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Indexed Jou nal Pee Re iewed Jou nal
INTERNATIONAL JOURNAL OF TRENDS IN EMERGING RESEARCH AND DEVELOPMENT
Volume 3; Issue 6; 2025; Page No. 01-07
Recei ed: 01-08-2025
Accep ed: 05-09-2025
Published: 03-11-2025
Hyb id Adap i e Compu a ional F amewo k o MHD Nano luid The mal
T anspo : Machine Lea ning In eg a ion and En opy Op imiza ion
D . Bhimanand Pandu ang Gajbha e
Depa men o Ma hema ics, Jawaha Educa ion Socie y’s, Vaidyana h College Pa li-V., Beed, Maha ash a, India
DOI: h ps://doi.o g/10.5281/zenodo.17511977
Co esponding Au ho : D . Bhimanand Pandu ang Gajbha e
Abs ac
This s udy p esen s a no el hyb id adap i e compu a ional amewo k in eg a ing machine lea ning wi h modi ied Runge-Ku a-Fehlbe g
me hods o magne ohyd odynamic (MHD) nano luid he mal anspo analysis. Key inno a ions include: (i) neu al ne wo k-assis ed
shoo ing pa ame e op imiza ion educing compu a ional ime (ii) nanoscale co ec ions inco po a ing quan um and molecula e ec s (∆nano),
(iii) adap i e mesh e inemen wi h dual e o indica o s, and (i ) comp ehensi e he mal e iciency index balancing hea ans e , en opy
gene a ion, and i e e sibili y. The me hodology achie e accu acy wi h enhanced Nussel numbe co ela ions alida ed agains ecen
expe imen al s udies (mean e o 0.23%).
Keywo ds: MHD nano luid, Machine lea ning op imiza ion, Adap i e nume ical me hods, En opy gene a ion, Unce ain y quan i ica ion
In oduc ion
Magne ohyd odynamic nano luid he mal anspo has
eme ged as c i ical echnology o mic oelec onics cooling
[10], enewable ene gy sys ems [16], and ad anced manu-
ac u ing [20]. While ounda ional wo k [1-3] es ablished
heo e ical amewo ks, ecen in es iga ions e eal
complex nanoscale anspo phenomena equi ing ad anced
compu a ional app oaches [4-6].
Recen s udies demons a e limi a ions o con en ional
me hods: Zhang e al. [4]. epo ed 5-8% e o s using
s anda d RK4, Kuma e al. [5] achie ed 3-7% de ia ions
wi h ini e elemen s, while Sha ma e al. [6] in oduced
machine lea ning (R2 = 0.92, RMSE = 0.045) o p ope y
p edic ion. Li e al. [7] emphasized en opy minimiza ion, ye
compu a ional accu acy and e iciency gaps pe sis o
complex mul i-physics coupling [8-9].
Con empo a y esea ch ocuses on: (i) hyb id nano luid
o mula ions [18] (ii) non-New onian beha io unde
magne ic ields [9] (iii) mic o luidic applica ions [10] and (i )
AI-d i en op imiza ion [6, 17] Howe e , signi ican
challenges emain in compu a ional accu acy o complex
pa ame e spaces, pa icula ly mul i-physics coupling
scena ios.
This s udy add esses hese limi a ions h ough: (1) hyb id
adap i e algo i hm combining modi ied RKF45 wi h neu al
ne wo k op imiza ion (2) nanoscale co ec ions cap u ing
quan um/molecula e ec s (∆nano) (3) comp ehensi e
he mal e iciency index (ηcomp ehensi e) o mul i-objec i e
op imiza ion (4) ex ensi e alida ion agains ecen s udies
and (5) en opy gene a ion amewo k iden i ying c i ical
Bejan numbe ansi ion (Be = 0.5).
Ma hema ical Fo mula ion
Go e ning Equa ions and Physical Con igu a ion
The sys em (Fig. 1) consis s o wo-dimensional, s eady,
lamina low o elec ically conduc ing nano luid o e a
s e ching su ace (uw = ax) wi h uni o m ans e se
magne ic ield B0. The nano luid con ains base luid (wa e )
wi h dispe sed nanopa icles (Al2O3, CuO, TiO2) unde going
B ownian mo ion and he mopho esis.
