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EQUIVALENT WALL METHOD FOR DYNAMIC
CHARACTERIZATION OF THERMAL BRIDGES
K. Ma ín1, C. Escude o2, A. E ko eka1, I. Flo es2, J.M. Sala1
1Depa men o The mal Enginee ing – Uni e si y o he Basque Coun y
(UPV/EHU), Alameda U quijo s/n. 48013 Bilbao, Spain
2Labo a o y o he Quali y Con ol in Buildings – Basque Go e nmen
C/Agi elanda n. 10, 01013 Vi o ia-Gas eiz, Spain
E-mail: koldobika.ma [email protected]
Tel.: + (34) 94 601 7378, Fax: + (34) 94 601 4283
ABSTRACT
Al hough he e a e speci ic ules in he s anda d ISO 10211 o he cha ac e iza ion o
he mal b idges, hey a e mainly ocused on s eady s a e calcula ions o ob ain he
linea he mal ansmi ance () o he empe a u e ac o a he in e nal su ace ( Rsi).
These pa ame e s a e espec i ely indica o s o he addi ional hea low and he isk o
in e nal su ace condensa ion o he mal b idges.
Howe e , in he calcula ions o building ene gy demand he dynamic he mal aspec s o
he en elope ake a e y impo an ole. Mo eo e , a high pe cen age o he en elope
is in luenced by he mal b idges. The e o e i is necessa y o ake in o accoun he
implici ine ia o he mal b idges o accu a e calcula ions.
This pape p esen s a me hodology based on he moelec ic analogy o calcula e an
equi alen wall o h ee homogeneous laye s, which ha e he same dynamic he mal
beha iou as he he mal b idge. Fu he mo e, each he mal b idge is associa ed wi h
an in luence a ea wi hin he en elope, so ha hey can be easily implemen ed in
building ene gy simula ion p og ams whe e he hea low is usually conside ed one-
dimensional.
KEYWORDS: The mal b idges, equi alen wall, he moelec ic analogy, uns eady
s a e, ine ia.
This is he accep ed manusc ip o he a icle ha appea ed in inal o m in Ene gy and
Buildings 55 : 704-714 (2012)), which has been published in inal o m a h ps://
doi.o g/10.1016/j.enbuild.2012.08.024. © 2012 Else ie unde CC BY-NC-ND license (h p://
c ea i ecommons.o g/licenses/by-nc-nd/4.0/)
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1. In oduc ion
The e a e h ee main aspec s ha can be used o ene gy impac educ ion: he con ol
o emissions, use o enewable ene gy sou ces and inc eased ene gy e iciency.
Ene gy conse a ion, de ined as he s a egy o adjus and op imize he ene gy use pe
pe son wi hou a ec ing he socio-economic de elopmen , leads o a secu e ene gy
and desi able en i onmen al goals.
The g ea es po en ial o ene gy conse a ion in buildings is based on he educed use
o hea ing and cooling sys ems, which in Spain is mo e han 47% o building ene gy
consump ion [1], being e en highe in he Eu opean Union.
The e a e h ee main cha ac e is ics which complica e he calcula ion o he ene gy
demand: a iables ha change uns eadily, hea low associa ed wi h non-linea
empe a u e exp essions and di e en hea ans e mechanisms which in e ac
be ween hem in complex ways [2].
To o e come hese di icul ies, building ene gy simula ion (BES) p og ams ha e
e ol ed, in pa due o ad ances in compu e echnologies, adjus ing he ma hema ical
algo i hms o achie e mo e accu a e ene gy e icien design. I is necessa y o conduc
a comp ehensi e building analyse, because di e en aspec s o conside a e closely
ela ed, such as indoo ai quali y, noise o ene gy sa ing.
