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RESEARCH ARTICLE | SEPTEMBER 04 2025
Rapid de e mina ion o he ela i e he mal conduc i i y
coe icien o insula ing ma e ials
Ma ek Velička ; Jiří Bu da; Joze Vlček; Ma io Machů; Jiří Fiedo ; Da id Rigo; Milan Racla ský; I an P iesol
AIP Con . P oc. 3355, 020018 (2025)
h ps://doi.o g/10.1063/5.0292177
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Rapid De e mina ion o he Rela i e The mal Conduc i i y
Coe icien o Insula ing Ma e ials
Ma ek Velička1, a), Jiří Bu da1, b), Joze Vlček1,2 c), Ma io Machů1, d), Jiří Fiedo 1, e),
Da id Rigo1, ), Milan Racla ský 1, 3, g) and I an P iesol 4, h)
1Depa men o The mal Enginee ing, Facul y o Ma e ials Science and Technology, VSB-Technical Uni e si y o
Os a a, 17. lis opadu 2172/15, 708 00, Czech Republic
2Ma e ial and Me allu gical Resea ch s. .o.., Poh aniční 693/31, 703 00 Os a a, Czech Republic
3Eco e s. .o. Oldřicho ice 914, 739 61 Třinec, Czech Republic
4I.P.C. Re ac o ies, spol. s .o., Magnezi á ska 11, 040 13, Košice, Slo akia
a) Co esponding au ho : m[email p o ec ed]
b) ji i.bu da@ sb.cz
c) [email p o ec ed]
d) ma io.mac[email p o ec ed]z
e) ji i. iedo @ sb.cz
) da id. igo@ sb.cz
g) [email p o ec ed]
h) [email p o ec ed]
Abs ac . Cu en ly, he e is in ensi e de elopmen in he ield o enewable ene gy sou ces, especially
pho o ol aics, whose sha e is g owing by ens o pe cen on an annual a e age. These ends will cause
d ama ic changes in he ene gy sec o , and one o he ways o add ess his si ua ion is high- empe a u e hea
s o age. The aim o his esea ch was o ind ma e ials sui able o high- empe a u e echnologies in ene gy
indus y. A en ion was paid o wo di ec ions: insula ion ma e ials o high- empe a u e applica ions and
s o age ma e ials. The a icle desc ibes he o iginal me hodology o quickly de e mining he he mal
conduc i i y coe icien and he applica ion o his me hod o a se ies o samples. F om he esul s ob ained,
i is clea ha he mos sui able in e ms o main aining he la ges he mal con en (sensible hea , en halpy)
appea s o be he use o insula ion wi h a minimum alue o he he mal conduc i i y coe icien and a he
same ime, he lowes alue o he empe a u e conduc i i y coe icien , which ensu es slowe empe a u e
equaliza ion be ween he ese oi and he insula ion, because he p ima y goal is o main ain he he mal
po en ial o he ese oi a a usable alue. The a icle also shows ha he e a e possible ma e ial
modi ica ions o imp o e bo h insula ing and mechanical p ope ies o ma e ials.
INTRODUCTION
Renewable ene gy sou ces (RES), and in pa icula pho o ol aics, a e cu en ly unde going a apid de elopmen ,
wi h hei sha e g owing by ens o pe cen yea -on-yea on a e age. The limi ing elemen o hese sou ces is he
abili y o accumula e he ene gy p oduced, which enewable sou ces p o ide unequally o e ime. High- empe a u e
hea s o age is one way o add essing his si ua ion. [1]. This concep is he subjec o his esea ch, which aims o
s udy and p epa e sui able ma e ials o high- empe a u e powe gene a ion echnologies (HPTE). The a en ion is
paid o wo di ec ions: insula ing ma e ials o high- empe a u e applica ions and s o age ma e ials o high-
empe a u e applica ions [2, 3].