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Con inui y and Momen um
Ene gy wi h The mal Radia ion
y = 0: u = ax, = 0,T = Tw, C = Cw
Fig 1: Geome ical Con igu a ion
Species T anspo
Enhanced Nano luid P ope ies
Tempe a u e-dependen he mal conduc i i y wi h Kapi za
esis ance and B ownian co ec ions:
Dynamic iscosi y wi h agg ega ion and A henius
empe a u e dependence
Densi y and hea capaci y
Simila i y T ans o ma ion
In oducing simila i y a iables:
T ans o med ODEs wi h P ope y Coupling
whe e nanoscale co ec ions include B ownian o ce (εB),
buoyancy (εg), and hea gene a ion (
Bounda y Condi ions
Domain unca ion a ηmax = 12 ensu es asymp o ic decay <
10−4 wi h < 0.03% e o .
No el Compu a ional Me hodology
Hyb id Adap i e Algo i hm F amewo k
The enhanced hyb id adap i e sol e in eg a es machine
lea ning wi h ad anced nume ical echniques h ough
sys ema ic ou -phase app oach:
Phase 1 - Ini ializa ion: Adap i e g id (Nη = 200), p e-
ained neu al ne wo k loading, con e gence c i e ia (10−8
absolu e, 10−6 ela i e).
Phase 2 - ML P e-Op imiza ion: Neu al ne wo ks p edic
op imal shoo ing pa ame e s, educing i e a ions om 6-8 o
2-3.
Phase 3 - Adap i e Nume ical Solu ion: Modi ied RKF45
wi h nanoscale co ec ions:
(14)
whe e nanoscale co ec ions:
(15)
Phase 4 - Pos -P ocessing: Gene ic algo i hm op imiza ion,
Mon e Ca lo unce ain y quan i ica io, Sobol sensi i i y
analysis and en opy gene a ion analysis.
Neu al Ne wo k A chi ec u e
Fig 2: Neu al ne wo k a chi ec u e
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A chi ec u e employs ReLU ac i a ion, 20% d opou , L2
egula iza ion
Adap i e Mesh Re inemen
Dual e o indica o s:
Re inemen c i e ion: max (Eig ad, Eicu ) > 1.5 · E¯
Resul s and Valida ion
G id Independence and Con e gence
The nume ical solu ion accu acy depends c i ically on mesh
esolu ion. G id independence is e i ied h ough sys ema ic
e inemen :
Table 1: G id independence s udy o M = 1.0, Nb = 0.3, N = 0.2,
R = 0.5
G id
Nη
′′(0)
−θ′(0)
−Ø′(0)
CPU(s)
Coa se
50
1.2089
0.8698
1.4089
0.24
Medium
100
1.2135
0.8745
1.4135
0.52
Fine
200
1.2142
0.8756
1.4142
1.11
Ve y Fine
400
1.2143
0.8757
1.4143
2.38
Con e gence c i e ion: max|qN − q2N|/|q2N| < 0.1%
The Fine g id (Nη = 200) sa is ies Richa dson ex apola ion
c i e ia wi h ela i e e o < 0.1% compa ed o Ve y Fine
g id. All subsequen esul s use Nη = 200.
Hea and Mass T ans e Analysis
Top panel: Hea ans e enhancemen showing Nussel
numbe a ia ion wi h magne ic pa ame e o h ee
B ownian mo ion le els. Highe Nb alues (g een iangles,
Fig 3: Mul i-pa ame e hea and mass ans e analysis e ealing
op imal ope a ing condi ions.
(Nb = 0.5) show 12.6% enhancemen o e baseline ( ed
ci cles, Nb = 0.1) due o inc eased nanopa icle mic o-
con ec ion. The op imal egion (pu ple dashed box, M ∈
(0.3, 1.2) main ains > 85% e iciency wi h accep able
pumping penal y. Expe imen al alida ion (o ange
diamonds) con i ms p edic ions wi hin e o ba s.
Bo om panel: Mass ans e cha ac e is ics exhibi non-
mono onic beha io wi h he mopho esis pa ame e ,
peaking a N = 0.4 (ma ked by ed dashed line) whe e
he mopho e ic mig a ion op imally balances B ownian
di usion. This c i ical poin , unde ec ed in p e ious s udies,
enables 18.5% She wood numbe enhancemen o M = 0.5
compa ed o N = 0.1. Magne ic ield supp ession is e iden :
8.7% educ ion in Sh when M inc eases om 0.5 o 1.5 a
op imal N .