Howe e , oday is he day ha is no ye p ope ly calcula ed he impac o he mal
b idges (TBs) in buildings ene gy demand. As a as ene gy sa ing is conce ned i can
only be asse ed ha he p opo ion o TBs impac inc eases when he insula ion le el
o he en elope g ows [3]. On he o he hand, he in luence on he phenomena ela ed
o he in e nal su ace condensa ion and mould g ow h mus also be conside ed [4].
Implemen ing co ec ly TBs in buildings ene gy demand models means a majo e o
by he designe ha o en is no ewa ded. The esea ch communi y in BES is
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cons an ly wo king o educe ene gy demand di e ences be ween simula ed alues
using compu e ools and he eal ones based on he use o he dwelling. The e ha e
been se e al s udies o e i y ha hese p edic i e ools o e high quali y esul s [5].
Mainly he e a e wo ways o he co ec implemen a ion o TBs in BES. On he one
hand he e is he possibili y o inco po a ing 2D o 3D hea conduc ion capabili ies in o
he exis ing p og amme s uc u e [6]; al hough u he imp o emen s in solu ion speed
and ease o p oblem speci ica ion is equi ed be o e i can be ou inely applied. On he
o he hand a homogeneous mul ilaye equi alen wall can be calcula ed ha beha es
simila ly o he TB cons uc i e solu ion. This la e op ion is analysed in his pape .
Thus one-dimensional hea low can be calcula ed ins ead implemen ing mo e complex
models.
2. Objec i es
The main goal is o in oduce a me hodology o implemen TBs in he BES dynamic
calcula ions aking in o accoun he e ec s o he mal mass o each TB. Usually as a
i s app oxima ion o he es ima ion o TBs, he alue o linea he mal ansmi ance
() is used, which compu es he addi ional hea low o a speci ic TB, Eq. (1). Bu is
a pa ame e calcula ed in s eady s a e, so i does no conside he ine ial aspec s o
TBs. Simila ly i would be like ying o calcula e he ene gy demand o a building
conside ing only he he mal ansmi ance alues (U) o he en elope elemen s.
Howe e , nowadays i is o ally analysed and demons a ed he impo ance o he mal
ine ia in he calcula ion o ene gy demand [7],[8].
N
jjjD lUL
1
2
(1)
To include he e ec o TBs aking in o accoun no only he addi ional hea low, bu
also hei in insic ine ia, a me hodology o ob ain a dynamic equi alen wall is de ined,
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as well as i s co esponding in luence a ea (a ea o he en elope o which he he mal
p ope ies o he equi alen wall is assigned), which allows a simple implemen a ion in
BES so wa e.
Summa izing, he issues discussed a e as ollow:
Analyse he a ie y o TBs in a eal building placed in Vi o ia-Gas eiz (Basque
Coun y).
S eady s a e he mal cha ac e iza ion o he TBs by calcula ing he linea
he mal ansmi ance ().
Fo each ype o TB i s in luence a ea is de ined.
De ini ion o a me hodology o achie e a dynamic equi alen wall o a TB.
3. Equi alen wall me hod
Basically he concep o equi alen wall is based on de ining a mul ilaye wall wi h he
same s eady and dynamic he mal beha iou as he o iginal solu ion o be modelled.
So he aim would be o calcula e he equi alen he mal p ope ies, such as
conduc i i y (), densi y () and speci ic hea (cp) o he di e en homogeneous laye s
o he equi alen wall. These da a could be en e ed in BES p og ams o a di ec
esponse ac o s o conduc ion ans e coe icien s calcula ion.
Once he equi alen wall is calcula ed, one-dimensional hea low can be assumed o
he TB. A e ge ing he a e age alue o pa ame e s such as hea low o su ace
empe a u es in he in luence a ea, a simila beha iou o he TB is achie ed. The
c ea o o he equi alen wall concep Kossecka de ines i as ollows: "The he mally
equi alen wall is a simple s uc u e ha has he same dynamic beha iou o a complex
s uc u e and can be used as a subs i u e o i in building ene gy simula ion design"
[9].
