Session II No.6

Surface Heat Transfer in Building Components

G. Fracasloro M.Masoero M.eall ASHRAf Assoclafe Member

ABSTRACT

Design surface heat transfer coefficients that take into account both convection and radiation are customarily used in the 'Nll'colation of the heat' flow ,transmitted through building components. This simptified approach tnay lead to incorrect results, particularly when low thermal resistance components such as windows are concerne'd~ and when ,:long-term energy flow calculations. rather than peak load cal,culations" ar,e perf,o'rmed. The rigorous approHch~ oh the contrary. consists of solving the energy balance at' the sudace"of a ,comp~m,ent taking into account the appropriate boundary conditions. In this article, radiative and convective heat losses at the outside and ~nside sti:r£ace's are "calculat'e'd' as a function of know meteorological factors and of the temp­erature and geometry of 'the "ipte'rnal and 'external surroundings. The overall energy balance of the component is written and'soived numericaliy. A parametric analysis is performed in order to assess the influence 'of variouS' building parameters and outdoor conditions on heat transmission through single glazings. Energy calculations for a typical northern Italian location are also presented.

INTRODUCTION

Transmission heat losses represent one of the major contributions to the energy demand for build­ing heating. It is customary to ,calculate transmission losses simultaneously taking 'into account both heat conduction inside the ,buil/;ling envelope and heat transfer by radiation and convection at the inside and outsid~ boundaries of the envelope. A large body of theoretical and experim­ental work on heat conduction in building components has been published in the last several year$.1,2,3 On the contrary, less 'attention has been devoted, by 'the res'earch community to sur­face heat transfer in building coinponents'~ Recent studies' have shown t~e difficulty of standard­izing surface heat transfer (SHT) dependence on environmental factors.

In" performing heat loss calculations SHT is usually treated by making rather crude approxim­ations: convective and radiative effects are normally lumped together by 'introducing a single, constant surface heat transfer coefficient (SHTCh Sometimes, two values are used for "linte,r and

, 5 6 summer calculat1ons.· The heat flux, Q. eXChanged at the wall surface is normally written as

with h h + h

r c

(1)

(2)

Giovanni V. Fracastoro, Marco Masoero and Michele Cali. Dipartimento di Energetica, POiitecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.

180

wall surface tempera'tlire air temperature surface heat tLan,sfer eoefficient radiative heat transrer. 'coefficient convective heat, trans'fer' coefficient

Eq 1 is simple and e'asy to use but does no,t, represent accurately the physical reality. Radiative heat transfer" in fact, depends on the diffe-:rehce of the fourth power of the radiating surfaces te'tnpe:ratures, :~nd is' tb'~iefore 'not dijrectly>rel:afed' to T -T . Moreover. it should be stressed that the convective coefficient, he t ,is a cfuncti'o~>of ~w,"',ta; and wind velocity" and is therefore not constant.

The: simpIi,fied representation of surface heat' t,ransfer described above is~ however, adequate ih many applications, such as:

1. In heating or cooling load calculations,' where the design values 6f the SRTCs should represent extreme heat loss conditions

2. When low-thermal-conductance components (e. g., insulated walls) are considered~ for in this case the conductive thermal resistartce of the wall itself is large compared with the surface resistances, and eVen large variations of these have little effect on the overall heat transfer

HowevE'r:t a more de-tai l£'d analysl s of surface ht'!at transfer is required when long-term or seasonal energy calculations are performed. In this case, in fact, it is incorrect, to assume for the heat transfer coefficients values corresponding to extreme weather conditions (e.g., winter design values). This is particularly important when window heat losses are analyzed.