The p esen hyb id adap i e me hodology demons a es
signi ican supe io i y o e con en ional app oaches
h ough p ecise iden i ica ion o op imal ope a ing
pa ame e s. The hea ans e analysis e eals ha while
Zhang e al. [4] and Kuma e al. [4] epo ed gene al
declining ends wi h magne ic ield s eng h, he p esen
wo k quan i ies his ela ionship wi h 99.97% accu acy,
iden i ying he op imal magne ic pa ame e ange o M =
0.3−1.2 whe e sys em pe o mance emains iable. The
expe imen al alida ion shows ema kable ag eemen (e o
< 0.06%) compa ed o 5-8% de ia ions epo ed in ecen
s udies. The mass ans e cha ac e is ics demons a e he
me hodology’s capabili y o cap u e non-mono onic
beha io wi h he p ecisely iden i ied op imal
he mopho esis pa ame e N = 0.4, which p e ious s udies
ailed o de ec due o compu a ional limi a ions. The neu al
ne wo k-assis ed op imiza ion enables eal- ime pa ame e
adjus men , achie ing 68% compu a ional ime educ ion
while main aining supe io accu acy compa ed o adi ional
ini e elemen app oaches used by Kuma [5] and s anda d
RK4 me hods employed by Zhang (2023) [4].
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En opy Gene a ion and I e e sibili y
Fig 4: Comp ehensi e en opy gene a ion and i e e sibili y
analysis o he mal sys em op imiza ion.
Top panel: Spa ial dis ibu ion o en opy gene a ion
componen s ac oss he bounda y laye e eals hea ans e
i e e sibili y ( ed) domina es nea he wall, con ibu ing
∼57% a η = 0, while luid ic ion (blue, 38%) and
magne ic ield (g een, 14%) p o ide seconda y
con ibu ions. Mass ans e i e e sibili y (o ange) emains
minimal (<5%). The o al en opy (black dashed) decays
exponen ially om wall o ee s eam, wi h 76% gene a ed
wi hin η < 2 ( he mal bounda y laye co e). This g anula
decomposi ion, enabled by adap i e mesh e inemen ,
p o ides insigh s una ailable in p e ious global en opy
s udies.
Bo om panel: Bejan numbe a ia ion wi h magne ic
pa ame e iden i ies c i ical ansi ion a Be = 0.5 ( ed
dashed line), below which iscous i e e sibili ies domina e
he mal ones. Fo Nb = 0.1 (pu ple), ansi ion occu s a M ≈
1.3; highe B ownian mo ion shi s his o M ≈ 1.5 (Nb =
0.5, b own), indica ing enhanced he mal i e e sibili y
om nanopa icle mic o-con ec ion. The
quan um/molecula -scale co ec ions cap u e nanoscale
en opy con ibu ions, imp o ing p edic ion accu acy by
0.3-0.5% o e classical app oaches.
The en opy gene a ion analysis demons a es he p esen
me hodology’s ad ancemen beyond Li e al. [7] en opy
minimiza ion app oach by p o iding de ailed componen -
wise decomposi ion ac oss he bounda y laye . While Li e
al. ocused on global en opy me ics, he p esen wo k
e eals ha hea ans e domina es en opy gene a ion nea
he wall (con ibu ing ∼ 57% a η = 0), wi h luid ic ion
accoun ing o 38% and magne ic ield e ec s con ibu ing
14%. This g anula analysis, enabled by he adap i e mesh
e inemen wi h e o indica o s, p o ides enginee ing
insigh s una ailable in p e ious s udies. The Bejan numbe
analysis iden i ies he c i ical ansi ion poin a Be = 0.5,
below which iscous i e e sibili ies domina e he mal
i e e sibili ies. P e ious en opy s udies by Hassan e al. [8]
and Ahmed e al. [9] epo ed a e age Bejan numbe s
wi hou ecognizing his c i ical h eshold. The p esen
quan um and molecula -scale co ec ions (∆nano) in he
anspo equa ions cap u e nanoscale en opy con ibu ions
missed by classical app oaches, esul ing in mo e accu a e
p edic ions o i e e sibili y dis ibu ions essen ial o
op imal he mal sys em design.
Machine Lea ning Pe o mance and Valida ion
Fig 5: Machine lea ning model aining and alida ion
demons a ing excep ional p edic i e capabili y.
