Academic Edi o : Mahmoud Bou ouis
Recei ed: 3 Ap il 2025
Re ised: 24 Ap il 2025
Accep ed: 26 Ap il 2025
Published: 12 May 2025
Ci a ion: Ga cia-Vilchez, M.; To es,
P.; Raush, G.; Cas illa, R.; To en , M.;
Mo e, M. Towa ds a Simpli ied
Nume ical Me hodology o
Es ima ing he E iciency o an Ai
Handling Uni . Ene gies 2025,18, 2468.
h ps://doi.o g/10.3390/en18102468
Copy igh : © 2025 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/).
A icle
Towa ds a Simpli ied Nume ical Me hodology o Es ima ing he
E iciency o an Ai Handling Uni
Me cè Ga cia-Vilchez 1,2,* , Paula To es 3, Gus a o Raush 1,2 , Robe Cas illa 1,2,* , Miquel To en 2
and Mónica Mo e 4
1Cen e o Ad anced Technologies in Mechanics, Escola Supe io d’Enginye ies Indus ial, Ae oespacial i
Audio isual de Te assa, Uni e si a Poli ecnica de Ca alunya, 08222 Te assa, Spain; [email p o ec ed]
2Depa men o Fluid Mechanics, Uni e si a Poli ecnica de Ca alunya, 08222 Te assa, Spain;
[email p o ec ed]
3Escola Supe io d’Enginye ies Indus ial, Ae oespacial i Audio isual de Te assa, Uni e si a Poli ecnica de
Ca alunya, 08222 Te assa, Spain; [email p o ec ed]
4Se oclima, S.A., 08120 La Llagos a, Spain
*Co espondence: me ce.ga [email p o ec ed] (M.G.-V.); [email p o ec ed] (R.C.)
Abs ac : This wo k p esen s a s udy on he calcula ion o ansmi ance in an ai handling
uni (AHU) h ough h ee me hods. A semi-empi ical es ima ion based on simpli ied
models o hea and mass ans e has been used. In addi ion, expe imen al es s we e
ca ied ou in a eal AHU unde con olled condi ions. The measu ed empe a u e inside
and ou side he AHU we e used o calcula e he ansmi ance. Finally, nume ical simu-
la ions we e pe o med on speci ic sec ions o he AHU and on a global model, wi h and
wi hou adia ion. The simula ions p o ided de ailed esul s on he low beha io and
empe a u e dis ibu ion. The esul s we e compa ed and analyzed o assess he accu acy
and applicabili y o he h ee me hods. The hea ans e ob ained wi h he semi-empi ical
me hod is 38% la ge han ha ob ained wi h he expe imen al measu emen , in con as
wi h he 8% o di e ence obse ed wi h nume ical simula ions. I is e ealed ha adia ion,
and hus he emissi i y o su aces, plays an impo an ole in hea ans e o he AHU.
This esea ch con ibu es o he knowledge and unde s anding o ansmi ance in AHUs,
p o iding aluable in o ma ion o he design and op imiza ion o hea ing, en ila ion, and
ai condi ioning (HVAC) sys ems.