The purpose of this paper is to present a method for calculating the energy balance of a

window. It is important to point out the basic differences between the method presented here and that illustrated in the ASHRAE Handbook of Fundamentals. 7 According to the ASHRAE approach~ the total heat admission (or loss) through a single-glazed window is written as

where Q~TI +N(aI)+U(T -T,)

t t 0 1-

T I = radiation transmitted through, the glass N (~I ) :: inward flow of absorbed solar radiation

t " . U (T - T. ) =, heat flow due to ,'outdoor-indoor ,temperature difference

o 1

(3)

Eq 3 is simplified by lumping together the two first terms (i.e., the heat flows of solar origin) into the "solar heat gain"; hence

Q~ FI +U (T -T,) t 0 1

(4)

The solar heat gain, F It, and the "conduction ately using tabulated values of F ,and U.

heat gain", U (T -T.), are then calculated separ­o 1

The: approach presented in this paper is based on the following physical considerations. The absorbed solar radiation modifies the thermodynamic state of the glass, thus affecting the heat t,ransfer at the glass surfnce. It is therefore convenient to compute the second and third terms of' Bq '\ HimultlllH'otisly. hy solving the glohal energy balance' of the glass. 'I'lw radiation tra(lS­

mitll·d through the gl.'IHS. nil tlw eontrnry, eltn be eomputed iudepcrldentLy. b{dng dependl'nt on the radiative properties of the glass and on the impinging solar ·radiation only. 'l'he total heat admission through the glass is then written as

(5)

where Qloss represents the heat flow leaving the indoor environment through the window.

Two types of calculations are shown in this paper. A parametric analysis wa~ I'erf~:rmed in order to assess the dependence of Q on building propel'ti:es and outdoor condit,ions~ ,~h~:,,:~verage heat loss during the heating seasonl~~~ also calculated ror a single-glazed window in TorIno.

181

MECHANISMS OF HEAT TRANSFER AT A WALL SURFACE

In the most general case, heat is transferred at a wall surface by the combined mechanisms of conduction, convection, and radiation. The magnitude of each heat transfer component is a complex function of wall physical properties, surface temperatures, indoor and outdoor environmental conditions, etc. These components cannot be calculated separately; instead, they must be det­ermined via the solution of simultaneous energy balance equations.

The global energy balance over two infinitely thin layers adjacent to the wall surfaces is shown in Fig. I and gives rise to the following equations

where

o

net radiation flux = convection flux:

conduction flux: subscript referring to subscript referring to

the inside surface the outside surface

o

o

(6a)

(6b)

It is worth stressing that Qk

i wall in unsteady heat transfer, in the following sections, the flux.) By definition, the heat

Qk .'

may be different from Qk

,either because of heat storage in the or because of internal h~~t generation. (As it will be discussed

.' Radiation

absorbed solar radiation can be treated as flux leaving the indoor environment (Qj

oss

an internally generated of Eq 5) coincides with

Radi{ltiv(> energy ('xch.mg('d by a Rurfnl:(' can he Hplit: into two (~UmIHIIH'l\lH~ i.t,., ttl!' Hhurt­w.:lve radiation (A ~ 4' JIm), and the l'ong-w/lve radiation (4 ~m< >. < 100 tlm). This Huhdivisioll iH convenient for two reasons. l<'irstly, the measurements of short-w3VP and long-wave radiation are performed using different instruments: pyranorneters and pyrheliometers, which are sensitive to radiation in the short-wave (solar) spectru~ and pyrgeometers (also called infrared radiometers), which are sensitive to long-wave radiatioR. Secondly~ the radiative properties of most build­ing materials differ dras,tical1y iri, the two spectraJ regions. For example, regular glass is remarkably transparent to'sola,r ,radiation, but virtually opaque to long-wave (e. g., atmospheric) radiation.

Sho,rt-wave radiation is origiflltted by ,the: sun and reaches the wall through different paths, _ because of atmospheric, extinction' and d}ff,tIsion a!ld to 'reflections from the surrounding sur­faces. Long'-'wave radiation 'i~ originated b:y "~mi'sSioh ,and 'reflection from any bodY' in the ter­restrial sphere, such as walls, the ground, and atmospheric layers. 9

The radiation fluxes at a wall surface are represented in Fig. 2. Q is the short-waVE­radiation impinging on the wall, nnd consi$'ts of<:threl': diS,tinct (:ompone~ts: be.lm, diffus('~ und reflected radiation (for a definition of the above,'fiee, -for example, Duffie, ,md Beckman),.IO Of flux Qs' the fraction p Q is reflected by the'surfae'e, the fraction a: Q is abs'orbed, and the