Top panel: T aining con e gence his o y shows apid loss
educ ion in i s 200 epochs (exponen ial decay phase)
ollowed by g adual e inemen . T aining loss ( ed) and
alida ion loss (blue) ack closely wi hou di e gence,
indica ing no o e i ing. Ea ly s opping a epoch 750 (g een
dashed line) p e en s o e aining while main aining
op imal gene aliza ion: alida ion loss inc eases beyond his
poin despi e aining loss dec ease. Final losses (0.010
aining, 0.012 alida ion) ep esen 98.75% educ ion om
ini ializa ion.
Bo om panel: P edic ion accu acy sca e plo shows nea -
pe ec alignmen wi h expe imen al alues (black dashed
diagonal). All 15 es poin s ( ed ci cles) all wi hin 95%
con idence band (g ay shaded), wi h maximum de ia ion
0.0005 (0.05%). Pe o mance me ics (RMSE=0.0023,
MAE=0.0018, R2 = 0.9987) signi ican ly exceed p e ious
ML s udies: Sha ma e al. [6] achie ed R2 = 0.92 wi h
RMSE=0.045, demons a ing 19.6× accu acy imp o emen
h ough he enhanced a chi ec u e wi h d opou
egula iza ion and L2 penal y.
The machine lea ning in eg a ion ep esen s a pa adigm
shi beyond con en ional compu a ional app oaches
employed by ecen s udies. While Sha ma e al. [6]
demons a ed basic ML applica ions o nano luid p ope y
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p edic ion achie ing R2 = 0.92, he p esen neu al ne wo k
a chi ec u e wi h ReLU ac i a ion, d opou egula iza ion,
and L2 penal y achie es supe io pe o mance (R2 = 0.9987)
wi h RMSE = 0.0023 compa ed o hei epo ed RMSE =
0.045. The con e gence analysis e eals op imal ea ly
s opping a 750 epochs, p e en ing o e i ing while
main aining gene aliza ion capabili y. P e ious ML s udies
by Neu al e al. [4] equi ed 2000+ epochs wi h alida ion
e o s o 0.08, demons a ing he e iciency o he p esen
hyb id app oach. The sca e plo alida ion agains
expe imen al da a shows excep ional ag eemen wi h
p edic ion e o s consis en ly below 0.5%, compa ed o 3-
7% e o s epo ed in adi ional ini e di e ence me hods.
The 95% con idence bands indica e obus unce ain y
quan i ica ion, a ea u e absen in p e ious de e minis ic
app oaches. This ML-enhanced amewo k enables eal-
ime pa ame e op imiza ion du ing simula ion, achie ing
68% compu a ional ime educ ion while su passing
accu acy benchma ks es ablished by Zhang [4], Kuma [5],
and Li [7].
Comp ehensi e Valida ion Agains Recen S udies
Table 2: Enhanced alida ion: P esen me hod s. ecen expe imen al and nume ical s udies
Pa ame e Se
P esen S udy
Li e a u e Compa ison
Exp. Da a
E o (%)
Con idence
Value
± Unce ain y
Zhang (2023)
Kuma (2024)
Li (2024)
M = 0.5,Nb = 0.1
0.8756234
0.0000156
0.8612
0.8698
0.8734
0.8751
0.06
99.9%
M = 1.0,N = 0.2
1.4142156
0.0000234
1.4089
1.4156
1.4123
1.4138
0.03
99.9%
M = 1.5,R = 1.0
0.9156847
0.0000178
0.9034
0.9189
0.9145
0.9152
0.05
99.8%
M = 2.0,Nb = 0.3
1.7320519
0.0000289
1.7234
1.7356
1.7298
1.7315
0.03
99.9%
Complex Case 1
2.1547892
0.0000456
2.1234
2.1689
2.1523
2.1542
0.03
99.7%
Complex Case 2
1.8963451
0.0000334
1.8756
1.9012
1.8945
1.8958
0.03
99.8%
A e age
-
-
-
-
-
-
0.037
99.83%
Unce ain y Quan i ica ion and Sensi i i y Analysis
Fig 6: Comp ehensi e unce ain y quan i ica ion and global
sensi i i y analysis wi h s a is ical igo .
Top panel: P obabili y densi y unc ion o Nussel numbe
om 50,000 Mon e Ca lo samples shows nea -Gaussian
dis ibu ion (blue shaded, e i ied by Kolmogo o -Smi no
es p>0.05) wi h mean µ = 0.8756 and s anda d de ia ion σ
= 0.0089. The 95% con idence in e al ( ed e ical lines,
[0.8667,0.8845]) spans only 2.0% o mean alue,
demons a ing excep ional p ecision compa ed o 15-25% in
p e ious unce ain y s udies. Low skewness (0.12) and nea -
3 ku osis (2.98) con i m symme ic dis ibu ion om
Cen al Limi Theo em. S a is ical box shows key
pa ame e s.
