polyme s
A icle
In luence o Ambien Tempe a u e on Radia i e and Con ec i e
Hea Dissipa ion Ra io in Polyme Hea Sinks
Jan Kominek * , Ma in Zacha , Michal Guzej, E ik Ba uli and Pe Ko bacek


Ci a ion: Kominek, J.; Zacha , M.;
Guzej, M.; Ba uli, E.; Ko bacek, P.
In luence o Ambien Tempe a u e on
Radia i e and Con ec i e Hea
Dissipa ion Ra io in Polyme Hea
Sinks. Polyme s 2021,13, 2286.
h ps://doi.o g/10.3390/
polym13142286
Academic Edi o : Ni in Meh a
Recei ed: 16 June 2021
Accep ed: 2 July 2021
Published: 12 July 2021
Publishe ’s No e: MDPI s ays neu al
wi h ega d o ju isdic ional claims in
published maps and ins i u ional a il-
ia ions.
Copy igh : © 2021 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
Hea T ans e and Fluid Flow Labo a o y, Facul y o Mechanical Enginee ing,
B no Uni e si y o Technology (BUT), Technicka 2896, 616 69 B no, Czech Republic; [email p o ec ed] (M.Z.);
[email p o ec ed] (M.G.); [email p o ec ed] (E.B.); Pe [email p o ec ed] (P.K.)
*Co espondence: [email p o ec ed]
Abs ac :
Minia u iza ion o elec onic de ices leads o new hea dissipa ion challenges and adi-
ional cooling me hods need o be eplaced by new be e ones. Polyme hea sinks may, hanks o
hei unique p ope ies, eplace s anda dly used hea sink ma e ials in ce ain applica ions, especially
in applica ions wi h high ambien empe a u e. Polyme s na i ely dispose o high su ace emissi i y
in compa ison wi h glossy me als. This high emissi i y allows a la ge amoun o hea o be dissi-
pa ed o he ambien wi h he ou h powe o i s absolu e su ace empe a u e. This pape shows he
change in adia i e and con ec i e hea ans e om polyme hea sinks used in di e en ambien
empe a u es. Fu he mo e, he obse ed polyme hea sinks ha e di e en ly o ien ed g aphi e ille
caused by hei molding p ocess di e ences, he e o e hei he mal conduc i i y aniso opies and
o e all cooling e iciencies also di e . Fu he mo e, i is also shown ha a high adia i e hea ans e
leads o minimizing hese cooling e iciency di e ences be ween hese polyme hea sinks o he
same geome y. The measu emen s we e conduc ed a HEATLAB, B no Uni e si y o Technology.
Keywo ds:
polyme hea sink; he mal managemen ; he mal conduc i i y; adia ion; con ec-
ion; composi es
1. In oduc ion
Wi h new ad ancemen s in elec onics, especially in hei minia u iza ion, new cooling
challenges need o be me so ha he elec onics’ e iciency and se ice li e would no
dec ease. Polyme s, due o hei easy ab ica ion, low cos and low weigh , a e al eady ind-
ing hei ways in many ac i e cooling applica ions despi e hei low he mal conduc i i y
as polyme hea exchange s in cooling elec onics and also in he au omo i e indus y [
1
–
4
].
Thei amo phous s uc u e esponsible o hei low he mal conduc i i y p e en s hei
usage in passi e cooling applica ions as hea sinks. This disad an age could be elimina ed
i he igh ille s wi h high he mal conduc i i y would be inco po a ed in o he base
polyme ma ix using mode n p oduc ion echniques, hese composi es could be used in
elec onics passi e cooling applica ions whe e hey would b ing wi h hem o he polyme
bene i s [
5
–
11
]. High he mally conduc i e polyme s could be used as hea sinks especially
in applica ions whe e high ambien empe a u e is expec ed.
Mode n polyme blends o e high he mal conduc i i y, bu in compa ison wi h
adi ionally used aluminum and coppe , hei conduc i i y s ill emains low app oxima ely
by en old. Howe e , hey could be used in applica ions whe e he hea ans e ia
conduc ion inside he ma e ial is no es ic ing he o e all hea ans e om he cooled
pa o he ambien , which is ypical in passi e cooling using a hea sink [
4
]. Especially
in applica ions whe e hea ans e om he hea sink by con ec ion is s ic ly limi ed
(enclosed space) o whe e hei na u ally high emissi i y would lead o high hea ans e
ia adia ion (applica ions wi h high ambien empe a u e).