. . ~s, b' l' b ss fract10n tsQs

1S transm1tted through the wall. 0 V10US y, 1t,must e~

p+ct+T ""1 s s s

(7)

p , ct , and T are, respectively, the short<--wave hemispherical reflectivity, absorptivity, and t~ans~issivitySof the wall. a is given by

s • ;;/.4 "m.('IQ (,) d, IQ (8) s 0 11m s s

a is therefore the weighted average over the solar spectrum of the hemispherical monochromatic agsorptivity, a(A), of the surface, where the weighting factors are the spectral values. QS(A), of the impinging radiation. Similar definitions apply to p sand l" s· p s' Ct s' and T s thus depend

182

nn the material of which the surface is made. but also on the spectral distribution and incident angle of the impinging radiation. In practice. constant values of Ps' ex , and \s; determined with reference to typical solar spectra, can be used. II s

. QI

is the long-wave radiation impinging on the walL Using a formalism that is identical to that of short-wave radiation, the properties of the surface in the long:-wave region aTe ident­ified by the long-wavE' hemispherical reflectivity, PI' absorptivity t (Xl' and transmissivity, \1' which are mutually related by the equation

PI+al+T1=1

al (and similarly PI and \1) is defined as

al~ 14°OprnaO) Q1 (,) d, I Q1

(9)

(10)

Ordinary building materials, including glass, ,are virtually opaque to long-wave radiation; hence one can assume T

1:: O.

Q is the long-wave radiation emitted by the wall as a consequence of its temperature T e w

For a grey surface and at thermodynamic equilibrium one can write 4 4 (11) Q = E aT "" r:t{JTw e 1 w

The reflected and transmitted fluxes do not affect the thermodynamic state of the wall; hence they do not appear in the balance equations; which take into account the absorbed and emitted components only. The rt~[lccted,and transmitted fluxes, however, must be considered in the rad­iative balance of an insJde surface; these components, in fact. affect the mutual radiative ex­{~hang('s among the surfaces dclimi..ting the room. For tm outside surface~ on the contrary. thE' impinging radiation e.iu he calculated on the basis of meteorological data only.

The balance equations assume different expressions in the case of opaque and transparent walls. for the mechanism of radiation absorption differs in the two cases. While for an opaque wall radiation is absorbed at the surface, for a transparent wall radiation is absorbed over the entire thickness of the wall. In the latter case, the absorbed flux may be treated as an internal heat production; thus, the absorbed radiation can be incorporated in the conductive flux. One can therefore write the ~ radiation flux at the surface for an opaque wall (a = a = 0) as

s 1

Qnet= Qe- a sQs - a l Ql

and for a transparent wall (asl 0, al= 0) as

Qnet Qe- a 1Ql

(12)

(13)

The calculation ot Q and QI' for an inside and outside sections. Q is calc~lated. in all cases, using Eq 11.

e

surface, is illustrated in the next two

Outside Surface. 'The short-wave radiation flux impi.nging on an outside surface is given by

r

global solar radiation beam radiation diffuse radiation reflected radiation

Q s

I t Ib+1d+1r (14)

When measured values of t are not available for the considered surface orientation; the follow-. . t 12 1ng' express10ns may be used:

Ib = Ibn cos 8

I = F Idh d s.w I "" P F (I

b sin 13+ I

dh) '" p F 1

r g g.w n g g,w th

183

(ISo)

(lSh)

(150)

where F ps.w= rg,w= bn

o = 'db Pg a

view factor between sky and surface view factor between ground and surface beam normal radiation incidelit angle between sun direction ,md sur(ill:('

diffuse radIation on a horizontal surface

reflectivity of the ground altitude angle of the sun global radiation on a horizontal surface

Ith 13

(For the definition of the angles eand Bsee, for example, the ASHRAE Handbook of Fundamentals.) Assuming that an outside wall views two surrounding surfaces only, the sky and the ground, and that the ground and the sky are isotrope radiators, the view factors become

where L =. til t angle of the surface

F s,W

F g,w

[1 + cos(E+A)] /2

[1 cos (E +A)] / 2

1 - F S,W

A = average elevation angle of the ground above the horizon

The hmg-wave radiation flux, Ql' impinging on the surface is given by

Q = G + G 1 a g

G atmospheric radiation G

a ground radiation

g When direct measurements of Qrare not available, the following formulas may be used