Keywo ds: emissi i y; he mal b idging; OpenFOAM; AHU; HVAC; ansmi ance
1. In oduc ion
An ai handling uni (AHU) is a machine ha condi ions ooms and chambe s using
hea exchange s [
1
]. They a e esponsible o ci cula ing ai in houses o buildings. AHUs
a e componen s o hea ing, en ila ion, and ai condi ioning (HVAC) sys ems. They a e
la ge me allic boxes comp ising a blowe , il e acks, sound a enua o s, and cooling and
hea ing coils. They a e ins alled inside and ou side buildings, wi h he oo op being
ypical o he la e whe e con ol is a challenging ask [
2
,
3
]. O en, hey a e connec ed
o he HVAC’s duc wo k [
4
]. The main componen s o an AHU sys em a e i s casing o
housing, he an, he hea ing and cooling coil, il e s, humidi ie s, and he mixing box. The
p ima y unc ion is hea exchange [
5
] and il e ing, imp o ing he ai quali y. To imp o e
hei e iciency, he design o ai handling uni s equi es s udies o he mal losses due
o conduc ion and con ec ion [
6
,
7
]. E iciency is only some imes an easy pa ame e o
ob ain [8]
. Many ac o s ha complica e designs a e he mal b idges [
9
] o pa ame e s ha
Ene gies 2025,18, 2468 h ps://doi.o g/10.3390/en18102468
Ene gies 2025,18, 2468 2 o 16
a e di icul o measu e, such as adia ion hea ans e coe icien s. In his case, he ype
o adia ion can be a limi ing ac o , as he su aces do no beha e he same depending
on he inciden wa eleng h. The mal b idges a e essen ial o he o e all e iciency o he
uni s [
10
]. Howe e , hei cons i u ion is complex [
11
], and hey can be a de e mining
ac o in he ou come o uni y. The b idging e ec s a e ema kable compa ed o low-
ansmission panels, hanks o acuum-insula ed panels. This is ma ked by egula ions
ha need o be pe manen ly imp o ed due o he implica ions o imp o emen s o comply
wi h en i onmen al egula ions, such as, o ins ance, EU egula ion 1253/2014 [12].
Recen publica ions ha e ocused on AHU op imiza ion by con ol, wi h model p e-
dic i e con ol [
13
,
14
] o la ge language models [
15
], in o de o p edic and op imize he
ene gy consump ion o pa icula HVAC applica ions. Compu a ional Fluid Dynamics
ha e been used by Lopes e al. [
16
] o Azem e al. [
17
] o he analysis o he low and
p essu e dis ibu ion p oduced by a an inside he AHU aimed o cons uc i e enhancemen
o he uni . O he au ho s ha e s udied he he mal e iciency o AHU equipped wi h hea
exchange s [
18
,
19
]. Howe e , o he bes o he au ho s’ knowledge, he e a e no published
s udies on he combined analysis wi h CFD and he hea ans e o he he mal e iciency
o he AHU wi h no ans o hea exchange s.
This pape p esen s a simpli ied me hodology o es ima e he ene gy e iciency o
an AHU design. The p ima y objec i e is o p esen a semi-empi ical p ocedu e o he
es ima ion o ene gy consump ion and e alua e he class o he p e-designed uni acco ding
o he Eu opean S anda d EN 1886:2008 [
20
]. This s udy in ol es he h ee known means
o hea exchange: conduc ion, con ec ion, and adia ion [
21
]. Fluid dynamic phenomena
ha de ine hei e iciency mus also be conside ed. This is especially ele an in he
case o il a ion e iciencies. The es condi ions equi e applying ele an echniques in
measu ing he empe a u es decoupled om adia i e in e e ence and empe a u es on
su aces, whe e he e ec s o adia ion mus be conside ed [
22
]. The esul s ob ained wi h
his me hodology a e alida ed bo h wi h nume ical compu a ions in a 2D model and wi h
expe imen al measu emen s on an AHU box uni .
This pape is o ganized as ollows. In Sec ion 2, a semi-empi ical es ima ion, is
p esen ed. Sec ion 3desc ibes an expe imen al se -up, emphasizing he mi iga ion o he
e o ha could be neglec ed. Nume ical s udies a e a ele an pa o be compa ed on he
semi-empi ical p oposal and a e alida ed using he expe imen al esul s. The nume ical
esul s a e p esen ed in Sec ion 3. Finally, Sec ion 4p esen s an ex ensi e discussion o
compa ing he esul s.
2. Semi-Empi ical Es ima ion
The mal ansmi ance (
U
) is de ined as he abili y o he uni o ansmi hea unde
s eady-s a e condi ions. I is es ima ed as he a io be ween hea ans e pe a ea uni and
he di e ence in empe a u e
U=qT
∆T=qT
To−Ti
(1)
whe e
qT
is he o al hea ans e , pe uni a ea, and
Ti
and
To
a e he inside and ou side
empe a u es o he AHU, as depic ed in Figu e 1. I can also be desc ibed as he sum o
he ecip ocals o he esis ances o he elemen s o he uni , and is exp essed in
W/(m2K)
.