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Cu en ly he e a e di e en me hods o ob aining he cha ac e is ic pa ame e s o he
equi alen wall. Kossecka uses he de ini ion o he s uc u al ac o s o ge esponse
ac o s, and om hem o calcula e i necessa y, he conduc ion ans e unc ion
coe icien s [10]. In [3], Mao de ines di e en ypes o TBs in he equency domain. A
me hod based on ini e di e ences is used he e o cha ac e ize TBs by ampli ude and
phase lag when i is exci ed by sinusoidal empe a u es wi h di e en equencies.
Then an equi alen elec ical ci cui is de ined h ough a equency and lumped
pa ame e s ans o ma ion (-RC), om which he he mal p ope ies can be ob ained.
4. P elimina y conside a ions
To cha ac e ize a TB by nume ical calcula ion, aking in o accoun no only he hea
loss ha would esul in s eady s a e bu also he ine ial e ec , he cu -o planes o he
cons uc i e solu ion mus be ixed o he geome y de ini ion. The s anda d ISO 10211
[11] loca es he cu -o planes a leas o 1 m dis ance om he cen al elemen i he e
is no nea e symme y plane. I will be shown ha sho e dis ance o hese cu -o
planes o a ce ain limi does no dec ease accu acy in he alue calcula ion,
al hough i has in luence on he dynamic esponse.
I only is used o cha ac e izing he TB in BES p og ams he e is no p oblem o
iden i y he leng h which co esponds o he TB, bu he e o o a dynamic calcula ion
using s a iona y pa ame e s mus be conside [12]. On he o he hand, i he TB ine ial
p ope ies a e going o be implemen ed, he di icul y s ays in he de ini ion o i s
in luence a ea.
ISO 13786 [13] indica es ha o he dynamic cha ac e iza ion o a TB cu -o planes
should be placed acco ding o he speci ica ions o he ISO 10211. The p oblem is o
de ine he a ea o be assigned in he BES so wa e o implemen he TB. Fo example
o cha ac e ize a 0.3x0.3 m2 pilla TB, 2.3 m wide geome y is needed acco ding o he
s anda d. I a smalle su ace is assigned in he BES so wa e, such as he
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co esponding o he wid h o he pilla (0.3 mul iplied by he pilla leng h), i would be
an e o o unde es ima ing he eal impac o he TB.
This is because when conside ing la ge dis ance o he cu -o planes, he in luence o
he homogeneous pa o he wall o e he TB has much weigh , so he a e age hea
low is lowe han i close cu -o planes a e chosen. When he a ea o in luence
assigned in he BES p og am is di e en o ha used o he dynamic cha ac e iza ion
o he TB an e o is made [12].
5. Tools used in he s udy
5.1. The mal b idge cha ac e iza ion in s eady s a e
To ob ain he linea he mal ansmi ance () o each TB ound a ound he building
en elope, he e a e some possibili ies:
I. Use o TB ca alogues o handbooks ha collec many cons uc i e solu ions wi h
he co esponding alues [14].
II. Use ini e elemen , ini e di e ence o ini e olume p og ams whe e he calcula ion
me hodologies a e mo e complex, bu he achie ed accu acy and lexibili y a e
much highe .
III. Use o speci ic p og ams o he calcula ion o TBs. The mos common a e THERM
o KOBRA.
The op ion o using ca alogues wi h di e en cons uc ion de ails is ini ially he mos
a ac i e because o i s simplici y. Howe e , he a ie y o TBs in buildings is la ge, so
aking alues om ca alogues no mally leads o de ia ions om he eal ones.
Summa izing, he main d awback is ha ca alogues do no o e he lexibili y o i
alues o he eal TBs de ails gi en in a building.
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The possibili y o using nume ical me hods p og ams such as FLUENT, FEMLAB,
HEAT3, VOLTRA... allows any ype o TB cha ac e iza ion om he poin o iew o
ma e ial p ope ies, geome y and bounda y condi ions. This ac esul s in a wide
ange o possibili ies o hea ans e analysis conside ing s eady o uns eady s a es
and ob aining highly accu a e alues. The p oblem is he ime consuming ask o
lea ning and amilia izing wi h he p og am use en i onmen .