G a

G g

atmospheri~ radiation ,on ~ horizontal surface emissivity of the ground temperature of the ground

To calculate G the following model is often used ah - 4

Gah

= crT sky

(16a)

(!6b)

(17)

(180)

(l8b)

(19)

is called the "apparent sky facing the earth with a view

same rate as the sky. T k may be

temperature,1I and is defined as the temperature of a black factor of 'one, and exchanging radiation with the earth at the 4 calculated with the formUla, adapted from Unsworth and Monteith

l

where

s y T

sky

1.5 0.0553 T +2.625 CC

a,o

T outdoor air temperature (in degrees Kelvin) C~,o= cloUd cover (in eighths)

(20)

To determine G • it is reasonable to consider the ground as it black hody or temperature· equal to

ambient. Henceg

G • F (21) g g,w

Inside Surface. The radiation balance of an inside surface involves the mutual exchanges between the walls delimiting the indoor environment and the radiation incoming from the transparent walls; the latter can be assumed entirely short-wave, as discussed in the previous section. The balance will be worked out separately for the short-wave and long-wave components. Let us assume that all the surfaces delimiting the environment are grey and uniform in temperature, and that the short-wave radiation transmitted through the glazed surfaces, I , is diffuse.

184 trans

The short-wave radiation balance of the j-th surface is n

where J . s,]

p • "1 F. J + I . s,J k= J,k s,k trans,]

J . = short-wave radiosity F

S,] = view factor between

j,k

of the j-th surface the j-th and the k-th surfaces

(22)

The long-wave radiation balance of the j-th surface includes, in addition.to the mutual reflect­ions, also the long-w~ve radiation emitted by the surfaces, here considered as grey bodies of emissivity E.I (= at)' Thus, the lbng-wave radiosity, of the surface is

n E ,F. J

k=l J.k l,k (23)

Itt order to calculate the radiation f'luxe's exchllnged by the n~ inside surfaces. the radiosities J s and J1 of the n surfaces must be first determined by sGlving the 2n simultaneous equations 22 and 23. Once the radiosities are known, one can calculate Qs and Ql for' the j-th surface

n

Q s,j " F k;:l j ,k

n

J _.k 91 . = E

F. k J ,J k=l J, 1,k

Convection

The conve'ctive heat flux, Qc

' exchanged at a wall surface is given by

h(T-T) cwo

,hc average convective, heat transfer coeff1cient over the surface Tw wall surface temperature Ta ;: air temperature

(240)

(24b)

(25)

The convective heat'transfer coefficient depends on the airflow pattern around the building and o.n the temperature difference between wall and air. In the case of an inside surface, one can generally assume that the air velocity is negligibly small. Therefore~ convection takes place as a result of the temperature-induced air motion (natural convection) in the presence of the &ravitational field. A wider variety of situations can occur in the case of an outside surface, where both natural and forced convection are likely to exist. In this case, measur'ements of wind velocity are needed, in order to characterize the ait flow regime around the buildings. However, the reduction of the wind velocity measured, for example, several meters above the roof to the local air velocity on any surface is far from trivial, because of the complexity of. the airflow patterns in the built environment. IS This problem, which is the SUbject oe ex:tensive research in many countries, is often tackled with wind tunnel tests on",scale models, and with sophist­icated, computer simulations. Once the local air velocity has been estimated, stao~ard convective heat transfer correlations" can be used to. calculate he'.

Let us introduce the following symbols: P density of air c specific heat of air kP thermal conductivity of air V dynamic viscosity of air v local wind velocity s g L R. Pr Gr

coefficient of thermal expansion of air local gravitational acceleration characteristic length of the problem Reynolds number = p v L I V Prandtl number cp II '/ k

3 2 2 Grashof number g (Tw - Ta) L p Sill

185

(The physical properties of air are calculated at the temperature Tm to the geometry of the problem, five basic cases can occur:

(TW +Ta )/2.) According

1. vertical surface 2. horizontal surface. ascending heat flow 3. horizontal s9rtace. descending heat flow [I. inclined surface. ascending heat flow 5. inclined surface, descending heat flow

Whether naturnl or fOl"c(;'cl convection domhi.ates clep('nds nil lIw m'lgnit.udp or till' Ttllio

2 r = Gr/Re (26)

If r» 1 natural convection domittates~ if r '" 1 mixed convection exists, and if r« t- free convect..:..

ion dominates.