The hea ansmi ed, pe su ace uni , by conduc ion, is gi en by Fou ie ’s law o
hea conduc ion,
qc=−αi
dT
dx =αi
Tow −Tiw
e(2)
Ene gies 2025,18, 2468 3 o 16
whe e
αi
is he isola ion he mal conduc i i y,
e
is he wall hickness, and
Tow
and
Tiw
a e,
espec i ely, he ou e and inne wall empe a u es (see Figu e 1) Con ec ion hea ans e
is de e mined wi h
qh=h∆T(3)
whe e
h
is he con ec ion hea ans e coe icien , which does no depend exclusi ely on
he luid, bu i is also in luenced by he geome y o he su ace, he na u e o he luid
mo emen , and i s a e age speed. Con ec ion hea ans e coe icien is compu ed wi h
he Nussel numbe
h=Nuα
d(4)
whe e
α
is he he mal conduc i i y o he medium and
d
is a cha ac e is ic leng h. In he
ollowing, he exp essions used o es ima e Nu and hence h, ha e been based on he book
by Çengel and Ghaja [
6
], and he e e ences he ein. Con ec i e hea ans e is es ima ed
bo h inside and ou side he AHU and he e m
∆T
in Equa ion
(3)
e e s o he empe a u e
di e ence be ween he wall and he a ield. Ou side he uni , only na u al con ec ion
holds, and he Nussel numbe is es ima ed wi h he exp ession
Nuo=cRan
o(5)
whe e
c
and
n
a e a unc ion o he wall o ien a ion and he alue o he ou e Rayleigh
numbe , Rao. Table 1shows he alues used in he p esen es ima ion.
Figu e 1. Scheme o he AHU wi h inside and ou side empe a u es.
Table 1. Coe icien s cand nused in he es ima ion o he Nussel numbe in Equa ion (5).
Raoc n
Ve ical wall <1080.59 1/4
Ve ical wall ≥1080.13 1/3
Ho izon al wall acing upwa ds <2 ×1070.54 1/4
Ho izon al wall acing upwa ds ≥2×1070.14 1/3
Ho izon al wall acing downwa ds - 0.27 1/3
The Rayleigh numbe is compu ed as he p oduc o G asho numbe and P and l
numbe ,
Rao=G oP (6)
whe e
P =µcp
α(7)
Ene gies 2025,18, 2468 4 o 16
and
G o=βL3gρ2
µ2
To−Tow
2(8)
whe e
µ
is he iscosi y o ai ,
cp
is he speci ic hea a cons an p essu e,
β
is he he mal
expansion coe icien o ai ,
L
is he heigh o he uni ,
g
is he g a i y accele a ion,
To
is
he a empe a u e, and
Tow
is he ou side wall empe a u e. Hence, ou e hea ans e
coe icien is compu ed as
ho=Nuoα
L(9)
No e ha , ac ually, he e a e h ee di e en alues o
Nuo
depending on he o ien a ion
o he su ace ela i e o g a i y (la e al walls, op wall and bo om wall).
Inside he AHU, besides na u al con ec ion, o ced con en ion has o be conside ed,
due o he ai ci cula ion equi ed by he S anda d [
20
] in o de o keep a uni o m dis ibu-
ion o inne empe a u e. The Nussel numbe o he o ced con ec ion is
es ima ed wi h
Nu =
0.66Re1
2P 1
3i Re <105
0.037Re0.8P 1
3i Re ≥105(10)
whe e
Re =ρua dh
µ
,
ua
is he a e age eloci y o ai inside he uni and
dh=2LW
L+W
is
he hyd aulic diame e . The na u al con ec ion inside he AHU is compu ed wi h he
co ela ion ound by Globe and D opkin [23] o a ec angula box hea ed om below
Nun=0.069Ra
1
3
iP 0.074 (11)
When bo h na u al and o ced con en ion a e combined, he e ec i e Nussel numbe
is usually es ima ed wi h [6]
Nui=hNu3
+Nu3
ni1
3(12)
and
hi=Nui
α
L(13)
The hea ans e by adia ion is es ima ed wi h
q =εe σT4
i−T4
o(14)
whe e
σ=
5.67
×
10
−8W/m2K4
is he S e an–Bol zmann cons an and
εe =∑4
11/εi−1
is he e ec i e emissi i y due o he ou su aces ha compose he isola ion bounding
walls. I is assumed ha he insula o and ai a e anspa en in he bandwid h o he mal
adia ion. The emissi i y o he su aces is measu ed wi h a he mog aphic came a.