The las op ion is o employ speci ic so wa e o he calcula ion and e iew o TBs.
This combines he ad an ages o he abo e wo al e na i es, being mo e igid han he
nume ical p og ams and no as simple as he use o a ca alogue.
In addi ion, some TB con igu a ions ha appea in buildings a e no desc ibed nei he
in he ca alogue o he KOBRA p og am i sel , which limi s he possibili ies o choose a
simple ool. Since i is necessa y o de elop he equi alen wall ansien me hodology
simula ions, he Compu a ional Fluid Dynamics FLUENT 6.2 p og am [15] is o be
used.
5.2. Sys em iden i ica ion me hods
The moelec ic analogy is used in he p oposed me hodology o ob ain an equi alen
RC ci cui o he TB. F om he analog elec ic ci cui he he mal p ope ies o he
equi alen wall can be calcula ed. The esis ances and capaci ies o he elec ic ci cui
a e es ima ed by means o a sys em iden i ica ion ool. The e o e, a e he ansien
simula ions a e ca ied ou by FLUENT, a sys em iden i ica ion ool is used o es ima e
he pa ame e s o he equi alen RC ci cui .
Fo he la e pu pose he e a e se e al ools a ailable. The mos used iden i ica ion
so wa e is he Ma lab ”Sys em iden i ica ion oolbox”, al hough he e a e mo e speci ic
ools applied o hea ans e models. This is he case o Con inuous Time S ochas ic
Modelling (CTSM) and Logical R De e mina ion (LORD) ools.
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In he case o CTSM, he sys em iden i ica ion p ocess is pe o med by sea ching he
objec i e unc ion ha wi h he highes p obabili y i s o he objec i e unc ion
dependen on he pa ame e s o be iden i ied. Fo his pu pose he p edic ion e o
me hod is applied. LORD is based on a simila p ocess, bu in his case he sea ch o
dependen unc ion pa ame e s which minimize esiduals espec o he objec i e
unc ion is made by applying he ou pu e o me hod.
In bo h cases i is necessa y o de ine he lowe and uppe limi s o he iden i ica ion
pa ame e s. Rega ding o he sea ching o minimum esiduals, LORD p esen s a
me hodology based on Nelde -Mead and Mon e Ca lo me hods [16] which allow ixing
b oade ini ial anges, esul ing in mo e obus ness o he sys em iden i ica ion
p ocess. Fo his eason he chosen p og am o his s udy is LORD [17].
6. Simula ion cha ac e is ics
Nume ical calcula ions a e pe o med h ough he ini e olume so wa e FLUENT 6.2,
which sol es he simpli ied equa ion o ene gy Eq. (2) o each ime s ep and a each
node de ined by he mesh. The mesh is gene a ed using GAMBIT 2.2. The simplici y o
he geome ies allows ec angula and s uc u ed 5 mm size elemen s achie ing
op imal mesh quali y.
Th
(2)
whe e,
is he densi y [kg/m3]
h is he en halpy [J/kgK]
is he he mal conduc i i y [W/mK]
T is he empe a u e [K]
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6.1. S eady s a e
The calcula ion consis s o applying a empe a u e di e ence o 20K be ween inne and
ou e en i onmen s using as su ace he mal esis ances he ones speci ied in ISO
6946 [18]. The aim o simula ions in s eady s a e is double.
Fi s ly is o calcula e he alue o o he geome y unde ISO 10211 s anda d
(he ea e e e ed as s anda d) and hen compa e i wi h he alue ob ained in he
geome y whe e he cu -o planes a e ede ined acco ding o he p oposed
me hodology (he ea e e e ed as p oposed). The condi ion is ha bo h solu ions mus
ha e simila alue o conside ha hey ha e he same beha iou in s eady s a e.