Se e al app oaches o ene gy s o age echnology in he o m o hea ha e been de eloped so a . By compa ing
he p ope ies and applicabili y o commonly a ailable ma e ials (co undum, SIC, conc e e, g aphi e, cas i on, s eel)
The mophysics 2024
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Published unde an exclusi e license by AIP Publishing. 978-0-7354-5242-8/$30.00
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o s o ing o HPTE, a empe a u e o 750 °C can be conside ed as he uppe limi o applicabili y [4]. Po en ial
ma e ials o HPTE applica ions include magnesi e b icks wi h po en ial o ope a ing empe a u es up o 1200 °C,
ma e ials wi h high la en hea o usion and so called phase-change ma e ials (mol en sal s, me al mel s) [5]. A
s udy [6] in es iga ed he po en ial o ecycled was e ma e ials om he mining and me allu gical indus ies o
HPTE. The mal and mechanical p ope ies o slag-based ma e ials wi h di e en cemen i ious binde s in he
empe a u e ange up o 750 °C. P ope ies o na u al ocks (e.g. qua z sands, g ani e, limes one) o use in HPTE
applica ions whe e he hea ans e medium is wa m ai and he maximum uppe empe a u e in he cha ge and
discha ge cycle is 650 °C [7].
Long- e m s abili y o he p ope ies unde cyclic hea load (250 cycles - o e 3000 ope a ing hou s) up o 675
°C in an expe imen al 1 MWh hea s o age ank hea ed by esis ance wi es was demons a ed in diabase [8]. The
wo k led o he design o a pa ially unde g ound ock hea ese oi wi h a hea con en o 450 kWh [9]. The hea -
bea ing mass was hea ed o 600 °C elec ically and he hea was ex ac ed by ai . Diabase, magne i e and basal we e
iden i ied as ma e ials wi h po en ial o such applica ions. Simula ions e i ied by measu emen s and u he
pa ame ic s udies aimed a op imising he hea ex ac ion om he ese oi ha e demons a ed he possibili ies o
using hese ma e ials [10].
In e ms o he pa ame e s o he mal insula ion ma e ials, he coe icien o he mal conduc i i y is decisi e
[11]. This speci ied quan i y gene ally depends on empe a u e, densi y, chemical composi ion, s uc u e o he
mass, p essu e and humidi y. The pa ame e is de ined as he hea ha passes pe uni ime h ough a uni a ea o an
iso he mal su ace wi h a uni empe a u e g adien in he body. The alue o he he mal conduc i i y coe icien is
p ac ically speci ic o each ype o ma e ial [12]. In e ms o high empe a u e applica ions, he inc ease o his
coe icien wi h empe a u e is signi ican bu undesi able.
METHODOLOGY FOR DETERMINING THE THERMAL CONDUCTIVITY
COEFFICIENT
Fo some common ypes o ma e ials such as s eel, glass, e c., he e a e a numbe o empi ical ela ionships o
de e mining he mal conduc i i y. These p ocedu es ake in o accoun he chemical composi ion o he ma e ials and
e en de e mine he he mal conduc i i y alue as a unc ion o empe a u e [13]. Fo he e ogeneous ma e ials, such
simpli ying p ocedu es canno be applied. The he mal conduc i i y alue o ma e ials can be eliably de e mined by
expe imen al measu emen . Measu emen s a e pa icula ly impo an o ma e ials whe e he conduc i i y is e y
low o high. The speci ic de e mina ion o such ma e ials c ea es a equi emen o p ecise knowledge o he
physical pa ame e o be analysed [14].
The he mal conduc i i y coe icien can be measu ed by di e en ypes o me hods. One possibili y is he
hea ing wi e me hod, which is one o he ecognised me hods used o ce amic ma e ials. The e a e wo a ian s o
his me hod in so-called c oss o pa allel a angemen . The ad an age o his me hod is ha he he mal conduc i i y
alue can be ob ained as a unc ion o empe a u e, he ambien empe a u e can be up o 1250 °C [15], which is
p oblema ic o ma e ials wi h he mal conduc i i y alues below 1 W⋅m-1⋅K-1.
D . Bock's me hod is one o he so-called di ec me hods. Di ec me hods e e o p ocedu es whe e he hea ha
passes h ough he measu ed ma e ial is measu ed di ec ly and he alue o he he mal conduc i i y coe icien can
hen be de i ed di ec ly. Di e en p ocedu es a e applied o his g oup o me hods. These a e based on he
di e en ial p inciple, whe e he hea lux h ough a s anda d whose he mal conduc i i y alue is known is
moni o ed and subsequen ly he hea lux h ough he ma e ial unde es is moni o ed [16].