Finally, he hea ans e in he me allic p o iles o he AHU is es ima ed, conside ing
only he conduc ion due o he me al and neglec ing he e ec o he ai chambe s.
The con ec i e and conduc i e hea ans e a e combined as
qcc =hcc(Ti−To)(15)
whe e
hcc =[1/hi+1/hc+1/ho]−1
. The o al hea ans e is he sum o his and he
adia ion e m
qT=q +qcc (16)
Ene gies 2025,18, 2468 5 o 16
Howe e , his o al hea ans e is unc ion o he wall empe a u es,
Tiw
and
Tow
,
which a e, a i s , unknown. This empe a u es a e compu ed wi h
Tiw =Ti−qT
hi+h i
(17)
Tow =To+qT
ho+h o (18)
whe e
h i =εiσT4
i−T4
iw
Ti−Tiw
(19)
h o =εoσT4
ow −T4
o
Tow −To(20)
whe e
εi
and
εo
a e, espec i ely, he emissi i y o he inne and ou e su aces o he AHU.
Equa ions
(16)
–
(18)
a e i e a i ely sol ed un il a solu ion o
qT
,
Tiw
, and
Tow
is eached,
and he mal ansmi ance is compu ed wi h
(1)
. The lowcha o his p ocedu e is
depic ed in Figu e 2.
Physical and
geome ical da a
P (7)
Ti,To
Q,u,dh
Re
Nu (10)
h (4)
hc
qc
(15)
G i(8)
Rai(6)
Nuni (11)
Nui(12)
hi
q n
Q n
G o
(8)
Rao
(6)
Nuno
(5)
hno
(9)
h b
q b (15)
Q b
h
(19)
(20)
εe
Emissi i ies
q
(14)
Q
QTqTTwi,Two
(17)
(18)
Con e ged?
NO
YES
U(1)
Fi s i e a ion
Fo ced con ec ion
and conduc ion
Na u al con ec ion
inside he box
Na u al con ec ion
ou side he box
The mal b idge
Radia ion
Figu e 2. Flowcha o he semi-empi ical compu a ion o he ansmi ance o he AHU. Di e en
ac o s such as conduc ion and o ces connec ion, na u al con ec ion, he mal b idge, and adia ion
a e indica ed wi h co esponding colo s. In he igh side o some compu a ions, he co esponding
equa ion in he ex is indica ed be ween b acke s.
Exp essions
(5)
,
(10)
, and
(11)
a e based on empi ical s a is ics and, hence, a e e-
s ic ed o ce ain condi ions, as in ini e walls. This implies an unce ain y ha has o
be conside ed. Howe e , he combina ion o na u al and o ced con ec ion inside he
box o he AHU, Equa ion
(12)
, can be ega ded as he majo sou ce o unce ain y in he
semi-empi ical es ima ion o hea ans e by con ec ion, acco ding o Siebe s [
24
], ha
ounded a disag eemen o up o 10% wi h expe imen al da a. Ne e heless, compu a ions
in he p esen wo k sugges ha he adia ion e m in Equa ion
(16)
is mo e impo an han
con ec ion, wi h app oxima ely 80% o he o al hea ans e , and i is e y sensi i e o he
compu a ion o su ace emissi i ies.