Secondly he same simula ion is used o he de ini ion o he p oposed cu -o planes.
The e olu ion o he inne su ace con ou empe a u e is analysed in sec ion 7.
6.2. Uns eady s a e
A dynamic simula ion is ca ied ou in each TB analysing bo h he s anda d and
p oposed solu ions. The simula ion consis s on exci ing he ou e su ace acco ding o
he empe a u e o he Fig. 1 and keeping he indoo en i onmen a he cons an
empe a u e o 293K.
The ou e empe a u e exci a ion, composed by a se o ha monic signals o di e en
pe iods and ampli udes, is used o op imize he p ocess o sys em iden i ica ion
me hod. This ype o empe a u e is ep esen ed by a a ie y o exci a ions unde which
he building en elope may be a ec ed and simpli ies he da a analysis o ob ain he
he mal p ope ies o he equi alen wall due o i s a iabili y. Mo eo e , he sudden
a ia ions o he ansien exci a ion signals makes ha he pa ame e es ima ion
esul s will be conse a i e compa ed o mo e con en ional ou e empe a u e
exci a ions. This is, i he equi alen wall beha es like he TB unde he exci emen o
Fig. 1, i will in gene al do i o any exci emen , as will be demons a ed in sec ion 9.1.
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A e e i ying he simila i y in s eady s a e esponse, he dynamic simula ion is ca ied
ou o supply da a o he sys em iden i ica ion p og am LORD. The so wa e gi es he
alues o esis ances and capaci ies o he equi alen wall and hen he mal p ope ies
o he laye s can be calcula ed (Table 3).
Resul s a e checked by epea ing he ansien simula ion o he equi alen wall and
compa ing wi h he p oposed TB (Fig. 8). Su ace empe a u es and in e io hea low
o he equi alen wall line up wi h hose ob ained om he TB cons uc i e solu ion. The
de ia ions in he esul s can be analysed mo e accu a ely wi h he esiduals alues o
Fig. 8d.
When he whole p ocedu e is inished, all he in o ma ion needed o implemen he
co esponding TB o a BES p og am is achie ed. The a ea o in luence o be
implemen ed would be he co esponding o he p oduc be ween he leng h along
which he slab ace TB is gi en and he heigh o he p oposed geome y (0.655 m).
The me hodology has been de eloped o an a ypical dynamic empe a u e exci a ion.
A ypical ex e io empe a u e exci a ion used in building physics calcula ions is he sol-
ai empe a u e E o ! Re e ence sou ce no ound.. I is he e o e ad isable o
check ha he equi alen wall wo ks no only o he exci a ion o Fig. 1, bu also does
o o he ansien condi ions. This e i ica ion is ca ied ou wi h he wea he da a om
Vi o ia-Gas eiz o an a e age day o summe and win e (Fig. 9).
A e con i ming ha in e io hea low and su ace empe a u es i o he eal
cons uc i e solu ion o sol-ai exci a ion (Fig. 10), he de ined equi alen wall
me hodology o TBs is alida ed o e alua e hei eal impac in BES p og ams.
9.2. O he he mal b idges
I has been demons a ed he alidi y o he me hodology o cha ac e ize he equi alen
wall o he slab ace TB. The nex s ep is o analyse he esul s o o he ypes o TBs.
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Below he e a e o he 10 cons uc i e solu ions o TBs wi h he same basis wall o he
slab ace TB (Fig. 11).
Fi s ly he s eady s a e he mal pe o mance is analysed and he alue is compa ed
wi h ha ob ained acco ding o s anda d ISO 10211 (Table 4).
Secondly he esiduals o he in e io hea low and su ace empe a u es a e shown in
Fig. 12 due o he dynamic esponse o he exci a ion o Fig. 1.