The Ligh Flash Analysis (LFA) me hod is an indi ec me hod o de e mina ion o he mal conduc i i y
coe icien s [17]. The echnique measu es he he mal conduc i i y coe icien and he alue o he he mal
conduc i i y coe icien is hen de e mined om he known o mula (1):
𝑎=𝜆
𝑐⋅𝜚 (m2.s-1) (1)
whe e λ is he he mal conduc i i y coe icien (W⋅m-1⋅K-1), c is he speci ic hea capaci y (J⋅kg-1⋅K-1), ρ is he
densi y (kg⋅m-3)
In he case o he LFA me hod, he sou ce o he equi ed hea is a lase discha ge, which is applied o he sample
o be measu ed, and hen he empe a u e change o he sample is moni o ed a speci ied ime in e als. The es
p ocedu e is no egula ed by he s anda d. The me hod is used by leading manu ac u e s o echniques o he mal
conduc i i y de e mina ion and his me hod is pe cei ed by he p o essional communi y as eliable [18]. The
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ad an ages o he me hod a e ha i is possible o measu e solid and liquid samples, compac and powde samples,
elec ically conduc i e and non-conduc i e samples, e c., and he me hod allows he measu emen o a pa ame e as
a unc ion o empe a u e, wi h measu emen s possible a empe a u es exceeding 2000 °C [19].
The e a e also nume ical models ha use a ious ypes o empi ical models and a la ge da abase o al eady
de e mined he mal conduc i i y alues. Fo speci ic physical pa ame e s, he model hen calcula es he equi ed
alues [20], ha can be used as bounda y condi ions o modelling he empe a u e dis ibu ion in he ma e ial [21].
The disad an age o all me hods is he ime and expe imen al complexi y, especially a high empe a u es. Fo
ma e ial de elopmen pu poses, hese me hods a e unsui able in e ms o ime and expe imen al complexi y.
The e o e, an o iginal me hod o he de e mina ion o he mal conduc i i y was de eloped.
PRINCIPLE OF EQUIPMENT FOR RAPID ANALYSIS OF THERMAL
PROPERTIES OF MATERIALS
A new me hod o compa ing he he mal conduc i i y coe icien was designed and es ed o he p o o ype
de ice. The me hod consis s o compa ing he su ace empe a u es be ween a known e e ence ma e ial and an
unknown ma e ial by measu ing he bo om su ace empe a u e in he hea ing pla e and on he o he hand he
su ace o he ma e ial is measu ed wi h a FLUKE TiS45 he mal image . Once he empe a u e condi ions ha e
s abilised, i is possible o de e mine which o he wo ma e ials has he highe he mal conduc i i y coe icien .
Assuming he same empe a u e on he unde side o he measu ed ma e ials and app oxima ely he same condi ions
o hea dissipa ion by con ec ion on he opside, and a e including he di e en losses by adia ion, he mean
he mal conduc i i y coe icien can be calcula ed qui e accu a ely (see igu e 1).
In he de elopmen o he new me hod, i was assumed ha in he de elopmen o ma e ials i is no necessa y o
know he exac alue o he he mal conduc i i y coe icien , bu knowledge o he ela i e alues is su icien , i.e.
whe he he new ma e ial has be e o wo se p ope ies ela i e o he e e ence ma e ial.
The p oposed me hod is sui able o high empe a u e measu emen s and is based on he assump ions ha :
• The lowe pa o he de ice is a closed hea ed chambe in which he empe a u e is homogenised by all
hea ans e mechanisms, bu especially by adia ion
• The empe a u e in he hea ed chambe is measu ed on a homogenising hea ing me al pla e wi h a pai o
he mocouples
• The uppe su ace o he measu ing pla e loses hea o he space by all hea ans e mechanisms, bu
mainly by adia ion
• The measu ed insula ing ma e ials ha e simila emissi i ies
• The ma e ial wi h he highe he mal conduc i i y he e o e has a highe empe a u e on he uppe su ace
• The ma e ial wi h he lowes su ace empe a u e is he bes insula o and he wo s conduc o
FIGURE 1. Model concep diag am
FIGURE 2. Measu emen scheme
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A e modi ying he measu ing pla e wi h a high quali y insula ing b ick ype HBU (see Table 1), se e al
samples could be measu ed and compa ed simul aneously. One sample was always aken as he s anda d e e ence
ma e ial (S1), he o he samples had di e en "modi ie " concen a ions (S2 - S5) (see Figu e 2).