Ene gies 2025,18, 2468 6 o 16
The he mal b idge ac o is de ined in he S anda d [
20
] as he a e be ween he
minimum di e ence o empe a u es inside and in he ou side wall, and he empe a u e
di e ence inside and ou side he AHU:
k b =Ti−Tow,max
Ti−To(21)
In he p esen es ima ion, since wall empe a u es a e conside ed uni o m, i is
compu ed as
k b =Ti−Tow
Ti−To(22)
3. Nume ical Me hodology
Nume ical expe imen s ha e been pe o med wi h he oolbox OpenFOAM
e sion 9 [25]
,
ha uses ini e olume me hod o sol e sys ems o pa ial di e en ial equa ions. The sol e
used has been ch Mul iRegionFoam, which is used o s eady o ansien luid low and
solid hea conduc ion. Fu he mo e, i conjuga es hea ans e be ween solid and luid
egions, including buoyancy e ec s, u bulence, eac ions, and adia ion modelling. The
simula ions a e s eady, and hey ha e been un un il he con e gence o hea lux is eached.
The mesh is wo-dimensional o he sake o simplici y and simula ion speed. I is
composed o se e al egions ha co e bo h luid and solid domains. Fluid egions include
he in e io and ex e io ai spaces o he AHU, while solids consis o me allic shee s
and insula ion ma e ials ha o m he walls o he AHU. In addi ion, a solid hea e wi h
cons an empe a u e is modeled in he lowe pa o he inne space. Using he symme y
o he sys em, only hal o he domain was simula ed.
The mesh was gene a ed using he
blockMesh
ool included in he OpenFOAM dis-
ibu ion, which cons uc s s uc u ed hexahed al blocks. To s eamline he c ea ion o
complex block con igu a ions, he Py hon ool o blockmeshdic helpe [26] was used.
The egions conside ed in he simula ions a e he inne ai , he ou e ai , he insula o ,
he me al shee s, bo h inne and ou e , and, inally, he hea e . These egions and he
bounda y condi ions a e schema ically shown in Figu e 3, excep me al shee s enclosing
he insula ion. Fi een blocks we e de ined o c ea e he s uc u ed mesh, one o he inne
luid egion, nine o he h ee laye s o me als and insula o , and inally i e o he ou e
ai egion.
Fo he luid egions, ch Mul iRegionFoam sol es con inui y equa ion
∂ρ
∂ +∇ · (ρu)=0, (23)
he momen um equa ion
∂ρu
∂ +∇ · (ρuu)=−∇p∗+∇ · τ, (24)
wi h τ=µe h∇u+∇uT−1
3(∇ · u)Ii, and he ene gy equa ion
∂
∂ (ρh+ρk−p∗)+∇ · (ρu(h+k)) =∇(αe ∇h)+∇ · (τ·u)+R, (25)
whe e
ρ
is he densi y,
u
is he eloci y,
p∗=p−ρg·
is he p essu e co ec ed wi h g a i y
e ec ,
τ
is he s ess enso ,
k=1
2∥u∥2
is he kine ic ene gy,
h
is he en halpy,
R
is he
adia ion e m, and
µe
and
αe
a e, espec i ely, he e ec i e iscosi y and hea ans e
coe icien s, co ec ed by u bulence modeling. In he p esen case, s anda d
k−ε
has been
Ene gies 2025,18, 2468 7 o 16
used as a u bulence model, as i has p o en o be a sui able model, combining accep able
accu acy and compu a ional esou ce consump ion o buoyancy-d i en lows [27].
Figu e 3. Regions o he compu a ional domain. Me al shee s enclosing he insula ion a e no shown
due o i s small wid h. G a i y accele a ion is also shown.
Fo he solid egions, only hea conduc ion is sol ed,
∂ρh
∂ =∇(α∇h)(26)
In he in e aces be ween solids and luids, he sol e imposes he same empe a u e
T =Ts(27)
and, also, he con inui y o hea ans e is ensu ed
αs(∇ρh)s=αe , (∇ρh) (28)
Fo he compu a ion o con ec ion, ai is ea ed as comp essible wi h he Boussinesq
app oxima ion and he densi y is uniquely unc ion o he empe a u e,
(ρ−ρ0) = −ρ0β(T−T0)(29)
whe e
ρ0=
1.22
kg/m3
,
T0=
287.65 K and
β=
3.36
×
10
−3K−1
is he he mal
expansion coe icien .