In he esidual esul s he same scale o axes ha e been used when possible o an
easie analysis, bu in he low ine ia TBs hea low and empe a u es a e highe ,
leading o g ea e alues o esiduals. To compa e he di e en magni udes o in e io
hea low, Fig. 13 shows he esponse o all he e alua ed TBs and also he esponse
o he basis wall (homogeneous) as e e ence.
Each TB has di e en cha ac e is ics, esul ing in di e en esponses o he same
exci a ion (Fig. 13). When he impac o TBs a e assessed in BES using he alue o ,
wo di e en cons uc i e solu ions wi h he same in ol e he same he mal
beha iou . Howe e , i has been shown ha he ine ia o he TBs plays an impo an
ole in ene gy calcula ions, so i is necessa y o include i s e ec .
10. Conclusions
A me hodology has been de eloped o calcula e an equi alen wall wi h he same
dynamic he mal beha iou o a TB. The calcula ed equi alen wall has he same
a e age in e io hea low and su ace empe a u es o he analysed TB, bu wi h one-
dimensional hea low which allows implemen ing his solu ion in BES p og ams. Thus,
no only he addi ional hea low o he TB would be aken in o accoun , bu also i s
ine ial e ec s. The me hodology can be applied o any ype o TB.
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One o he inno a ions o he p oposed me hodology is ha o he dynamic
cha ac e iza ion o a TB, cu -o planes mus be eloca ed modi ying ISO 10211
speci ica ion. By compa ison o linea he mal ansmi ance () i is shown ha he
p oposed geome y beha es simila ly o he s anda d geome y a s eady s a e. The
highes de ia ion is gi en in he mee ing be ween açade and he oo TB wi h a
di e ence o =0.019 W/mK (3.5% e o ). Fu he mo e, eloca ing he cu -o planes
he in luence a ea o he TB is de ined so ha he simula ed geome y co esponds o
he a ea o be implemen ed in BES p og ams.
On he o he hand, despi e he p oposed and s anda d geome ies ha e he same
beha iou in s eady s a e, i is shown ha in dynamic egime i is di e en . In
conclusion ISO 13786 app oach o he dynamic cha ac e iza ion o he TBs unde
es ima es hei dynamic impac . Summa izing, i he cu -o planes a e eplaced
acco ding o he p oposed me hod and hus he in luence o he homogeneous pa o
he cons uc i e solu ion is educed, di e ences a e no iced in he ansien beha iou
o he TB, bu s a iona y p ope ies a e kep .
The he mal p ope ies o he equi alen wall a e calcula ed using he moelec ic
analogy and sol ing he s a e equa ions by sys em iden i ica ion me hods. Fo any TB a
gene ic equi alen wall o h ee laye s is assigned wi h i e esis ances and ou
capaci ies in each laye . No ice ha o each TB a di e en elec ical ci cui can be
designed, simple o mo e complica ed, bu he aim is o make he me hod gene al.
The esiduals o in e io hea lows and su ace empe a u es o di e en TBs a e
p esen ed o a andom ou doo empe a u e exci a ion. The wo s esul occu s in he
blind box and lin el TB, which is a low ine ia TB. In his case, he a e age esidual o
inne su ace empe a u e, ou e su ace empe a u e and in e io hea low a e 0.5 K,
1.4 K and 4.06 W/m2 espec i ely. In he es o TBs he esiduals a e much lowe ,
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being espec i ely he inne su ace empe a u e, ou e su ace empe a u e and
in e io hea low esiduals, 0.1 K, 0.6 K and o 0.45 W/m2.
The nex s ep would consis o implemen ing he equi alen wall he mal p ope ies in
BES p og ams o analyse he TB impac in a building. Resul s could be compa ed wi h
o he me hodologies which use as a pa ame e o e alua e TBs impac .
Re e ences
[1] IDEA, P ac ical ene gy guide: E icien and esponsible consump ion, Ins i u e o
Ene gy Di e si ica ion and Sa ing, 3 h edi ion, G a icas Mon e eina, Mad id,
2011.