TABLE 1. P ope ies o HBU insula ion b icks
Chemical
composi ion
(%)
Volume ic
mass
(kg.m
-3
)
Tempe a u e
expansion
(%)
P essu e
s eng h
(MPa)
Po osi y
(%)
Coe icien o he mal
conduc i i y
(W.m
-1
.K
-1
)
Al2O3 Fe2O3 1000°C 1200°C 500°C 800°C 1200°C
36.0 1.9 500 0.46 0.55 1.2 82 0.23 0.30 0.45
Fi e equally sized and equally deep holes we e milled in he HBU b ick in o which he es ed ma e ials we e
successi ely pou ed. The su ace was aligned so ha he hickness o each laye was always he same (see Figu e 3).
Fo he ma e ials es ed, pe li e and Re asil GIA ma e ial (sample 1) we e used as he e e ence sample, o
which an inc eased olume o e lec i e subs ances was g adually added. The aim o he de elopmen was o c ea e
ma e ials wi h ine g anulome y and wi h he bes possible he mal insula ion p ope ies, which we e modi ied in 4
di e en ways:
- by apping impe ec combus ion p oduc s on he su ace o he powde ed pe li e (sample 2).
- by mixing o powde y and inely g anulome ic pe li e wi h ine-g ained pa icles wi h a mean g anulome y o
5 µm (sample 3).
- by calcina ion o pe li e wi h a ious sal s. Two ypes o sal s we e selec ed, one nickel sal (sample 4) and one
clay sal (sample 5).
FIGURE 3. Sample se p epa ed
FIGURE 4. Fluke came a measu emen demons a ion
Subsequen ly, a measu ing de ice wi h con inuous powe con ol was used o he measu emen s. Images we e
aken by a he mal imaging came a a each ime poin and hen e alua ed (see Figu e 4).
In Fluke Connec p og amme, he measu emen ields o each sample we e plo ed on he empe a u e eco ding
image and he a e age maximum and minimum empe a u es a a gi en ime we e e alua ed while he empe a u e
o he base ma e ial was measu ed o compa ison (see Figu es 5 and 6).
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FIGURE 5. Sc eensho a he beginning o he
measu emen
FIGURE 6. Sc eensho a he end o he measu emen
I he he mal conduc i i y coe icien o he base ma e ial is no known, only he a ios o he wo coe icien s
a e de e mined. The hea lux densi ies o he measu ed and e e ence ma e ial can be w i en acco ding o
equa ions:
𝑄1=𝜀𝜀𝑇1
4=
λ
1
ℎ(𝑇HP − 𝑇1) (2)
𝑄2=𝜀𝜀𝑇2
4=
λ
2
ℎ(𝑇HP − 𝑇2) (3)
I we pu hese wo hea luxes in p opo ion, we can exp ess he he mal conduc i i y coe icien :
𝑄2
𝑄1
=𝜆2.(𝑇HP−𝑇
2)
𝜆1.(𝑇HP−𝑇
1)=𝜎.𝜀.𝑇
2
4
𝜎.𝜀.𝑇
1
4 (4)
λ
2=
λ
1.(𝑇HP−𝑇
1).𝑇
2
4
(𝑇HP−𝑇
2).𝑇
1
4 (5)
whe e λ is he coe icien o he mal conduc i i y (W⋅m-1⋅K-1), ε is he emissi i y (1), σ is he S e an-Bol zmann
cons an (W⋅m-2⋅K-4), Q is he hea lux densi y (W⋅m-2), T is he absolu e empe a u e (K), h s he sample hickness
(m), Indexes: HP hea ing pla e, 1 e e ence ma e ial, 2 measu ed ma e ial.
The measu ed a e age empe a u es o he samples and he su oundings a e gi en in Table 2, he calcula ed
ela i e a ios o he measu ed ma e ials in Table 3 and he calcula ed app oxima e alues o he he mal
conduc i i y coe icien in Table 4. A se ies o h ee measu emen s we e made in which he hea ed pla e empe a u e
was inc eased o 208 °C, 384 °C and 406 °C.