The adia ion e m
R
in Equa ion
(25)
is compu ed by he sol e using he iew ac o
me hod [
6
,
21
], whe e he adia i e hea ans e is es ima ed by gene a ing disc e e ays
be ween solid su aces. Fo he sake o compa ison, his e m has been disabled on some
nume ical expe imen s.
Two se ies o nume ical expe imen s ha e been pe o med. In he i s se ies, a sec ion
o he uni has been conside ed and he g a i y o ien a ion has been modi ied in o de o
simula ion con ec i e hea ans e and alida e semi-empi ical exp essions, gi en by he
combina ion o Equa ions
(5)
and
(11)
, o he h ee possible o ien a ions o he wall, e ical,
ho izon al acing upwa ds and ho izon al acing downwa ds. The domain used in hese
simula ions is 2D, and composed by an ex e nal ai egion o 250
×
250
mm
, an in e nal
ai egion o 250
×
100
mm
, a solid egion wi h an insula o ma e ial, o 250
×
50
mm
and
2 solid
me allic shee s o 250
×
0.6
mm
. The di e ence o empe a u es be ween he inne
and he ou e bounda ies has been se as 20 K, speci ically 313 K end 293 K, espec i ely.
Rega ding he second se o nume ical simula ions, he whole domain wi h a solid
hea e in he cen e ed bo om pa is conside ed, as shown in Figu e 3. The ex e nal
bounda y o he domain has been de ined as a wall wi h no-slip condi ions o eloci y
and cons an empe a u e. The le side o he domain has been se as a symme y plane
Ene gies 2025,18, 2468 8 o 16
when adia ion was disabled. Howe e , since he iew ac o me hod does no suppo
symme y cons ain s, hese bounda ies ha e been de ined as slip condi ion o eloci y
and ze o g adien o o he a iables when adia ion was enabled. The empe a u e o
he hea e solid has been es ablished a a cons an alue o 334 K. The empe a u e o he
ex e nal bounda ies was se a a alue o 293.15 K (see Figu e 3). A de ail o he mesh is
also shown in his igu e.
T ansmi ance is nume ically compu ed wi h
U=∑q
Tin −Tex , (30)
whe e he sum o hea ans e s includes he hea ans e om he conduc ion/con ec ion
and he hea ans e om he adia ion. In e nal and ex e nal empe a u es, Tin and Tex ,
a e compu ed as he a e age o empe a u e ield a a dis ance o 100 mm, as s a ed by he
S anda d [20]. The he mal b idge ac o is es ima ed using Equa ion (33).
G id Con e gence Valida ion and Bounda y Laye
The hea ans e in he inne side o he AHU has been compu ed o h ee di e en
mesh sizes in o de o assess he g id con e gence, acco ding o Celik e al. [
28
]. I has been
made wi h he second se o nume ical simula ions (global domain). Resul s a e shown
in Table 2. The g id e inemen a io
, de ined as he a io be ween subsequen g id sizes
a e 1.4 o bo h cases, ine o medium and medium o coa se. The g id con e gence index
(GCI) is compu ed as
GCI =F|ε|
p−1×100 (31)
whe e
F
is a sa e y ac o , wi h a ypical alue o 1.25, and
p=log (εi+1/εi)
log( i+1/ i)
is he o de
o con e gence and
ε
a e ela i e e o s o adjacen mesh sizes. In he p esen case, he
o de o con e gence is
p=
1.91. The ex apola ed alue o hea ans e , he heo e ical
alue o in ini e mesh size, is 1.957
W/m2K
. The alues o he GCI a e 0.36% o he ine
mesh, 0.7% o he medium and 1.3% o he coa se one. The alue o he asymp o ic a io,
compu ed wi h
AR = pGCI ine
GCImedium
, is 0.997, and i s closeness o 1 indica es ha he meshes
a e in he asymp o ic egion and he medium mesh can be conside ed as alid, wi h an
accu acy o 0.7%, ha has been ansla ed o he inal esul s o Sec ion 5.