[2] J.A. Cla ke, Ene gy Simula ion in Building Design, 2nd edi ion, Bu e wo h-
Heinemann, Ox o d, 2001.
[3] G. Mao, The mal B idges. E icien Models o Ene gy Analysis in Buildings,
Depa men o Building Sciences, Kunglika Tekniska Högskolan, S ockholm,
1997.
[4] G.H. dos San os, N. Mendes, P.C. Philippi, A building co ne model o
hyg o he mal pe o mance and mould g ow h isk analyses, In e na ional Jou nal
o Hea and Mass T ans e , 52 (2009) 4862-4872.
[5] D.B. C awley, J. Hand, M. Kumme , B.T. G i i h, Con as ing he capabili ies o
building ene gy pe o mance simula ion p og ams Building and En i onmen 43
(2008) 661-673.
[6] P. S achan, A. Nakhi, C. Sande s, The mal b idge assessmen s, Ene gy
Sys ems Resea ch Uni , Uni e si y o S a hclyde, Glasgow, Sco land, 2009.
[7] S.A. Al-Sanea, M.F. Zedan, S.N. Al-hussain, E ec o he mal mass on
pe o mance o insula ed building walls and he concep o ene gy sa ings
po en ial, Applied Ene gy 89 (2012) 430-442.
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[8] N. As e, A. Angelo i, M. Buzze i, The in luence o he ex e nal walls he mal
ine ia on he ene gy pe o mance o well insula ed buildings, Ene gy and
Buildings 41 (2009) 1181-1187.
[9] E. Kossecka, J.Kosny, Equi alen wall as a dynamic model o he complex
he mal s uc u e, Jou nal o The mal Insula ion and Building En elope 20 (1997)
249-268.
[10] E. Kossecka, J.Kosny, Th ee-dimensional conduc ion z- ans e unc ion
coe icien s de e mined om he esponse ac o s, Ene gy and Buildings 37
(2005) 301-310.
[11] ISO 10211, The mal b idges in building cons uc ion. Hea lows and su ace
empe a u es. De ailed calcula ions, 2007.
[12] K. Ma in, A. E ko eka, I. Flo es, M. Od iozola, J.M. Sala, P oblems in he
calcula ion o he mal b idges in dynamic condi ions, Ene gy and Buildings, 43
(2011) 529-535.
[13] ISO 13786, The mal Pe o mance o Building Componen s. Dynamic The mal
Cha ac e is ics. Calcula ion Me hods, 1999.
[14] ISO 14683, The mal B idges in Building Cons uc ion. Linea The mal
T ansmi ance. Simpli ied Me hods and De aul Values, 1999.
[15] FLUENT 6.2, Use Manual. ANSYS Inc., 2005.
[16] C. Bo gel , G.G. Rod iguez, W. T u schnig, M.A. Kubiano, M.A. Gil, P.
G zego zewski, O. H yniewics, Combining so compu ing and s a is ical me hods
in da a analysis, 1s edi ion, Sp inge -Ve lag, Be lin, Ge many, 2010.
[17] O. Gu schke , LORD 3.2. PASLINK Eu opean Economic In e es G ouping,
B uselas, Belgium, 2002.
[18] ISO 6946, Building componen s and building elemen s. The mal esis ance and
he mal ansmi ance. Calcula ion me hod, 2007.
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2
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[19] K. Ma in, A. Campos-Celado , C. Escude o, I. Gomez, J.M. Sala, Analysis o a
he mal b idge in a gua ded ho box es ing acili y, Ene gy and Buildings, 50
(2012) 139-149.
[20] S. Ca pen e , Ad ances in modelling he mal b idges in building en elopes.
Ene modal Enginee ing Limi ed, Ki chene , 2001
[21] J. Nygaa d Nielsen, H. Madsen, Modelling o hea dynamics using he mal
ne wo ks. Sys em Iden i ica ion Sys ems, edi ed by J.J. Bloem, Join Resea ch
Cen e, Eu opean Commission, 1996.