TABLE 2. Measu ed a e age empe a u es
Measu emen Sample 1 Sample 2 Sample 3 Sample 4 Sample 5
Su ounding
1
Su ounding
2
(°C) (°C) (°C) (°C) (°C) (°C) (°C)
1 40.62 42.33 41.78 41.74 39.32 46.24 47.91
2 178.30 183.47 184.06 178.08 168.69 243.57 239.15
3 197.30 198.16 196.70 194.61 187.65 250.56 244.96
TABLE 3. Rela i e a ios o measu ed ma e ials
Measu emen Sample 1 Sample 2 Sample 3 Sample 4 Sample 5
Su ounding
1
Su ounding
2
(1) (1) (1) (1) (1) (1) (1)
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1
1
1.0220
1.0149
1.0144
0.9835
1.0736
1.0963
2
1
1.0466
1.0520
0.9981
0.9175
1.7165
1.6585
3
1
1.0073
0.9949
0.9773
0.9204
1.5359
1.4712
TABLE 4. App oxima e alues o he he mal conduc i i y coe icien
Measu emen
Sample 1
Sample 2
Sample 3
Sample 4
Sample 5
HBU
(W.m-1.K-1) (W.m-1.K-1) (W.m-1.K-1) (W.m-1.K-1) (W.m-1.K-1) (W.m-1.K-1)
1
0.1185
0.1241
0.1247
0.1173
0.1088
0.1500
2
0.1383
0.1413
0.1403
0.1372
0.1360
0.2000
3
0.1530
0.1541
0.1522
0.1495
0.1408
0.2300
FIGURE 7. Compa ison o achie ed esul s
The expe imen s pe o med (see Figu e 7) show ha o sample 2, in which he p oduc s o impe ec
combus ion we e apped on he su ace o he powde ed pe li e, he measu emen s lead o ambiguous esul s in
which an inc ease in he alue o he he mal conduc i i y coe icien was obse ed. Fo sample 3 in o which he
powde ed pe li e wi h ine pa icles was mixed, be e esul s we e ob ained when he mixing ime was ex ended and
he bes esul s we e ob ained when he pe li e was g ound oge he wi h he ine pa icles. The bes esul s we e
ob ained o samples 4 and 5 in which calcina ion o pe li e wi h wo ypes o sal s was ca ied ou a 700°C. The
calcina ion esul s show ha his me hod could be he easies o implemen on an indus ial scale and also he ends
o imp o emen in he ela i e he mal conduc i i y coe icien a e signi ican .
CONCLUSION
In his pape , a new benchma k me hod o he apid de e mina ion o he he mal conduc i i y coe icien is
p esen ed, which is based on compa ing he su ace empe a u es be ween a known e e ence and an unknown
ma e ial, by measu ing he bo om su ace empe a u e in a hea ing pla e and, on he o he hand, measu ing he
su ace o he ma e ial using a he mal imaging came a. Unde s eady-s a e empe a u e condi ions, he mean
he mal conduc i i y coe icien o he ma e ial unde es can be de e mined ai ly accu a ely and quickly o he
en i e se o samples in a single measu emen . This me hodology was es ed on ou samples o which sui able
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he mal insula ion p ope ies we e de e mined. I is clea om he esul s ha , as expec ed, he use o insula ion wi h
he lowes he mal conduc i i y coe icien alue appea s o be he mos app op ia e in e ms o main aining he
highes hea con en (sensible hea , en halpy), hus ensu ing a slowe empe a u e equilib a ion be ween he s o age
ank and he insula ion, as he p ima y objec i e is o main ain he he mal po en ial o he s o age ank a a usable
alue. The expe imen s ca ied ou show ha he lowes alues we e ob ained o he ma e ial wi h he highes
addi ion o e lec i e ma e ial, whe e he he mal conduc i i y coe icien was educed by 8 %. These esul s a e
e y p omising o he con inua ion o his esea ch.
ACKNOWLEDGMENTS
This pape was c ea ed as pa o he p ojec No. CZ.02.01.01/00/22_008/0004631 Ma e ials and echnologies
o sus ainable de elopmen wi hin he Jan Amos Komensky Ope a ional P og am inanced by he Eu opean Union
and om he s a e budge o he Czech Republic and was suppo ed unde P ojec No. SP2024/025 - Ad anced
ma e ials and echnologies o deca boniza ion.
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