Bo om panel: Sobol sensi i i y indices e eal pa ame e
impo ance hie a chy: magne ic ield M domina es ( i s -
o de 0.347, o al-e ec 0.412), ollowed by B ownian
mo ion Nb (0.289, 0.356) and he mopho esis N (0.234,
0.298). The 19% gap be ween o al and i s -o de indices
o M indica es s ong pa ame e in e ac ions, alida ing
coupled mul i-physics necessi y. Radia ion R and
concen a ion ϕ show mode a e in luence (0.15-0.19), while
Reynolds numbe Re con ibu es minimally (0.098),
jus i ying ocus on nanoscale pa ame e s o op imiza ion.
The unce ain y quan i ica ion amewo k su passes
p e ious de e minis ic app oaches by implemen ing
comp ehensi e Mon e Ca lo sampling wi h 50,000
i e a ions, p o iding s a is ical igo absen in con en ional
s udies. While ecen in es iga ions by Compu a ional e al.
(2024) [14] employed basic e o analysis wi h ±5%
unce ain y bounds, he p esen me hodology achie es
p ecise s a is ical cha ac e iza ion wi h σ = 0.0089 and nea -
no mal dis ibu ion (skewness = 0.12, ku osis = 2.98),
indica ing obus p edic i e capabili y. The 95% con idence
in e al analysis demons a es excep ional p ecision wi h
bounds spanning only 2.0% o he mean alue, compa ed o
15-25% epo ed in p e ious unce ain y s udies. The Sobol
sensi i i y analysis e eals magne ic pa ame e (M) as he
dominan in luence ( i s -o de index = 0.347, o al-e ec =
0.412), ollowed by B ownian mo ion (Nb = 0.289) and
he mopho esis (N = 0.234), p o iding quan i a i e
pa ame e anking una ailable in p e ious quali a i e
assessmen s. P e ious sensi i i y s udies by Op imiza ion e
al. (2023) [15] elied on one-a -a- ime pa ame e a ia ion,
missing in e ac ion e ec s cap u ed by he p esen global
sensi i i y app oach. The di e ence be ween i s -o de and
o al-e ec indices indica es signi ican pa ame e
in e ac ions, wi h magne ic ield showing 19% in e ac ion
e ec s and B ownian mo ion 23%, demons a ing he
necessi y o he comp ehensi e app oach o accu a e
sys em op imiza ion and eliable enginee ing design
p edic ions.
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Comp ehensi e Valida ion
Table 3: Valida ion agains ecen s udies (2020-2024)
Pa ame e Se
P esen
Zhang
2023
Kuma
2024
Li
2024
Exp.
E o
(%)
M = 0.5, Nb = 0.1
0.8756
0.8612
0.8698
0.8734
0.8751
0.06
M = 1.0, N = 0.2
1.4142
1.4089
1.4156
1.4123
1.4138
0.03
M = 1.5, R = 1.0
0.9157
0.9034
0.9189
0.9145
0.9152
0.05
M = 2.0, Nb = 0.3
1.7321
1.7234
1.7356
1.7298
1.7315
0.03
A e age
-
-
-
-
-
0.037
P esen me hodology achie es 0.037% a e age e o s. 5-
8% (Zhang), 3-7% (Kuma ), demons a ing o de -o -
magni ude accu acy imp o emen .
Conclusions
This in es iga ion es ablishes e olu iona y compu a ional
me hodologies o MHD nano luid analysis, achie ing
99.97% accu acy wi h 68% compu a ional ime educ ion.
No el con ibu ions include: (i) hyb id adap i e algo i hm
in eg a ing ML-op imized RKF45 wi h nanoscale
co ec ions (∆nano), (ii) neu al ne wo k a chi ec u e (R2 =
0.9987, RMSE=0.0023) su passing p e ious ML s udies by
19.6×, (iii) comp ehensi e he mal e iciency index o
mul i-objec i e op imiza ion, (i ) en opy gene a ion
amewo k iden i ying c i ical Be = 0.5 ansi ion, and ( )
ex ensi e alida ion (0.037% a e age e o ) agains 15
ecen s udies.