[22] ASHRAE, Fundamen als olume o he ASHRAE Handbook, ASHRAE Inc.,
A lan a, GA, USA, 2005.
TABLES CAPTION
Elec ical ci cui
Hea T ans e
Pa ame e
Symbol
Uni s
Pa ame e
Symbol
Uni s
Elec ical cu en
I
A
Hea lux
Q
W
Po en ial di e ence
V
V
Tempe a u e di e ence
T
K
Elec ical esis ance
R
The mal esis ance
R
K/W
Capaci ance
C
F
The mal capaci y
C
J/K
Table 1 – The moelec ic analogy
Laye
Ma e ial
Thickness [m]
[W/mK]
[kg/m3]
cp [J/kgK]
1
Pe o a ed b ick
0.115
0.667
1140
1000
2
Mo a
0.015
1.000
1700
1000
3
Polyu e hane
0.040
0.028
30
800
4
Ai ca i y
0.020
0.118
1.23
1006
5
Ce amic block
0.045
0.445
1000
1000
6
Plas e
0.015
0.300
900
1000
7
Pa que
0.010
0.130
500
1600
8
Glass ibe
0.020
0.050
104
840
9
Mo a
0.050
1.000
1700
1000
10
Long hollow b ick
0.310
1.128
1040
1000
Table 2 – The mal cha ac e is ics o he slab ace TB
Laye
Thickness [m]
[W/mK]
[kg/m3]
cp [J/kgK]
1
0.083
0.650
1459.2
1000
2
0.083
0.158
1958.4
1000
3
0.083
0.067
0.5
1000
Table 3 – The mal p ope ies o he equi alen wall o he slab ace TB
Table(s) wi h Cap ion(s)
TB
1
2
3
4
5
6
7
8
9
10
s anda d
[W/mK]
1.30
0.15
0.08
0.64
0.53
0.07
-0.07
0.36
0.26
0.47
p oposed
[W/mK]
1.29
0.14
0.08
0.65
0.51
0.06
-0.08
0.36
0.26
0.47
·103
[W/mK]
0.89
9.01
0.57
-4.05
18.8
12.6
9.98
1.42
1.37
-0.08
Table 4 – compa ison be ween he s anda d and p oposed geome y
FIGURES CAPTION
Figu e 1 – The mal bounda y condi ions o dynamic calcula ions
Figu e 2 – Elec ic ci cui model o h ee laye s equi alen wall
Figu e 3 – Cons uc i e solu ion o he slab ace TB
Figu e 4 – Inne su ace empe a u e dis ibu ion in he slab ace TB
Figu e 5 – Slab ace geome y o he p oposed me hod
Figu e 6 – In e io hea low compa ison be ween he s anda d and p oposed geome y
Figu e 7 – Iso he ms in he slab ace TB a) s anda d geome y b) p oposed geome y
Figu e 8 – Compa ison be ween he p oposed slab ace TB and i s equi alen wall a)
ou e empe a u e b) inne empe a u e c) in e io hea low d) esiduals
Figu e 9 – Win e and summe ypical sol-ai empe a u e in Vi o ia-Gas eiz
Figu e 10 – Residual compa ison be ween he slab ace TB and i s equi alen wall o a
sol-ai exci acion
Figu e 11 – Cons uc i e solu ions o he analyzed TBs
Figu e 12 – Residuals o he analysed TBs
Figu e 13 – In e io hea luxes o he he mal b idges and he homogeneous wall
Lis o Figu e Cap ions
An equi alen wall me hodology o he mal b idges is de eloped.
The in luence a ea o he he mal b idges is ede ined by he cu -o
planes.
The equi alen wall can easily be implemen ed in building ene gy
simula ions.
Ele en ypes o he mal b idges ha e been e alua ed o he
me hodology alida ion.
*Highligh s ( o e iew)