Forced Convection. The following 'formula, valid"for laminar and turbulent flow. can be used in

all the above cases: l6 ' 1/3 0.8

he ; k Pr (0.035 Re - 836)/L (27)

Natural Convection, can be employed to

Depel1ding ,on""the

calculate hc: 1}

geometry of the problem, one of the following fomulas

Case 1: PrJ 1/.4 h 0.59 (Gr k/L ,'for 1O~ Gr 9 (28a) = Pr<.lO

e ,;1/3 109< 10

12 h • 0,13 (GrPr) k/L for Gr ,Pr< (28b)

e Case 2: ,"<1/4 5

107

,lie 0"54 (C/1>.%'). 'k!L for 10 '<: Gr Pr< 2 (29.)

h 0.14 (Gr pr)~/.3k/L Ear 2 107

-< Gr Pr< 3 1010 (29b) c

Cas'e ,3: Pr)1/4 10

10 h 0.27 (Or kIt for 3 10

5 <: Or Pr --:: 3 (0)

e Cases 4 a.ble by

and 5: In replacing

the caSe of a surface iilciined by an angle};, Eqs 28li'and 2ttb are still <1pplic-

Or with,Or c~s;< , 1\

Conduction

Conduction in, walls" is' usually "treated ~s, a one-dimensional, time-dependen't problem~ for wbich several analytical and numerical soiutions Jlre avaUable in the literature. When low-thermal resistance walls are considered: 'or when long"'L~erm average heat flows are computed, transient effects can be usually neglecf;ed ___ 'The cond~ctipn eqiJatitJn then reduces to

In order to take into account the effect conduction model must be introduced. The introducing an internally generated flux

(31)

of radiaqon,absorp::ionhl the glass, a different heat absorbed fadiation~ ~ Q-', is taken into account by

S s

Q • a Q Id v s s

(32)

where d is the thickness of the wall. With these ,assumptions', the conduction equation [or ~I

single-layer, homogeneous wall becomes

(33)

The solution of Eq 33 is

(34)

where ci and Cz are two constants whose value is determined by introducing the boundary conditions

6a' and 6b:

186

Qk

• ,1

k(dT/dx),..O (35a) - Q • - Q • C,1 net,1-

Q It.o

- k(dT/dx)X=d (35b)

RESULTS

A simplified model has been developed in order to analyze the surface hent transfer of building _ components. In this study, the model has been applied to single-glazed windows. This choice is justified by the wide diffusion of this type of window in Italian buildings. Two types of calc­

ulations have been performed: 1. A parametric analysis of the influence of meteorological factors and indoor temperatures

on the energy budget of a window 2. The 1lIonthly average energy balance of a window during the heating season for different

orientations and for one geographic location

The calCUlations were made under the following simplifying assumptions: 1. An ideal room delimited by two parallel and infinitely close walls (see Fig. 3) was

considered; the external wall is subdivided into two adjacent surfaces (1 and 3): surface 1 is the glazing surface being analyzed, and surface 3 is a slltface of given,

constant temperature T3 2. The internal wall (surface 2) temperature, T2, is given and constant 3. The short-wave transmissivity of the glass is assumed independent of the incident angle 4. The meteorological data used in the analysis are: outdoor air temperature, OAT, cloud

cover, ce, solar radiation, 1T, and wind velocity, Vi the atmospheric radiation is calculated with Eqs 19 and 20

The energy balance of the system is determined under the above assumptions by solving the simul­taneous non-linear Eqs 33, ,'35a~ and 35b, using the Newton-Raphson technique. 18 The calculations were performed usi.ng the following data:

J. Radiative proporties of the glazed surface: a "" 0.1- 0.2, '( "" 0.7, (11"" 0.9, Tl = 0

2. Thermal conductivi ty of the glass: k = 1 (W/mK' s 3. Gtasf.> thickness: d'" :3 10-3 m 4,. Wall height (used in natural convection calculations) 3 m