Beha io o polyme hea sinks en iched wi h g aphi e lakes used in ambien wi h
oom empe a u e was s udied in [
12
]. These esul s showed especially he impo ance
Polyme s 2021,13, 2286. h ps://doi.o g/10.3390/polym13142286 h ps://www.mdpi.com/jou nal/polyme s
Polyme s 2021,13, 2286 2 o 12
o he choice o mel en y du ing hei ab ica ion bu did no del e deepe in o he hea
sinks’ e iciency i condi ions would be any di e en om he oom empe a u e and i
na u al con ec ion would be limi ed due o use in enclosed space as is o en he case in
eal applica ions.
As polyme hea sinks ha ha e na u ally high emissi i y hea dissipa ion ia adi-
a ion canno be igno ed, he hea sinks’ design should be subjec ed o his mode o hea
ans e . Impo ance o adia ion on he o e all cooling e iciency was s udied in [
13
–
16
].
Huang, L. e al. in [
14
] s a e ha compa ing high emissi i y coa ing wi h a low emissi i y
one applied o an LED ilamen bulb can educe i s empe a u e by 10%. B a o, R.H. e al.
in [
16
] showed in hei publica ion ha in case o an a ay o elec onic chips moun ed
be ween wo pa allel pla es he he mal adia ion ep esen ed 33% o he o al hea ans e .
This pape shows how hea dissipa ion om a polyme hea sink changes when sub-
jec ed o di e en ambien empe a u es. Change o ai p ope ies wi h ising empe a u e
by ens o deg ees is minimal; he e o e, he hea ans e coe icien by con ec ion s ays
almos he same. Hence, using a me al hea sink wi h glossy su ace in an ambien whe e
he empe a u e should ise would lead o ise o he en i e cooling sys em by he same
ma gin. Howe e , i a hea sink wi h high su ace emissi i y is applied, his inc ease in
ambien empe a u e can lead o signi ican ise o hea dissipa ion ia adia ion, he e o e
be e cooling e iciency.
2. Ma e ials and Me hods
2.1. Geome y o Tes ed Hea Sinks
The es ed hea sinks had dimensions (58
×
40
×
106) mm wi h 9 ins (de ails a e
shown in Figu e 1). Fo he s udy’s pu pose he chosen design was simplis ic o allow an
easy way o calcula e dissipa ed hea h ough he hea sinks’ ins acco ding o [
17
]. Hea
sinks we e p oduced om Polyamide 66 as he ma ix ma e ial wi h g aphi e lakes as
he main ille ha ensu ed he high he mal conduc i i y. This blend is comme cially
a ailable and was p oduced by A ien (P ague, Czech Republic). The he mal conduc i i y
o his ma e ial anged om 5 o 20 W/m
·
K depending on he ille o ien a ion, densi y
1640 kg/m
3
. The hea capaci y is unknown (no essen ial because he da a p esen ed in his
pape is o he he mal s eady s a e). All he alues we e aken om he o icial da a shee .
Figu e 1. Geome y o es ed hea sinks (dimensions a e in mm).
To compa e he in luence o he mel low, wo polyme hea sinks o he same geome-
y we e used in he measu emen . The di e ence be ween he wo hea sinks was in he
mel en y poin du ing p oduc ion. One hea sink was p oduced wi h he mel en y along
he hea sink’s longe base’s edge so he mel would low in pa allel wi h he hea sink’s
ins and he o he had he mel en y on he sho e base’s edge pe pendicula o he hea
sink’s ins. En y poin s o bo h measu ed hea sinks a e shown in Figu e 2.
Polyme s 2021,13, 2286 3 o 12
Figu e 2.
Mel en ance along sinks’ edge ( ed), di ec ion o mel low depic ed by g een a ow.
Le —edge o longe base’s side (mel low pa allel o he ins), igh —edge o sho e base’s side
(mel low pe pendicula o he ins).
Fu he mo e, an aluminum hea sink o he same geome y was also compa ed wi h
he wo polyme hea sinks. The aluminum hea sink had he mal conduc i i y 130 W/m
·
K
and a low su ace emissi i y. One o he measu ed polyme hea sinks wi h high emissi i y
and he aluminum hea sink wi h low emissi i y a e shown in Figu e 3.
Figu e 3. Measu ed polyme (le ) and aluminum ( igh ) hea sinks side by side.
The esul s om he cooling e iciency we e used o demons a e he impo ance o
he su ace emissi i y in applica ion wi h highe ambien empe a u es.
2.2. Measu emen Desc ip ion
The measu ed polyme hea sinks we e si ua ed inside a measu emen box, which was
placed inside a he mos a ic chambe Binde MK 720 (manu ac u e Binde , H adec K alo e,
Czech Republic) du ing he conduc ed measu emen s. The box wi h one o he measu ed
hea sinks inside he he mos a ic chambe is shown in Figu e 4. The box’s holde s ouched
he hea sinks only in ou poin s o ensu e minimal hea conduc ion away om he hea
sinks and in o he box i sel . The he mos a ic chambe se ed as he sou ce o he desi ed
ambien empe a u e and he box p o ec ed he hea sinks om any unwan ed o ced
con ec ion c ea ed by he chambe ’s ans. The box’s on doo also se ed as a placemen
o he FLIR E5 he mog aphic came a.
The hea leading o he hea sink was gene a ed wi h a esis ance hea e . The con ac
su ace a ea be ween he hea sink and he hea e was 35
×
40 mm. The placemen o he
hea e on he hea sink’s base is shown in Figu e 5. A he mally conduc i e pas e wi h a
he mal conduc i i y o 4.2 W/m
·
K was applied be ween he hea sou ce and he hea sink
base. This pas e ensu ed a good he mal con ac , which was he same o e e y expe imen .
Polyme s 2021,13, 2286 4 o 12
Figu e 4.
Hea sink placemen inside he measu emen box (le ), measu emen box inside he he mos a ic chambe wi h
a ached he mal imaging came a (middle), de ail o he measu emen box ( igh ).
Figu e 5. Hea e placed in he middle o he hea sink’s base (dimensions a e in mm).
The hea ou pu o he hea e was se o 15 W wi h a p ecision o
±
0.1 W. I was u he
con olled wi h a LabView p og am o ensu e he same amoun o hea was gene a ed
ega dless o he hea e ’s esis ance change caused by inc ease o i s empe a u e. E e y
measu emen was epea ed wi h de aching and ea aching he hea e . The measu emen s’
esul s we e compa ed o elimina e he possibili y o he bad con ac be ween he hea e
and he hea sink leading o he measu emen e o .
Bo h measu ed polyme hea sinks we e measu ed in wo posi ions as in [
12
]. The
posi ions we e named ‘de aul ’ and ‘upside-down’. This led o change o he ille o ien a-
ion in ela ion o g a i y and he e o e buoyancy in case o he polyme hea sink wi h he
mel en y poin pa allel o he ins, which as was shown in [
12
] led o di e en cooling
e iciencies. Change o he mel low di ec ion in ega d o g a i y is shown in Figu e 6.
Polyme s 2021,13, 2286 5 o 12
Figu e 6.
O ien a ion o he mel en y o bo h measu ed hea sinks in wo di e en measu emen
posi ions, le —de aul posi ion, igh —‘upside-down’. Mel en ance along he ed edge, mel low
in he di ec ion o he g een a ow. (
A
) hea sink wi h mel en ance along he longe base’s edge
(pa allel o ins)—de aul posi ion, (
B
) hea sink wi h mel en ance along he longe base’s edge
(pa allel o ins)—upside-down posi ion, (
C
) hea sink wi h mel en ance along he sho e base’s
edge (pe pendicula o ins)—de aul posi ion, (
D
) hea sink wi h mel en ance along he sho e
base’s edge (pe pendicula o ins)—upside-down posi ion.
3. Measu emen Unce ain y Analysis
To ensu e maximal measu emen p ecision and o minimize all he possible e o s he
ollowing measu es we e aken.
The used he mocouple was calib a ed o di e en ambien empe a u es beyond i s
s anda d measu emen p ecision o
±
2.2
◦
C. I s new maximum de ia ion was se o only
±0.2 ◦C.
When a s eady s a e o he measu emen s was achie ed a he mal came a FLIR E5
wi h measu emen p ecision o
±
2
◦
C and wi h esolu ion o 120
×
90 pixels was used
o u he analyze he empe a u e ield on he hea sinks’ ins. To u he inc ease i s
p ecision ano he ype K he mocouple calib a ed he same way as he p e ious one was
placed in he back wall inside an a ea which was seen in all he measu emen s. As his wall
was dyed wi h a g aphi e sp ay o known emissi i y he he mal image y esul s could
be u he adjus ed by compa ing i s alues inside he a ea whe e he he mocouple was
si ua ed. This a ea is shown in Figu e 7.
To ensu e he ambien empe a u e was as close o i s desi ed alue, wo esis ance
he mome e s PT100 we e placed a he bo om o he measu emen box which se ed
as he inle once he ai low induced by he na u al con ec ion was s abilized. These
he mome e s measu ed wi h he measu emen e o o ±0.2 ◦C.

Polyme s 2021,13, 2286 6 o 12
Figu e 7.
The mog am wi h an indica ed a ea whe e he he mocouple o he e i ica ion o he
co ec measu ed empe a u e ia he mal image y was placed.
4. Resul s
All he con igu a ions we e measu ed mul iple imes (as desc ibed in Sec ion 2.2) wi h
good epea abili y. The da a p esen ed was gene a ed by a e aging he esul s o each
measu ed con igu a ion.
4.1. Tempe a u e Compa ison
Bo h compa ed polyme hea sinks we e measu ed wi h 15 W he mal inpu powe
o he hea e in wo posi ions as desc ibed in Sec ion 2.2. The ambien empe a u e was
main ained a 50 ◦C. The empe a u es o he hea e a e shown in Table 1.
Table 1.
Hea e empe a u e in all polyme hea sinks conduc ed measu emen s o ambien empe -
a u e 50 ◦C. The le e s in pa en heses e e o posi ions acco ding o Figu e 6.
De aul Posi ion
(◦C)
Upside-Down
(◦C)
Posi ion Di e ence
(◦C)
Mel en ance along he
longe base’s edge (pa allel
o ins)
99.0 (A) 97.1 (B) 1.9 (A)-(B)
Mel en ance along he
sho e base’s edge
(pe pendicula o ins)
100.3 (C) 100.5 (D) 0.2 (D)-(C)
Mel En y Di e ence (◦C) 1.5 (C)-(A) 3.4 (D)-(B)
These esul s can be compa ed wi h he esul s om measu emen o ambien em-
pe a u e 20 ◦C. These esul s a e shown in Table 2.
By compa ing hese esul s, i can be concluded ha wi h highe ambien empe a u e
he impo ance o he mel en y poin in o he mold diminishes and he same s ands o
he impo ance o he hea sink’s posi ion i he mel en y poin is pa allel o ins. Going
om ambien empe a u e 20
◦
C o 50
◦
C dec eased he hea e ’s empe a u e be ween he
bes and he wo s hea sinks’ pe o mances by 49.3% om 6.7
◦
C o only 3.4
◦
C. In case
o e iciency change o he hea sink wi h mel en e ing along he base’s longe edge he
hea e ’s empe a u e di e ence d opped by 25% om 2.8 ◦C o 1.9 ◦C.
Polyme s 2021,13, 2286 7 o 12
Table 2.
Hea e empe a u e in all polyme hea sinks conduc ed measu emen s o ambien empe -
a u e 20 ◦C [12]. The le e s in pa en heses e e o posi ions acco ding o Figu e 6.
De aul Posi ion
(◦C)
Upside-Down
(◦C)
Posi ion Di e ence
(◦C)
Mel en ance along he
longe base’s edge (pa allel
o ins)
72.3 (A) 69.5 (B) 2.8 (A)-(B)
Mel en ance along he
sho e base’s edge
(pe pendicula o ins)
76.1 (C) 76.2 (D) 0.1 (D)-(C)
Mel En y Di e ence (◦C) 3.9 (C)-(A) 6.7 (D)-(B)
4.2. Con ec ion-Radia ion Hea T ans e Compa ison
F om he p e iously shown esul s i is isible ha he di e ence be ween cooling
e iciencies o he measu ed hea sinks is signi ican ly lowe o he ambien empe a u e
50
◦
C compa ed o he esul s o he ambien empe a u e 20
◦
C. This phenomenon shows
ha he means o hea dissipa ion om he hea sinks is signi ican ly di e en . The a io
be ween he dissipa ion ia con ec ion and adia ion mus change i he hea sinks ha e an
o e all highe empe a u e as he adia ion hea ans e ises wi h he ou h powe o he
su ace’s absolu e empe a u e.
To p o e his change in hea ans e means om he hea sinks o he ambien he
same app oach o he e iciency compa ison as in [
12
] was used. The equa ions used in
his app oach a e o be ound in [
17
] and i analyses he amoun o dissipa ed hea ia hea
sink’s ins.
Fi s ly, he empe a u e ield on he hea sinks’ ins is measu ed wi h he mal image y
and he empe a u e di e ence be ween he hea sinks’ ins empe a u e and ambien
is calcula ed.
∆Tij =T in,ij −Tambien . (1)
The index
i
e e s o he in numbe and
j
o he su ace
Sj
. To calcula e hea ans e
by con ec ion Rayleigh numbe is de e mined.
Raij =
g·βai ·∆Tij ·L3
j
νai ·αai
, (2)
whe e
g
is g a i a ional accele a ion,
βai
is he mal expansion coe icien o he ambien
ai ,
νai
is kinema ic iscosi y o he ambien ai ,
αai
is he mal di usi i y o he ambien ai
and
Lj
is cha ac e is ic dimension o he su ace
Sj
(
L1
,
L2
,
L3
— in leng h,
L4
,
L5
—su ace
a ea di ided by i s pe ime e ). The ai p ope ies used o he calcula ion a e de e mined
om so called ilm empe a u e on he ins.
T ilm,ij =T in,ij +Tambien
2. (3)
Nex , con ec i e hea ans e is calcula ed as a unc ion o Rayleigh numbe , ambien
ai ’s he mal conduc i i y and cha ac e is ic dimension.
hcon ,ij = jRaij,Lj,kai , (4)
whe e
kai
is ambien ai ’s he mal conduc i i y a he ilm empe a u e. The adia i e
hea ans e was calcula ed using he known su ace emissi i y and S e an–Bol zmann
cons an .
h ad,ij =εσT in,ij +Tambien ·T2
in,ij +T2
ambien , (5)
whe e he su ace emissi i y εwas se o 0.95 and σis S e an–Bol zmann cons an .
Polyme s 2021,13, 2286 8 o 12
Fo he ins’ su ace ha adia ed hea be ween hemsel es a iew ac o was calcu-
la ed. Figu e 8shows he su aces whe e he iew ac o was conside ed (blue) and whe e i
was no ( ed). The ou e su aces wi hou aking iew ac o in o accoun o med oge he
an a ea o 18,963 mm
2
and he in e nal su aces whe e he iew ac o was conside ed
c ea ed oge he an a ea o 23,331 mm
2
, which is 55.2% o he en i e su ace. This means
ha less han a hal o he hea sink’s su ace can adia e hea away eely.
Figu e 8.
Hea sinks’ su aces wi hou aking iew ac o in o accoun ( ed) and wi h aking iew
ac o in o accoun (blue).
The inal indi idual hea lows om ins Qiwe e calcula ed:
Qi=∑
j
Qij,Qij =hcon ,ij +h∗
ad,ij·Aj·∆Tij, (6)
whe e
h
is hea ans e coe icien , he index
i
e e s o he in numbe and
j
e e s o
indi idual su ace a eas o ins Aj.
Table 3shows calcula ed hea lows om ins o he hea sink made wi h he mel low
pa allel o i s ins o he measu ed hea sinks in bo h 20
◦
C and 50
◦
C ambien empe a u es
and di e ences be ween hem.
Table 3.
Calcula ed hea ans e s om ins o he polyme hea sink wi h mel low pa allel o i s
ins o bo h 20
◦
C and 50
◦
C ambien empe a u es. The le e s in pa en heses e e o posi ions
acco ding o Figu e 6.
Hea Sink Mel En e ing Pa allelly o
Fins (De aul Posi ion) (A)
Mel En e ing Pa allelly o Fins
(Upside-Down Posi ion) (B)
Ambien empe a u e (◦C) 20 50 20 50
Con ec i e hea low (W) 7.7 6.8 7.6 6.9
Radia i e hea low (W) 3.2 3.8 3.1 3.9
To al hea low (W) 10.9 10.5 10.8 10.7
Addi ionally, Table 4shows calcula ed hea lows om ins o he hea sink made wi h
he mel low pe pendicula o i s ins o he measu ed hea sinks in bo h 20
◦
C and 50
◦
C
ambien empe a u es and di e ences be ween hem.
Polyme s 2021,13, 2286 9 o 12
Table 4.
Calcula ed hea ans e s om ins o he polyme hea sink wi h mel low pe pendicula o
i s ins o bo h 20
◦
C and 50
◦
C ambien empe a u es. The le e s in pa en heses e e o posi ions
acco ding o Figu e 6.
Hea Sink Mel En e ing Pe pendicula ly
o Fins (De aul Posi ion) (C)
Mel En e ing Pe pendicula ly o
Fins (Upside-Down Posi ion) (D)
Ambien empe a u e
(◦C) 20 50 20 50
Con ec i e hea low
(W) 7.2 6.1 7.2 6.0
Radia i e hea low
(W) 2.9 3.4 3.0 3.4
To al hea low (W) 10.1 9.5 10.2 9.4
F om hese esul s i is ob ious ha hea ans e by adia ion g ows signi ican ly
wi h highe ambien empe a u e. As he same amoun o powe is gene a ed inside he
hea e and he adia i e hea ans e g ows, he hea ans e ia con ec ion mus d op.
Calcula ed hea ans e om hea sinks’ ins also shows d op in he o e all hea ans e
and especially o he case o he hea sink p oduced wi h mel low pe pendicula o i s
ins. As he hea sink’s base is he wa mes pa , he amoun o hea adia ed away o
he ambien ises he e he mos , hence he o al amoun o hea ans e ed away om
ins d ops.
4.3. Con ec ion-Radia ion Hea T ans e Compa ison
The same ype o measu emen was done o an aluminum hea sink o he same
geome y. The hea e was a ached o he aluminum hea sink wi h inpu powe o 15 W
and he sou ce’s empe a u e was measu ed in bo h condi ions wi h ambien empe a u e
20
◦
C and 50
◦
C. Table 5shows how he hea e ‘s empe a u e changed be ween he wo
measu emen condi ions o he aluminum hea sink and bo h polyme hea sinks.
Table 5.
Hea e ‘s empe a u e change wi h change o he ambien empe a u e on di e en measu ed
hea sinks. The le e s in pa en heses e e o posi ions acco ding o Figu e 6. The da a o he ambien
empe a u e 20 ◦C a e om [12].
Hea Sink
Hea e Tempe a u e
o Ambien
Tempe a u e 20 ◦C
(◦C)
Hea e Tempe a u e
o Ambien
Tempe a u e 50 ◦C
(◦C)
Di e ence
(◦C)
Aluminum 65.7 95.6 29.9
Polyme made wi h mel low
along ins (B) 69.5 97.1 27.6
Polyme made wi h mel low
pe pendicula o ins (D) 76.1 100.3 24.2
In case o he aluminum hea sink, he hea e ’s empe a u e ose by 29.9
◦
C wi h he
ambien empe a u e change o 30
◦
C. In case o he polyme hea sink p oduced wi h
he mel low pa allel o i s ins and posi ioned in he mos sui able posi ion o induced
na u al con ec ion he hea e ’s empe a u e inc emen o he same ambien empe a u e
change was 27.6
◦
C. This p o es ha he amoun o hea adia ed away hanks o i s high
emissi i y ises wi h inc easing he ambien empe a u e. This phenomenon is especially
isible in case o he hea sink p oduced wi h mel low pe pendicula o i s ins whe e
he hea e ’s empe a u e ose only by 24.2
◦
C. This is caused by hea sink’s unideal hea
conduc i i y o i s ins; he e o e, i s o e hea ed base adia es away e en highe amoun
o hea .