Table 2. G id compa ison.
Fine Middle Coa se
Numbe o cells 121.875 60.150 30.850
Hea ans e [W/m2K]
( om insula ion o in e io ) 9.18 9.21 9.25
The local Reynolds numbe ela ed o he bounda y laye is expec ed o be e y low,
wi h a ypical eloci y o less han 0.1
m/s
and a ypical leng h scale o abou 2 m, which
gi es
ReL≈
10
4
. Wi h he cell size in he walls o a medium mesh, an a e age alue o
y+=ycuw
ν≈
1 is ob ained, whe e
yc
is he cell cen e dis ance o he wall,
uw=pτw/ρ
is
he ic ion eloci y,
τw
is he wall ic ion and
ρ
and
ν
a e, espec i ely, he densi y and
kinema ic iscosi y o ai . Acco ding o OpenFOAM documen a ion, o
y+<
6, no wall
unc ion has o be de ined in he wall and he
nu LowReWallFunc ion
bounda y condi ion,
which ac ually esol es he bounda y laye , has been used.
Ene gies 2025,18, 2468 9 o 16
4. Expe imen al Me hodology
The scheme o he expe imen al ig is p esen ed in Figu e 4. The gene a ion and
con ol o he in e nal empe a u e o he AHU, 4 axial ans, 2 hea e s, and a empe a u e
con olle we e ins alled. A Ci cu o CVM-C10 analyze (Ci cu o , Ba celona, Spain) was
used o measu e he powe consumed. The ans ha e a capaci y o 45.5
m3/h
each and
ci cula e he ai a abou 100 AHU olumes pe hou . They we e ins alled in he middle
longi udinally o he AHU o ci cula e he ai c osswise. The hea e s a e elec ic esis ance
ype and each ha e a capaci y o 400 W. They a e egula ed by an ON/OFF empe a u e
con olle . I is equipped wi h an NTC empe a u e senso which is loca ed inside he uni .
Fo empe a u e acquisi ion, a o al o 20 coppe T- ype he mocouples (TC Di ec ,
Mad id, Spain) wi h 0.2 mm wi e we e ins alled. Six een we e ins alled inside he box
as shown in Figu e 5 om 1 o 16, and he o he ou we e ins alled ou side ma ked
om 17 o 20. The in e nal he mocouples we e ins alled 100 mm om he panels by
using ou wi es c ossing he longes pa o he enclosu e. The ex e nal he mocouples
we e ins alled cen e ed 250 mm om he ace o he co esponding wall, he op, he
back and he wo side walls. The 20 he mocouples we e connec ed o a da a acqui-
si ion uni , DAQ970A by Keysigh (Keysigh , San a Rosa, CA, USA), equipped wi h a
20 channels mul iplexo (Keysigh , San a Rosa, CA, USA).
Figu e 4. Scheme o he expe imen al ig o he es ima ion o he ansmi ance.
Figu e 5. In e nal ( ed poin s) and ex e nal (g een poin s) he mocouple dis ibu ion o he AHU.
The ansmi ance is expe imen ally es ima ed wi h
U=Pel
A∆Tai
(32)
whe e he elec ic powe consumed
Pel
is gi en by he analyze and he ou e su ace o
he box is A = 9.5
m2
. The expe imen al campaign consis ed o se en expe imen s o 2 h o
measu emen each.
The he mal b idge is es ima ed wi h
kb=∆Tmin
∆Tai
(33)
whe e ∆Tmin =Tin −Tsmax.
Ene gies 2025,18, 2468 16 o 16
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Disclaime /Publishe ’s No e: The s a emen s, opinions and da a con ained in all publica ions a e solely hose o he indi idual
au ho (s) and con ibu o (s) and no o MDPI and/o he edi o (s). MDPI and/o he edi o (s) disclaim esponsibili y o any inju y o
people o p ope y esul ing om any ideas, me hods, ins uc ions o p oduc s e e ed o in he con en .