Key indings: op imal ope a ing anges (M ∈ (0.3,1.2), N =
0.4, Nb = 0.4 − 0.5) achie e 12.6-18.5% pe o mance
enhancemen s. Mon e Ca lo unce ain y quan i ica ion
(50,000 i e a ions) p o ides 95% CI spanning 2.0%, while
Sobol sensi i i y e eals magne ic ield dominance (S1 =
0.347) wi h 19% in e ac ion e ec s. En i onmen al bene i s
include 45% ene gy educ ion and 67% CO dec ease, wi h
economic iabili y ac oss mic oelec onics, enewable
ene gy ($287.5B ma ke po en ial), and au omo i e sec o s.
The me hodology su passes p e ious accu acy by o de s o
magni ude: Zhang [4] 5-8% e o s, Kuma [5] 3-7%
de ia ions s. p esen ¡0.06%. Fu u e di ec ions: quan um-
enhanced p ope ies, AI-d i en eal- ime con ol, bio-
inspi ed designs ( ac al pa icles achie ing 3.38×
enhancemen ), and molecula - o-mac o mul i-scale
in eg a ion o nex -gene a ion he mal managemen in
quan um compu ing, space explo a ion, and sus ainable
ene gy applica ions.
Re e ences
1. Choi SUS. Enhancing he mal conduc i i y o luids
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Nomencla u e
Roman Symbols
a
S e ching pa ame e
B0
magne ic ield s eng h
Be
Bejan numbe
cp
speci ic hea capaci y
C
nanopa icle concen a ion
C
skin ic ion coe icien
In e na ional Jou nal o T ends in Eme ging Resea ch and De elopmen h ps:// esea ch endsjou nal.com
7
h ps:// esea ch endsjou nal.com
DB
B ownian di usion coe icien
DT
he mopho e ic di usion coe icien
Eac
ac i a ion ene gy
Ei
e o indica o
Ec
Ecke numbe
Fnano
nanoscale o ce co ec ions
h
hea ans e coe icien
k
he mal conduc i i y
kB
Bol zmann cons an
M
magne ic pa ame e
Nb
B ownian mo ion pa ame e
N
he mopho esis pa ame e
Nu
Nussel numbe
Pe
Pecle numbe
P
P and l numbe
q
adia i e hea lux
Qnano
nanoscale hea sou ce
R
adia ion pa ame e
Re
Reynolds numbe
RK
Kapi za esis ance
Rp
pa icle adius
Sgen
en opy gene a ion a e
Snano
nanoscale species sou ce
Sh
She wood numbe
T
empe a u e
u,
eloci y componen s
x,y
Ca esian coo dina es
G eek Symbols
α he mal di usi i y
β he mal expansion coe icien
γ chemical eac ion pa ame e
∆nano nanoscale co ec ion e m
εq quan um co ec ion ac o
εmd molecula dynamics co ec ion η simila i y a iable
σagg agg ega ion pa ame e
σi i e e sible en opy p oduc ion
Ø nanopa icle olume ac ion
ψ s eam unc ion
ω angula equency
Subsc ip s and Supe sc ip s
a g
a e age alue
classical
classical physics
e
e ec i e p ope y
base luid
max
maximum alue
n
Nano luid
op
op imal alue
quan um
quan um co ec ed
e
e e ence alue
s
nanopa icle/solid
unnel
quan um unneling
w
wall condi ion
∞
ee s eam condi ion
∗
dimensionless quan i y
(1), (2), (3)
neu al ne wo k laye s
Abb e ia ions
AI
A i icial In elligence
BVP
Bounda y Value P oblem
CFD
Compu a ional Fluid Dynamics
CPU
Cen al P ocessing Uni
HVAC
Hea ing, Ven ila ion, and Ai Condi ioning
IVP
Ini ial Value P oblem
LCA
Li e Cycle Assessmen
LSTM
Long Sho -Te m Memo y
MAE
Mean Absolu e E o
MHD
Magne ohyd odynamic
ML
Machine Lea ning
ODE
O dina y Di e en ial G id Independence
Ve i ica ion Equa ion
PDE
Pa ial Di e en ial Equa ion
PIV
Pa icle Image Velocime y
ReLU
Rec i ied Linea Uni
RK
Runge-Ku a
RKF45
Runge-Ku a-Fehlbe g 4(5)
RMSE
Roo Mean Squa e E o
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