. 31, 517 共1999兲.
6
G. S. Sheffield and J. R. Schorr, Ceram. Bull. 70,102共1991兲.
7
K. Inoue, Trans. JWRI 20,35共1991兲.
8
M. Golombok and L. C. Shirvill, J. Appl. Phys. 63,1971共1988兲.
9
T. R. Lee, Ph.D. Thesis, Purdue University, 1977.
10
L. M. Clark and R. E. Taylor, J. Appl. Phys. 46,714共1975兲.
11
J. A. Koski, Proceedings of the Eighth Symposium on Thermophysical
Properties, Gaithersburg, Maryland 共ASME, New York, 1982兲 Vol. II, pp.
94–103.
12
W. Parker, R. J. Jenkings, C. P. Butler, and G. L. Abbot, J. Appl. Phys. 32,
1679 共1961兲.
13
E. Garcı
´
a, R. Martinez, M. I. Osendi, and P. Miranzo, Bol. Soc. Esp.
Ceram. Vidrio 40, 289 共2001兲.
14
E. Litovsky, M. Shapiro, and A. Shavit, J. Am. Ceram. Soc. 79, 1366
共1995兲.
15
W. N. Santos, J. B. Baldo, and R. Taylor, Mater. Res. Bull. 35, 2091
共2000兲.
16
Engineered Materials Handbook, Vol. 4: Ceramics and Glasses 共ASM
International, Metals Park, OH, 1991兲.
17
J. C. Maxwell, Teatrise on Electricity and Magnetism 共Dover, New York,
1954兲 Vol. I pp. 435-441.
2349J. Appl. Phys., Vol. 92, No. 5, 1 September 2002 Garcı
´
a, Osendi, and Miranzo
Downloaded 10 Feb 2010 to 161.111.180.191. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp
