polyme s
A icle
Sel -Hea ing Mould o Composi e Manu ac u ing
And ii Kond a ie 1, Václa Píš ˇek 2, S i lana Pu hina 3, Ma yna She so a 3, Anna Fomina 4
and Pa el Kuˇce a 2,*


Ci a ion: Kond a ie , A.; Píš ˇek, V.;
Pu hina, S.; She so a, M.; Fomina,
A.; Kuˇce a, P. Sel -Hea ing Mould o
Composi e Manu ac u ing. Polyme s
2021,13, 3074. h ps://doi.o g/
10.3390/polym13183074
Academic Edi o : Emin Bay ak a
Recei ed: 31 Augus 2021
Accep ed: 9 Sep embe 2021
Published: 12 Sep embe 2021
Publishe ’s No e: MDPI s ays neu al
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4.0/).
1
Depa men o Building Technology and Cons uc ion Ma e ials, O.M. Beke o Na ional Uni e si y o U ban
Economy in Kha ki , Ma shal Bazhano S . 17, 61002 Kha ki , Uk aine; [email p o ec ed]
2Ins i u e o Au omo i e Enginee ing, B no Uni e si y o Technology, Technická2896/2,
616 69 B no, Czech Republic; [email p o ec ed].cz
3Depa men o Composi e S uc u es and A ia ion Ma e ials, Na ional Ae ospace Uni e si y “Kha ki
A ia ion Ins i u e”, Chkalo a S . 17, 61070 Kha ki , Uk aine; s.pu [email p o ec ed] (S.P.);
[email p o ec ed] (M.S.)
4
Depa men o Railway, Au omobile T anspo and Handling Machines, Ins i u e o T anspo and Logis ics,
Volodymy Dahl Eas Uk ainian Na ional Uni e si y, Cen al A enue 59a, 93400 Sewe odone sk, Uk aine;
[email p o ec ed]
*Co espondence: [email p o ec ed].cz; Tel.: +420-541-142-274
Abs ac :
The shipbuilding indus y, engine manu ac u ing, a ia ion, ocke and space echnology a e
p omising ields o applica ion o polyme ic composi e ma e ials. Shape-gene a ing moulding ools
wi h in e nal hea ing a e used o he c ea ion o a mo e economically iable me hod o moulding
o in e nally hea ed composi e s uc u es. The use o a ine- ibe ed esis i e s uc u e in he hea ed
ools allows implemen a ion o e ec i e hea ing o he composi e and elimina ion o he need o
expensi e and ene gy-in ensi e hea ing equipmen . The aim o his pape was he educ ion o
ene gy consump ion o in e nally hea ed moulding ools by choosing he op imal pa ame e s o
hei esis i e laye . A me hod o de e mina ion o he pa ame e s o he moulding ool esis i e laye
was de eloped. This me hod allows calcula ion o he hea ing laye pa ame e s and implemen a ion
o he speci ied ime– empe a u e egime o moulding o he composi e s uc u e. I was shown ha
ene gy sa ing o he hea ed ibe glass shape-gene a ing moulding ools was om 40 o 60%. I was
ound ha he inc ease in he hickness o he moulded package o he polyme ic composi e ma e ial
esul ed no only in a highe supplied powe o he hea ing sys em, bu also in a complica ion
o he me hod o sys em con ol, because o he g owing exo he mic e ec o he binde cu ing
eac ion. Fo composi e p oduc s based on Hysol EA 9396 binde , hicknesses mo e han 4 mm a e
c i ical, because i is no possible o cope wi h he sel -hea ing e ec only by cooling wi h ambien ai
al eady u ilized a he wen ie h minu e o he moulding p ocess. The in luence o he physical and
mechanical cha ac e is ics o he moulding ool ma e ial and s i ening ibs was analysed in e ms o
ene gy consump ion and con ollabili y o he hea ing sys em. Fibe glass shows he lowes ene gy
consump ion. Hea ing o he aluminium and s eel moulding ools o he same pu pose will equi e
20% and 45% mo e powe , espec i ely. An inc ease in he numbe o s i ening ibs has a s ong
e ec on he hea emo al o he hea ing sys em. Wi h a small numbe o aluminium ibs i is no
possible o main ain he speci ied empe a u e– ime egime o a ibe glass moulded package o 5 mm
hick wi h he use o he equipmen . Howe e , when he numbe o s i ene s is inc eased o 10, he
exo he mic e ec o he eac ion becomes smoo he and hen he hea ing equipmen can cope wi h
he ask. An expe imen al p o o ype o hea ing equipmen o moulding ools o he manu ac u ing
o s uc u es o polyme ic composi e ma e ials, as well as a lexible he mal blanke o epai o
non-sepa able s uc u es, we e de eloped. The esul s can be he basis o a new me hod o op imal
design o pa ame e s o moulding ool s uc u e a minimal hea emo al o he en i onmen .
Keywo ds:
esis i e elemen ; in e nal hea ing; exo he mic e ec ; hea ing sys em powe ; laying pi ch;
he mal blanke
Polyme s 2021,13, 3074. h ps://doi.o g/10.3390/polym13183074 h ps://www.mdpi.com/jou nal/polyme s
Polyme s 2021,13, 3074 2 o 18
1. In oduc ion
A he p esen ime, composi e ma e ials based on ul a hin ca bon, glass, o ganic and
o he ypes o ib es in combina ion wi h polyme ic binde s a e widely used in a ious
b anches o echnology [
1
–
4
], such as gene al cons uc ion, b idge enginee ing, oad
in as uc u e, anspo , ag icul u al machine y, he powe sec o , biomedicine, and pe o-
chemis y [
5
–
10
]. The shipbuilding indus y, engine manu ac u ing, a ia ion, ocke and
space echnology a e he mos p omising ields o applica ion o polyme ic composi e
ma e ials [
11
,
12
]. High speci ic s eng h and s i ness, as well as a numbe o o he unique
p ope ies o he composi es, which allow he implemen a ion o special quali ies in he
s uc u e, a e in demand in hese ields [13,14].
One o he mos a ional me hods o epai o ypical ope a ional de ec s (c acks,
pene a ion de ec s o skin, delamina ions) in me al and composi e panel cons uc ions
is he ins alla ion o pa ches made o polyme ic composi e ma e ials [
15
,
16
]. The high
physical and mechanical p ope ies o he composi es and he signi ican ad an ages o
he adhesi e join s o e mechanical ones, de e mine he success ul use o pa ches made
o polyme ic composi e ma e ials o he epai o bo h polyme ic and me al s uc u es o
a ious applica ions [
17
–
19
]. Because he need o epai o s uc u es in he u u e will
con inue o g ow, inc ease in he e iciency o epai p ocesses is no less impo an han
imp o emen o he me hods o designing o new s uc u es [20–22].
Moulding o p oduc s o polyme ic composi e ma e ials is pe o med, as a ule, wi h
he use o hea e s ( u naces o au ocla es) [
23
]. The e iciency o any hea ing me hod is
de e mined by he a io o p oduced and ans e ed hea , he e o e he in oduc ion o
con ac hea e s in he manu ac u ing o composi es is an u gen ask [
24
]. I allows educ ion
o he ime and cos s o he p oduc ion o composi e s uc u es. Now he e a e se e al a eas
in he de elopmen o hea ing equipmen , which p o ide educed ene gy consump ion
in he p ocess o c ea ion and econdi ioning epai o composi e s uc u es. In o de o
implemen new me hods o composi e s uc u e moulding, binde composi ions cu ed by
ul a iole adia ion o ano he ype o adia ion ha e been de eloped, as well as hea ing
complexes whe e he shaping su ace o he ools is an in eg a ed pa [
25
]. Howe e , such
complexes a e cha ac e ized, apa om high cos , by he g ea complexi y o p oduc ion,
ope a ion, and main enance; he e o e, hey do no ind wide indus ial applica ion.
Fo he c ea ion o a mo e economically iable me hod o moulding o composi e
s uc u es, hea ed moulding ools a e de eloped, o which he hea is supplied by con-
ec i e o con ac hea ans e . The use o esis i e blocks in he hea ed ools allows
implemen a ion o e icien hea ing o he polyme ic composi e ma e ials wi hou signi i-
can changes o he ool design [
26
]. The hea ing uni s can be manu ac u ed on he basis
o he ine- ibe ed esis i e s uc u e o pla es/small co es. The main disad an age o
pla es and uni s wi h a co e is he gap occu ing in he p ocess o uni ins alla ion; he
esul ing empe a u e di e ence can be compensa ed only by a su icien hickness o he
shaping su ace o he ool. Resis i e blocks based on ine- ibe ed esis i e s uc u es a e
he only uni s, which allow implemen a ion o he uni o mi y o he empe a u e ield on
he shaping su ace, when he esis i e blocks a e ins alled wi h a gap equal o he pi ch o
he laying o he esis i e h ead [27].
Au ho s o he pape [
28
] p opose a cu e o he binde by applying an elec ic cu en
o he ca bon ib e composi e pa . I was shown ha he elec ical conduc i i y o ca bon
ib e allows indi idual ib es o ac as hea ing elemen s. As a esul , he e is a la ge numbe
o in e nal hea ing elemen s h oughou he composi e pa . The deg ee o cu ing was
compa ed o composi es cu ed in he adi ional way. The h ee-poin bending es was
used o de e mine he lexu al s eng h and modulus o elas ici y. The esul s showed ha
he p oposed echnology p o ided polyme ic composi e ma e ial pa ame e s on a le el
wi h au ocla e p oduc ion.
A me hod o di ec esis i e hea ing o he composi e wo kpiece o cu ing was
p oposed in [29]. The hea p oblem was sol ed nume ically by he ini e elemen me hod.
In his case, he hea conduc ion equa ion and kine ics o he binde cu ing eac ion in
Polyme s 2021,13, 3074 3 o 18
he composi e wo kpiece we e modelled. Since he esis i i y o ma e ials is empe a u e
dependen , a sys em wi h nonlinea ela ionship was de eloped. Compa ison o he
ob ained esul s wi h expe imen al da a showed sa is ac o y epea abili y.
The pape [
30
] deals wi h he s udy o he me hod o sel - esis i e elec ic hea ing o
he apid moulding o pa s o ca bon ib e ein o ced plas ic. Fo he gene a ion o hea
and di ec cu ing o he binde , he use o he elec ic cu en passing h ough he ca bon
ib e was p oposed. A sel - esis i e ool wi h an au oma ic empe a u e con olle was
de eloped. The pape p esen s he esul s o expe imen s on he moulding o composi e
pa s wi h he use o he de eloped equipmen . The deg ee o cu ing o a ious specimens
was cha ac e ized, and hei c oss-sec ional geome y and po osi y e alua ed. On he
basis o he expe imen al esul s, he beha iou o he hea ans e o a ious p ocesses
was analysed.
To educe he au ocla e cos s, he use o a sel -hea ing composi e mould made o
ca bon ib e composi e was p oposed in [
31
]. I was sugges ed o use he ein o ced ca bon
ib e composi e shaping su ace as he hea ing elemen s. The pape shows ha due o he e y
low coe icien o he mal expansion o ca bon ib e composi e, his ma e ial is an excellen
choice o he manu ac u ing o such moulds. The p edic ed uni o mi y o he empe a u e
ield was con i med expe imen ally using he mocouples and an in a ed came a.
A sel -hea ing composi e ool wi h buil -in esis i e laye was de eloped in [
32
]. I was
shown ha his laye e enly dis ibu es he hea in close p oximi y o he su aces o he
pa while ensu ing a high le el o mechanical cha ac e is ics o he polyme ic composi e
ma e ials. Fini e elemen modelling o hea ans e con i med ha he ool con igu a ion
and selec ed hea ing elemen s p o ide su icien hea uni o mi y o achie e he desi ed
binde cu ing. Ne e heless, he pape indica es he necessi y o sol e he p oblem o
choosing he op imal posi ion o he esis i e laye , as well as u he es ing o e i y and
calib a e he sys em o ob ain he he op imal deg ee o binde cu ing.
The me hod o calcula ion o he hea ed ools p o iding igidi y and se ice li e, wi h
he hea ing laye based on he esis i e blocks, was p oposed in [
33
]. The pa ame e s o
he hea ing sys em (ma e ial o he hea ing elemen s, hei geome y, and ma e ial o he
insula ing sys em) and he diag am o i s connec ion we e de e mined om he condi ion
o secu ing he equi ed hea ing mode. The hea ing was con olled by changing he cu en
s eng h du ing he p ocess, de e mined om he solu ion o he hea conduc ion p oblem,
aking in o accoun he exo he mic e ec o he cu ing eac ion and condi ions o hea
ans e on he su ace.
The he modynamic model o uns eady hea ans e du ing moulding o he poly-
me ic composi e ma e ial in hea ed ools was de eloped in [
34
]. The model allowed he
empe a u e dis ibu ion o e he hickness o he sys em unde s udy o be ob ained, he
in luence o he exo he mic e ec o he binde cu ing eac ion o be e alua ed, and he
equi ed powe o he hea ing sys em o be de e mined. The disad an age o his pape is
he assump ion ha he model does no ake in o accoun he ibbing o he lowe su ace
o he moulding ools.
As shown om he e iew and analysis o he p oblem, he possibili y o ou -o -
au ocla e p oduc ion o he composi e pa s wi h he use o moulding ools wi h in e nal
hea ing has now been subs an ia ed. I elimina es he need o he expensi e and ene gy-
in ensi e hea ing equipmen . Fo he imp o emen o he p ep oduc ion ac i i y h ough
a easonable choice o he design o he moulding ools, i is necessa y o de elop an
in eg a ed solu ion, which allows educing cos s and sho ening he p oduc ion cycle.
The e o e, he aim o he pape was o educe ene gy consump ion o in e nally hea ed
moulding ools by choosing he op imal pa ame e s o he esis i e laye .
To achie e his pu pose, i was necessa y o sol e he asks below:
1.
De elopmen o he me hod o de e mina ion o he pa ame e s o he esis i e laye
o moulding ools, which would allow he hea ing laye pa ame e s o be calcula ed
and he speci ied ime- empe a u e egime o moulding o he composi e s uc u es
o be implemen ed;
Polyme s 2021,13, 3074 4 o 18
2.
Cons uc ion o a he modynamic model o uns eady hea ans e o he sys em
“shaping he su ace-polyme ic composi e ma e ial”;
3.
De elopmen o an expe imen al p o o ype o hea ing equipmen o moulding ools
o he manu ac u e o s uc u es o polyme ic composi e ma e ials.
2. Ma e ials and Me hods
The analy ical solu ion o asks was ca ied ou using heo e ical s udies in he ield o
he modynamics, he heo y o he moelas ici y o lamina ed pla es, elec ical enginee ing,
as well as expe imen al esea ch unde labo a o y condi ions wi h he use o s anda d
equipmen , ins umen s, o de ices.
Nume ical alida ion o he de eloped me hod was ca ied ou on he example o
moulding equipmen o he o ma ion o package based on ibe glass and Hysol EA 9396
(P oduce : Henkel AG & Co. KGaA) binde wi h he esis i e elemen made o ca bon.
The expe imen al p o o ypes o he hea ing equipmen o he moulding ools and he
lexible he mal blanke we e made om ibe glass wi h he use o epoxy low- empe a u e
binde wi h he esis i e elemen made o ca bon.
The dis ibu ion o empe a u e on he su ace o he hea ed shape-gene a ing mould-
ing ools was ob ained by means o The mal Image Fluke Ti20 (Fluke Eu ope B.V., P.O.
Box 1186, 5602 BD Eindho en, The Ne he lands).
3. Theo e ical Backg ound
A moulding ool is a shaping su ace, which is suppo ed by a ame (Figu e 1).
Polyme s 2021, 13, x FOR PEER REVIEW 4 o 18
and he speci ied ime- empe a u e egime o moulding o he composi e s uc u es
o be implemen ed;
2. Cons uc ion o a he modynamic model o uns eady hea ans e o he sys em
“shaping he su ace-polyme ic composi e ma e ial”;
3. De elopmen o an expe imen al p o o ype o hea ing equipmen o moulding ools
o he manu ac u e o s uc u es o polyme ic composi e ma e ials.
2. Ma e ials and Me hods
The analy ical solu ion o asks was ca ied ou using heo e ical s udies in he ield
o he modynamics, he heo y o he moelas ici y o lamina ed pla es, elec ical enginee -
ing, as well as expe imen al esea ch unde labo a o y condi ions wi h he use o s anda d
equipmen , ins umen s, o de ices.
Nume ical alida ion o he de eloped me hod was ca ied ou on he example o
moulding equipmen o he o ma ion o package based on ibe glass and Hysol ЕА 9396
(P oduce : Henkel AG & Co. KGaA) binde wi h he esis i e elemen made o ca bon.
The expe imen al p o o ypes o he hea ing equipmen o he moulding ools and he
lexible he mal blanke we e made om ibe glass wi h he use o epoxy low- empe a u e
binde wi h he esis i e elemen made o ca bon.
The dis ibu ion o empe a u e on he su ace o he hea ed shape-gene a ing
moulding ools was ob ained by means o The mal Image Fluke Ti20 (Fluke Eu ope B.V.,
P.O. Box 1186, 5602 BD Eindho en, The Ne he lands).
3. Theo e ical Backg ound
A moulding ool is a shaping su ace, which is suppo ed by a ame (Figu e 1).
Figu e 1. Moulding ool wi h he esis i e laye , 1—shaping su ace, 2— esis i e blocks, 3—cu en -
ca ying wi es, 4—moun ing posi ion, 5— ame, 6— esis i e laye .
De e mina ion o he empe a u e pa e n o such a sys em is based on sol ing he
hea conduc ion p oblem o a mul ilaye wall, as well as a ibbed su ace [33]. To assess
he impac o he sys em unde s udy on en i onmen al pa ame e s, o ice e sa, a
me hod o he modynamic esea ch is used. I consis s in acking he he modynamic
changes when he sys em is isola ed om he en i onmen [34].
We used he ma hema ical model o uns eady hea ans e [34] o he la s i ened
moulding ool wi h an a ea o wo king zone o a × b and he moulded package o poly-
me ic composi e ma e ial laid on i . The s i ening ibs o he moulding ool we e made o
me al and a e loca ed pe pendicula o he la ge side a; he shaping su ace was made o
he composi e. The sys em unde s udy consis ed o i e laye s: he lowe laye o he
he mal ix u e, he esis i e laye wi h in e nal hea sou ces, he uppe laye o he he -
mal ix u e, he moulded package o polyme ic composi e ma e ial, and he auxilia y laye
(Figu e 2).
Figu e 1.
Moulding ool wi h he esis i e laye , 1—shaping su ace, 2— esis i e blocks, 3—cu en -
ca ying wi es, 4—moun ing posi ion, 5— ame, 6— esis i e laye .
De e mina ion o he empe a u e pa e n o such a sys em is based on sol ing he hea
conduc ion p oblem o a mul ilaye wall, as well as a ibbed su ace [
33
]. To assess he
impac o he sys em unde s udy on en i onmen al pa ame e s, o ice e sa, a me hod o
he modynamic esea ch is used. I consis s in acking he he modynamic changes when
he sys em is isola ed om he en i onmen [34].
We used he ma hema ical model o uns eady hea ans e [
34
] o he la s i ened
moulding ool wi h an a ea o wo king zone o a
×
band he moulded package o polyme ic
composi e ma e ial laid on i . The s i ening ibs o he moulding ool we e made o me al
and a e loca ed pe pendicula o he la ge side a; he shaping su ace was made o he
composi e. The sys em unde s udy consis ed o i e laye s: he lowe laye o he he mal
ix u e, he esis i e laye wi h in e nal hea sou ces, he uppe laye o he he mal ix u e,
he moulded package o polyme ic composi e ma e ial, and he auxilia y laye (Figu e 2).
Polyme s 2021,13, 3074 5 o 18
Polyme s 2021, 13, x FOR PEER REVIEW 5 o 18
Figu e 2. The modynamic sys em: 1—lowe laye o he he mal ix u e, 2— esis i e laye wi h in-
e nal hea sou ces, 3—uppe laye o he he mal ix u e, 4—moulded package o polyme ic com-
posi e ma e ial, 5—auxilia y laye .
The sys em o disc e ely loca ed hea ing elemen s was eplaced by a homogeneous
laye , he hickness o which was de e mined om he condi ion o equali y o he powe
o he in e nal hea sou ces. The elec ic ene gy supplied o he moulding ool is consumed
in main aining he gi en a e o hea ing o he p oduc and o he compensa ion o hea
losses esul ing om con ec i e hea ans e om he su aces o he hea ing sys em.
When cons uc ing he he modynamic model o he sys em unde s udy, we made
he assump ions below [34]:
1. A uni o m empe a u e dis ibu ion o e he su ace o he moulding ool; neglec ing
hea exchange om he ends;
2. The main adii o cu a u e o he shaping su ace o he ool a e much g ea e han
i s hickness, so he e ec o cu a u e on he empe a u e dis ibu ion can be ne-
glec ed;
3. The he mophysical p ope ies o he ma e ial a e cons an wi hin each laye and do
no depend on he empe a u e;
4. The e is a pe ec con ac a he bounda ies o he laye s o he hea ing sys em.
The assump ions made allow he use o he hea conduc ion equa ions o a plane wall
o sol e he p oblem; hey a e w i en sepa a ely o each laye o he sys em:
𝑐(1)𝜌(1)𝜕𝑇(1)
𝜕𝑡 =𝜆(1)𝜕2𝑇(1)
𝜕2𝑥;
𝑐(2)𝜌(2)𝜕𝑇(2)
𝜕𝑡 =𝜆(2)𝜕2𝑇(2)
𝜕2𝑥+𝑞𝑒;
𝑐(3)𝜌(3)𝜕𝑇(3)
𝜕𝑡 =𝜆(3)𝜕2𝑇(3)
𝜕2𝑥;
𝑐(4)𝜌(4)𝜕𝑇(4)
𝜕𝑡 =𝜆(4)𝜕2𝑇(4)
𝜕2𝑥+𝑞𝑟;
𝑐(5)𝜌(5) 𝜕𝑇(5)
𝜕𝑡 =𝜆(5) 𝜕2𝑇(5)
𝜕2𝑥,
(1)
whe e 𝑐(𝑘),𝜌(𝑘),𝜆(𝑘)— espec i ely, speci ic hea , densi y and hea conduc ion coe icien
o he 𝑘- h laye ; 𝑇(𝑘)— empe a u e in he k- h laye as a unc ion o he coo dina e x and
ime ; 𝑞𝑒—speci ic hea lux c ea ed by he esis i e laye ; 𝑞𝑟—speci ic hea lux o he
exo he mic e ec o he binde cu ing eac ion.
In he p ocess o sol ing he hea conduc ion p oblems wi h he in e nal hea sou ces,
he condi ions o hea exchange on he ou e su aces a e o g ea impo ance, since hey
signi ican ly a ec he empe a u e dis ibu ion o e he wall hickness. I a known em-
pe a u e is main ained on bo h su aces o he wall (bounda y condi ions o he i s kind),
Figu e 2.
The modynamic sys em: 1—lowe laye o he he mal ix u e, 2— esis i e laye wi h
in e nal hea sou ces, 3—uppe laye o he he mal ix u e, 4—moulded package o polyme ic
composi e ma e ial, 5—auxilia y laye .
The sys em o disc e ely loca ed hea ing elemen s was eplaced by a homogeneous
laye , he hickness o which was de e mined om he condi ion o equali y o he powe
o he in e nal hea sou ces. The elec ic ene gy supplied o he moulding ool is consumed
in main aining he gi en a e o hea ing o he p oduc and o he compensa ion o hea
losses esul ing om con ec i e hea ans e om he su aces o he hea ing sys em.
When cons uc ing he he modynamic model o he sys em unde s udy, we made
he assump ions below [34]:
1.
A uni o m empe a u e dis ibu ion o e he su ace o he moulding ool; neglec ing
hea exchange om he ends;
2.
The main adii o cu a u e o he shaping su ace o he ool a e much g ea e han i s
hickness, so he e ec o cu a u e on he empe a u e dis ibu ion can be neglec ed;
3.
The he mophysical p ope ies o he ma e ial a e cons an wi hin each laye and do
no depend on he empe a u e;
4. The e is a pe ec con ac a he bounda ies o he laye s o he hea ing sys em.
The assump ions made allow he use o he hea conduc ion equa ions o a plane wall
o sol e he p oblem; hey a e w i en sepa a ely o each laye o he sys em:
c(1)ρ(1)∂T(1)
∂ =λ(1)∂2T(1)
∂2x;
c(2)ρ(2)∂T(2)
∂ =λ(2)∂2T(2)
∂2x+qe;
c(3)ρ(3)∂T(3)
∂ =λ(3)∂2T(3)
∂2x;
c(4)ρ(4)∂T(4)
∂ =λ(4)∂2T(4)
∂2x+q ;
c(5)ρ(5)∂T(5)
∂ =λ(5)∂2T(5)
∂2x,
(1)
whe e
c(k)
,
ρ(k)
,
λ(k)
— espec i ely, speci ic hea , densi y and hea conduc ion coe icien
o he
k
- h laye ;
T(k)
— empe a u e in he k- h laye as a unc ion o he coo dina e xand
ime ;
qe
—speci ic hea lux c ea ed by he esis i e laye ;
q
—speci ic hea lux o he
exo he mic e ec o he binde cu ing eac ion.
In he p ocess o sol ing he hea conduc ion p oblems wi h he in e nal hea sou ces,
he condi ions o hea exchange on he ou e su aces a e o g ea impo ance, since hey
signi ican ly a ec he empe a u e dis ibu ion o e he wall hickness. I a known empe -
a u e is main ained on bo h su aces o he wall (bounda y condi ions o he i s kind),
i is equi alen o he ac ha se e al hea luxes a e applied o he su aces, which a e
necessa y o main aining his empe a u e. When simula ing he eal hea ing sys ems

Polyme s 2021,13, 3074 6 o 18
wi h he use o bounda y condi ions o he i s kind, i is necessa y o be su e ha he
equi ed hea luxes can be c ea ed by means o he exis ing equipmen . When he hea ed
moulding ools a e used, i should be no ed ha cooling o he package o he polyme ic
composi e ma e ial is ca ied ou only due o con ec i e hea exchange o he ou e su ace
o he auxilia y laye s and he lowe su ace o he moulding ool. I can be assumed ha ,
wi h he signi ican hea e ec o he cu ing eac ion, he speci ied empe a u e egime
may no be implemen ed a ull scope, since cooling due o con ec i e hea ans e only,
will no be enough o align he empe a u e cu e a he momen o in ense o e hea ing o
he s uc u e. In addi ion, i is necessa y o conside he one-way supply o hea om he
ool side in he sys em unde s udy; he e o e, i does no seem possible o main ain he
gi en empe a u e on bo h su aces o he polyme ic composi e ma e ial package. Thus, o
sol e he p oblem we used bounda y condi ions o he hi d kind, whe e he con ec i e
hea ans e is se on he ou e su ace o he auxilia y laye s and he lowe su ace o he
moulding ool. Wi h he use o he abo e se ing, i was possible o assess he easibili y o
he selec ed empe a u e egime using he a ailable equipmen . The e o e, on he ou e
su aces o he wall a
x=x5
we w i e he bounda y condi ions o he con ec i e hea
ans e as ollows:
−λ(5)∂T(5)
∂x=αTк−T(5), (2)
and condi ions o equali y o hea luxes a e w i en o he con ac su aces o he laye s:
x=x1:T(1)=T(2);λ(1)∂T(1)
∂x=λ(2)∂T(2)
∂x;
x=x2:T(2)=T(3);λ(2)∂T(2)
∂x=λ(3)∂T(3)
∂x;
x=x2:T(3)=T(4);λ(2)∂T(3)
∂x=λ(4)∂T(4)
∂x;
x=x4:T(4)=T(5);λ(4)∂T(4)
∂x=λ(5)∂T(5)
∂x;
(3)
while on he lowe su ace o he moulding ool a
x=
0 he bounda y condi ions a e
w i en, aking in o accoun he ibbing (no p e iously aken in o accoun in [29]):
λ(1)∂T(1)
∂x=αTк−T(1)+T(1)
2αP1
1m1
cosh(m1L1)+αP2
2m2
cosh(m2L2), (4)
whe e
α
—coe icien o con ec ion; T
к
—ambien empe a u e. Ini ial condi ions a
=
0
ake he o m: T(1)=T(2)=T(3)=T(4)=T(5)=Tк.
The powe o he in e nal hea sou ces caused by he exo he mic e ec o he binde
cu ing eac ion a e w i en as ollows
q=∆H(1−θ)ρb
dη
d , (5)
whe e
∆H
—amoun o hea eleased wi h he exo he mic e ec by a kilog am o he binde ;
θ
— olume ic con en o ein o cing ille in he composi e;
ρb
— olume densi y o he
binde ; dη
d — a e o chemical eac ion o a e o cu ing; η—deg ee o cu ing; — ime.
Since he eac ion a e depends on empe a u e, he sys em o hea conduc ion
Equa ion (1)
has o be sol ed oge he wi h he kine ic equa ion unde he ini ial con-
di ions ( =0)η=η0, whe e η0—ini ial deg ee o he binde cu ing.
The main cha ac e is ic o he esis i e laye is he c ea ion o a uni o m empe a u e
dis ibu ion o e he shaping su ace o he ool [
30
,
31
]. To sa is y his equi emen , we
de e mined he dep h o he esis i e laye deepening h, as well as he pi ch o laying he
hea ing elemen s (Figu e 3) o he moulding ool o powe N.
Polyme s 2021,13, 3074 7 o 18
Polyme s 2021, 13, x FOR PEER REVIEW 7 o 18
de e mined he dep h o he esis i e laye deepening h, as well as he pi ch o laying he
hea ing elemen s (Figu e 3) o he moulding ool o powe N.
Figu e 3. Shaping su ace wi h in e nal hea sou ces.
The speci ic na u e o he esis i e s uc u e in oduces some di e ences in he hea -
ing sys em pa ame e calcula ion me hod [33,34].
Le us conside he empe a u e dis ibu ion om wo hea sou ces o he esis i e
elemen based on a me al wi e o ca bon h ead. As can be seen in Figu e 3, he alue o
he laying pi ch should be p o ided so ha hal o i co esponds o hal o he empe a u e
om he hea ing wi e. Then, wi h he s ep-by-s ep laying o he nex hea ing elemen s he
empe a u e ield will be e en.
Using he equali y o he hea lux 𝑄𝑣 eleased by hea sou ces and he hea lux Q,
passing h ough he dis ance o he laying pi ch, as well as co espondence o he powe
o sou ces and he low o eleased ene gy
𝑄 =𝑄𝑣=𝑁
(6)
we ob ain he ollowing ans o ma ion o Fou ie ’s law:
2𝜆
𝑡𝐹(𝑇−𝑇
2)=𝑁
(7)
whe e 𝐹 =2𝜋𝑟𝐿—hea ing a ea, — adius o hea ing wi e wi h he leng h o L.
Howe e , when choosing he diame e and leng h o he h ead, i is impo an o
conside wo ac o s: he ma e ial o he elemen s o he in e nal sou ces and he hea ing
su ace a ea. Fo each ma e ial o he hea ing wi e wi h diame e d, he known alues a e
he maximum b eakdown cu en Imax and he esis ance pe uni leng h ρ, de e mined by
he o mula:
𝜌=𝑅
𝐿,
(8)
whe e R— esis ance o he ma e ial o he hea ing wi e wi h he leng h o L.
Using he dependence o he powe o cu en sou ces
𝑁 =𝐼2𝑅 =𝐼𝑈 =𝑈2
𝑅,
(9)
we de e mine he equi ed esis ance alue
𝑅 = 𝑁
𝑙𝑚𝑎𝑥
2.
(10)
Based on he esis ance alue, he laying pi ch is calcula ed as ollows
𝑡 = 2𝜆𝑇𝜋𝑟𝐿
𝑁=2𝜆𝑇𝜋𝑟
𝑙𝑚𝑎𝑥
2𝜌.
(11)
Hal o he laying pi ch alue de e mines he alue o he deepening h. The e o e,
pa ame e s o he hea ing laye and h o a speci ic conduc o wi h he leng h o L a e
Figu e 3. Shaping su ace wi h in e nal hea sou ces.
The speci ic na u e o he esis i e s uc u e in oduces some di e ences in he hea ing
sys em pa ame e calcula ion me hod [33,34].
Le us conside he empe a u e dis ibu ion om wo hea sou ces o he esis i e
elemen based on a me al wi e o ca bon h ead. As can be seen in Figu e 3, he alue o
he laying pi ch should be p o ided so ha hal o i co esponds o hal o he empe a u e
om he hea ing wi e. Then, wi h he s ep-by-s ep laying o he nex hea ing elemen s he
empe a u e ield will be e en.
Using he equali y o he hea lux
Q
eleased by hea sou ces and he hea lux Q,
passing h ough he dis ance o he laying pi ch, as well as co espondence o he powe o
sou ces and he low o eleased ene gy
Q=Q =N(6)
we ob ain he ollowing ans o ma ion o Fou ie ’s law:
2λ
FT−T
2=N(7)
whe e F=2π L—hea ing a ea, — adius o hea ing wi e wi h he leng h o L.
Howe e , when choosing he diame e and leng h o he h ead, i is impo an o
conside wo ac o s: he ma e ial o he elemen s o he in e nal sou ces and he hea ing
su ace a ea. Fo each ma e ial o he hea ing wi e wi h diame e d, he known alues a e
he maximum b eakdown cu en I
max
and he esis ance pe uni leng h
ρ
, de e mined by
he o mula:
ρ=R
L, (8)
whe e R— esis ance o he ma e ial o he hea ing wi e wi h he leng h o L.
Using he dependence o he powe o cu en sou ces
N=I2R=IU =U2
R, (9)
we de e mine he equi ed esis ance alue
R=N
l2
max
. (10)
Based on he esis ance alue, he laying pi ch is calcula ed as ollows
=2λTπ L
N=2λTπ
l2
maxρ. (11)
Hal o he laying pi ch alue de e mines he alue o he deepening h. The e o e,
pa ame e s o he hea ing laye and h o a speci ic conduc o wi h he leng h o La e
de e mined based on he equi ed powe o he sys em. Howe e , in o de o p o ide he
Polyme s 2021,13, 3074 8 o 18
equi ed wo king a ea o hea ing, he leng h Lo he conduc o is no always su icien .
The e o e, a his s age o he calcula ion i is possible o change he ini ial pa ame e s o
he esis i e elemen and ecalcula e he hea ing sys em pa ame e s. As an al e na i e, i is
possible o swi ch o a pa allel wi ing diag am. Le us gi e an algo i hm which allows he
equi ed numbe o esis i e blocks o be ob ained o ming a esis i e laye o speci ied
dimensions a×b.
The a ea o laying o hea ing elemen s is de e mined by he o mula
F1=b(n−1) , (12)
whe e n—numbe o pi ches o laying o he hea ing elemen s, is de e mined by he o mula:
n=L+
b+ . (13)
I should be no ed ha o he pa e n o laying o he elemen s o he ine- ibe ed
esis i e s uc u e (Figu e 4a), he nnumbe has o be e en, and o he pa e n shown in
Figu e 4b i is an odd numbe .
Polyme s 2021, 13, x FOR PEER REVIEW 8 o 18
de e mined based on he equi ed powe o he sys em. Howe e , in o de o p o ide he
equi ed wo king a ea o hea ing, he leng h L o he conduc o is no always su icien .
The e o e, a his s age o he calcula ion i is possible o change he ini ial pa ame e s o
he esis i e elemen and ecalcula e he hea ing sys em pa ame e s. As an al e na i e, i
is possible o swi ch o a pa allel wi ing diag am. Le us gi e an algo i hm which allows
he equi ed numbe o esis i e blocks o be ob ained o ming a esis i e laye o speci-
ied dimensions a × b.
The a ea o laying o hea ing elemen s is de e mined by he o mula
𝐹1=𝑏(𝑛−1)𝑡,
(12)
whe e n—numbe o pi ches o laying o he hea ing elemen s, is de e mined by he o -
mula:
𝑛=𝐿+𝑡
𝑏+𝑡.
(13)
I should be no ed ha o he pa e n o laying o he elemen s o he ine- ibe ed
esis i e s uc u e (Figu e 4а), he n numbe has o be e en, and o he pa e n shown in
Figu e 4b i is an odd numbe .
Figu e 4. Pa e ns o laying o in e nal cu en sou ces (a) e en numbe o pi ches, (b) odd num-
be o pi ches.
Since we know he elemen laying a ea, he equi ed hea ing a ea is ep esen ed as
ollows:
𝐹 =𝑚𝐹1+𝑏𝑡(𝑚−1),
(14)
whe e m—co e age coe icien o coe icien o possible pa allel connec ions, equal o:
𝑚 = 𝐹+𝑏𝑡
𝐹1+𝑏𝑡 =𝑎+𝑡
𝑛𝑡 .
(15)
I m < 1, he hea ing wi e ma e ial should be eplaced, as sho ening o he conduc o
can lead o a sho ci cui . A m ≥ 1 i is mo e ad an ageous o swi ch o he pa e n o
pa allel conduc o laying. The co e age coe icien is o en a ac ional numbe , which
needs o be ounded down only. Howe e , when changing he alue o he coe icien , i
is necessa y o ecalcula e he conduc o leng h, he laying pi ch, he esis ance, and he
cu en s eng h.
Thus, he de eloped he modynamic model allows de e mina ion o he ime de-
pendence o he speci ic powe o in e nal hea sou ces in he esis i e laye , which is nec-
essa y o main ain he gi en empe a u e egime on he middle su ace o he moulded
p oduc . The cons uc ed model akes in o accoun he con ec i e hea ans e om he
Figu e 4.
Pa e ns o laying o in e nal cu en sou ces (
a
) e en numbe o pi ches, (
b
) odd numbe
o pi ches.
Since we know he elemen laying a ea, he equi ed hea ing a ea is ep esen ed
as ollows:
F=mF1+b (m−1), (14)
whe e m—co e age coe icien o coe icien o possible pa allel connec ions, equal o:
m=F+b
F1+b =a+
n . (15)
I m< 1, he hea ing wi e ma e ial should be eplaced, as sho ening o he conduc o
can lead o a sho ci cui . A m
≥
1 i is mo e ad an ageous o swi ch o he pa e n o
pa allel conduc o laying. The co e age coe icien is o en a ac ional numbe , which
needs o be ounded down only. Howe e , when changing he alue o he coe icien , i
is necessa y o ecalcula e he conduc o leng h, he laying pi ch, he esis ance, and he
cu en s eng h.
Thus, he de eloped he modynamic model allows de e mina ion o he ime depen-
dence o he speci ic powe o in e nal hea sou ces in he esis i e laye , which is necessa y
o main ain he gi en empe a u e egime on he middle su ace o he moulded p oduc .
The cons uc ed model akes in o accoun he con ec i e hea ans e om he ou e
su aces o he hea ing sys em and he exo he mic e ec o he polyme iza ion eac ion.
Fu he , acco ding o he maximum alue o he speci ic powe , i is possible o de e mine
he esis i e elemen pa ame e s in he hea ing sys em.
Polyme s 2021,13, 3074 9 o 18
4. Nume ical Implemen a ion
Nume ical alida ion o he de eloped me hod was ca ied ou on an example o
moulding equipmen o he o ma ion o package based on ibe glass and Hysol EA 9396
binde , whe e he amoun o hea
∆
H= 400 kJ is eleased in he p ocess o cu ing o one
kilog am o he binde .
Figu e 5shows he dependence o he equi ed powe o he esis i e laye on he
ime equi ed o main enance o he gi en empe a u e– ime egime on he lowe su ace
o a moulded package o 2 mm hickness, as well as he dis ibu ion o he empe a u es on
he ou e su aces o he manu ac u ed package o he polyme ic composi e ma e ial.
Polyme s 2021, 13, x FOR PEER REVIEW 9 o 18
ou e su aces o he hea ing sys em and he exo he mic e ec o he polyme iza ion eac-
ion. Fu he , acco ding o he maximum alue o he speci ic powe , i is possible o de-
e mine he esis i e elemen pa ame e s in he hea ing sys em.
4. Nume ical Implemen a ion
Nume ical alida ion o he de eloped me hod was ca ied ou on an example o
moulding equipmen o he o ma ion o package based on ibe glass and Hysol ЕА 9396
binde , whe e he amoun o hea ΔН = 400 kJ is eleased in he p ocess o cu ing o one
kilog am o he binde .
Figu e 5 shows he dependence o he equi ed powe o he esis i e laye on he
ime equi ed o main enance o he gi en empe a u e– ime egime on he lowe su ace
o a moulded package o 2 mm hickness, as well as he dis ibu ion o he empe a u es
on he ou e su aces o he manu ac u ed package o he polyme ic composi e ma e ial.
Figu e 5. Dependences o pa ame e s o he s anda d condi ions o moulding o a package o 2 mm
hick: 1— empe a u e e sus ime on he lowe su ace o he p oduc ; 2— empe a u e e sus ime
on he uppe su ace o he p oduc ; 3— empe a u e e sus ime o he heo e ical condi ions; 4—
powe e sus ime.
As can be seen in Figu e 5, he sha p d op in he equi ed powe in sec ion AB is
explained by he exo he mic e ec o he cu ing eac ion o he Hysol ЕА 9396 binde . As
a esul o sel -hea ing o he sys em, he equi ed powe o he esis i e laye no iceably
d ops in he ime in e al om 10 o 25 min, a e which he g aph o dependency o he
equi ed powe on ime becomes linea . The jump a poin В is explained by he ansi ion
om he hea ing s age o he holding s age, a which he supplied ene gy is consumed
only o he compensa ion o he con ec i e hea ans e om ou e su aces o he he -
modynamic sys em. An insigni ican jump in empe a u e on he uppe su ace o he
moulded package co esponding o he a ea o he equi ed powe d opping is explained
by he ac ha he p esen ed he modynamic sys em allows con ol o he empe a u e
on one su ace o he moulded p oduc only. As p e iously de e mined, he choice o he
lowe su ace as he con ol will p e en o e hea ing o he s uc u e on he uppe laye s
o he moulded package, so ha a highe quali y p oduc can be ob ained.
Figu e 6 shows he empe a u e– ime ela ionship on he ou e su aces o he
moulded p oduc o a simila he modynamic sys em, when he hickness o he
moulded package is 5 mm, as well as he dependence o he equi ed powe o he hea ing
sys em on ime. In his case, he powe o he esis i e laye d ops o ze o a poin B, which
is explained by he g owing exo he mic e ec o he cu ing eac ion wi h he inc ease in
hickness o he moulded package. Figu e 6 shows ha in sec ion BC he exo he mic e ec
o he cu ing eac ion canno be compensa ed only by con ec i e hea emo al om he
Figu e 5.
Dependences o pa ame e s o he s anda d condi ions o moulding o a package o 2 mm
hick: 1— empe a u e e sus ime on he lowe su ace o he p oduc ; 2— empe a u e e sus ime on
he uppe su ace o he p oduc ; 3— empe a u e e sus ime o he heo e ical condi ions; 4—powe
e sus ime.
As can be seen in Figu e 5, he sha p d op in he equi ed powe in sec ion AB is
explained by he exo he mic e ec o he cu ing eac ion o he Hysol EA 9396 binde . As
a esul o sel -hea ing o he sys em, he equi ed powe o he esis i e laye no iceably
d ops in he ime in e al om 10 o 25 min, a e which he g aph o dependency o
he equi ed powe on ime becomes linea . The jump a poin B is explained by he
ansi ion om he hea ing s age o he holding s age, a which he supplied ene gy is
consumed only o he compensa ion o he con ec i e hea ans e om ou e su aces o
he he modynamic sys em. An insigni ican jump in empe a u e on he uppe su ace
o he moulded package co esponding o he a ea o he equi ed powe d opping is
explained by he ac ha he p esen ed he modynamic sys em allows con ol o he
empe a u e on one su ace o he moulded p oduc only. As p e iously de e mined, he
choice o he lowe su ace as he con ol will p e en o e hea ing o he s uc u e on he
uppe laye s o he moulded package, so ha a highe quali y p oduc can be ob ained.
Figu e 6shows he empe a u e– ime ela ionship on he ou e su aces o he moulded
p oduc o a simila he modynamic sys em, when he hickness o he moulded package
is 5 mm, as well as he dependence o he equi ed powe o he hea ing sys em on ime. In
his case, he powe o he esis i e laye d ops o ze o a poin B, which is explained by
he g owing exo he mic e ec o he cu ing eac ion wi h he inc ease in hickness o he
moulded package. Figu e 6shows ha in sec ion BC he exo he mic e ec o he cu ing
eac ion canno be compensa ed only by con ec i e hea emo al om he ou e su aces
o he sys em, and leads o he empe a u e peak on he lowe su ace o he moulded
p oduc a he hea ing sec ion.
Polyme s 2021,13, 3074 16 o 18
ools wi h in e nal hea ing is be ween 40 and 60%, depending on he adap abili y o he
moulding pa ame e s o he equipmen , which p o ides he hea ing (Table 5) [25,34]
Table 5. Compa ison o ene gy consump ion o adi ional and new equipmen .
Pa ame e s o Specimen
Cu ing Mode
Elec ic Fu nace Moulding Tool
wi h In e nal Hea ing ∆N,%
τ, h Nn, W τ, h Nm, W
V1= 1 ◦C/min, V2= 1 ◦C/min,
T1= 60 ◦C, T2= 160 ◦C,
1= 60 min, 2= 120 min
14.3 940 5.63 587 40
V
1
= 1
◦
C/ min, V
2
= 1
◦
C/min,
T1= 60 ◦C, T2= 160 ◦C,
1= 60 min, 2= 65 min
12.6 67 4.13 250 63
A he modynamic model o uns eady hea ans e o he “su ace shaping-polyme
composi e ma e ial” sys em was de eloped [
34
]. The model in con as o ha in o he
pape s [
28
,
29
] allows he empe a u e dis ibu ion o e he hickness o he sys em o be
ob ained, he in luence o he exo he mic e ec o he binde cu ing eac ion o be e alua ed,
and he equi ed powe o he hea ing sys em o be de e mined. Fu he mo e, he model in
con as o pape [34] conside s he ibbing o he lowe su ace o he moulding ools.
I was ound ha he inc ease in he hickness o he moulded package o he polyme ic
composi e ma e ial esul ed no only in a highe supplied powe o he hea ing sys em, bu
also in a complica ion o he me hod o sys em con ol, because o he g owing exo he mic
e ec o he binde cu ing eac ion. The esul s ob ained pa ly con i m he p elimina y
conclusions om o he wo ks [29,31,32].
The in luence o he physical and mechanical cha ac e is ics o he moulding ool ma-
e ial and s i ening ibs was analysed in e ms o ene gy consump ion and con ollabili y
o he hea ing sys em simila o he pape s [
33
,
34
]. Fibe glass shows he lowes ene gy
consump ion. Hea ing o he aluminium and s eel moulding ools o he same pu pose
will equi e 20% and 45% mo e powe , espec i ely. The esul s ob ained pa ly con i m
he p elimina y conclusions om o he wo ks [24,25,27].
In con as o he pape s [
32
,
34
], he inc ease in he numbe o s i ening ibs has a
s ong e ec on he hea emo al o he hea ing sys em. Fo binde s wi h an unp onounced
exo he mic e ec , he p esence o he ame in he s uc u e o he moulding ool leads
o an inc ease in he ene gy consump ion o he sys em. Howe e , o binde s wi h a
s ongly p onounced exo he mic e ec , he p esence o he ame allows he con ollabili y
o he hea ing p ocess o be imp o ed and he gi en ime— empe a u e egime o be
achie ed when he sys em is being cooled wi h ee con ec ion only. Fo he i s ime, he
dependences o he pa ame e s o he hea ing sys em on he hea ing a e a e shown. As he
hea ing a e g ows, he powe consump ion inc eases, bu he ene gy consump ion o he
sys em dec eases. In his case, he con ollabili y o he hea ing sys em is educed, since he
sel -hea ing eac ion o he binde inc eases wi h he implemen a ion o high hea ing a es.
An expe imen al p o o ype o hea ing equipmen o a moulding ool o he manu-
ac u e o s uc u es o polyme ic composi e ma e ials, as well as a lexible he mal blanke
o he epai o non-sepa able me al and composi e s uc u es, we e de eloped.
The ob ained esul s in he end make i possible o educe he ene gy consump ion o
in e nally hea ed moulding ools by choosing he op imal pa ame e s o he esis i e laye .
7. Conclusions and Fu he Resea ch
A me hod o de e mina ion o pa ame e s o he esis i e laye o moulding ools was
de eloped, which allowed calcula ion o he hea ing laye pa ame e s and implemen a ion
o he speci ied ime– empe a u e egime o moulding o composi e s uc u es.
A he modynamic model o uns eady hea ans e o he sys em “shaping su ace-
polyme ic composi e ma e ial” was cons uc ed.

Polyme s 2021,13, 3074 17 o 18
An expe imen al p o o ype o hea ing equipmen o he moulding ools o he
manu ac u e o s uc u es o polyme ic composi e ma e ials was de eloped.
The esul s o he s udy can be he basis o a new me hod o op imal design o
pa ame e s o moulding ool s uc u e a minimal hea emo al o he en i onmen .
Au ho Con ibu ions:
Concep ualiza ion, A.K. and V.P.; me hodology, M.S. and S.P.; alida ion, A.F.
and P.K.; o mal analysis, V.P. and P.K.; in es iga ion, S.P. and M.S.; esou ces, A.F. and S.P.; da a
cu a ion V.P., M.S. and A.K.; w i ing—o iginal d a p epa a ion, S.P. and A.F.; w i ing—o iginal d a
p epa a ion, S.P. and M.S.; w i ing— e iew and edi ing V.P. and A.K.; isualiza ion, S.P. and A.F.;
supe ision, M.S.; p ojec adminis a ion, A.K. All au ho s ha e ead and ag eed o he published
e sion o he manusc ip .
Funding:
The au ho s g a e ully acknowledge unding om he Speci ic esea ch on BUT FSI-S-20-6267.
Ins i u ional Re iew Boa d S a emen : No applicable.
In o med Consen S a emen : No applicable.
Acknowledgmen s: The au ho s hank B no Uni e si y o Technology o suppo .
Con lic s o In e es : The au ho s decla e no con lic o in e es .
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