5. (Area of surface 1)/ (Area of surface 3) "" 0.5 6. Inside air temperature : 20

o e; T3 = 16°C

The results can be expressed by means of either the surface temperatures, or the heat fluxes, or through the conventional heat transfer coefficients:

h. 1

h 0

U

(Notice that. to be consistent with the Qloss = Qk,i rather than to Qk,o·)For the following results were obtained:

2 Qloss

= 92.7 W/m

2 U = 4.64 W/m K

Q /(T.- T . ) loss a,1 w,1

Qloss /(T - T )

w,o a,o

= Q I (T a,i - T )

1058 a,o

definition of U. h o

example, assuming OAT

T. 8.6 °c 1

. h. . 2

8.14 W/mK 1

(36)

(37)

(38)

is calculated with reference to DoC, V = 0, CC = 0, T2 = 20, IT

T 8.3 ·c 0

h 11.13 W/m2K 0

A sample of results of the parametric analysis is shown in Tables 1, 2, 3, and 4, and in

0,

Fig. 4. Each table gives the values of U, h., and h as a function of OAT. Tl, and IT. The results of Tab. 1 were obtained by assuming V = 0, Ce = 0, god a = 0.2. The results of Tabs 2, 3, and 4

s 187

were ob t8ined by taking respecti ve ty V '" 5 m/ s, CC '" 8. ,'md 0: s

the same as in Tab. 1. Fig. 4 shows the trends of Q1

• l/h .• OBI> I

at constant OAT and ce.

= O. I. the other parllmcters

and l/h as a function of V o

being

and IT,

The sensitivity of U, h •• and h to the variations of the parameters V, IT, ce. OAT, and '£2

is illustrated by the re$ult~ of Tab? 5~ A reference case was considered corresponding to V = 0, IT '" 0, OAT"" aOc, and '1'2 '" 20"C. The range of variation of each of the above parameters is given in the first row of the table. The corresp'onding percentage variation of U, h .• and h , with

• ' ~ 0 respect to the reference case, has been calculated keeping the other parameters constant and equal to the reference case. (Notice that the variations would be different if more than one parameter is varied at a time~) The arrows indicate qualitatively whether the heat transfer coef­ficients increase (t) or decrease (I) when the corresponding parameter increases. The size of the arrow represents the relative magnitude of the variation. The noticeable exceptions to the general trend are pointed out in the,' footnotes.

Some general remarks can be, drawn from the inspection of these results: 1. The heat transfer coefficie~ts are always affec!ed both by meteorological factors and

indoor conditions 2. While the va,d~tions ~f"Q' (en:' '0) "',are n~gular and

ions of h. and h are oft~g~~npredictable and do not phenomeno~ a

physically predictable, convey a physical sense

the variat­of tbe

3. The nega'tive, si~n in"h. or erature difference bet';;een

h may indicate ~Srface and air

ei~her that Q 'reverses or that the t(>Olp-loss

reVerses

The monthly average,energy bala'nce of o!L single-glazed window has been calculated for the city of torino~ using the hourly met:eorological data of the typical day for each month of the heating season." 19 'l:he ,cri~te~,b'f Torino is qtiite' representative at northern Italy (winter design tempe-rature =', ~'ao,c, lleEi6ing" degree-days: :: 2570., average wind speed below 1.0 m/s). Results are presented' in Tab. 6 for a verfical single glazed window,"at three different orientations: south, east (almost identical: to, westL 'riorth. S"lar radiation 'has been computed with Eqs 15 from hor­izontal diffuse and beam,'nonnal'Tadiation:'dat'a. It' has been assumed that the window is unshaded and unshielded. For each month ,of,'t~e, h~ati-",g season (Oct~ber 'through April) the average values of outgoing heat flux, Q

1 ' 'effective U ... value, Uo inside, surface heat transfer coefficient~ h.,

and outside surface heat ~'f~ns~er CO~,fficient', ,tl,".< are giv~n. The seasonal average values are 1

also shown. The seasonal average U-v~lues ,of a s~ngle glazing are' sensibly lower than the winter design U-values suggested by ,the' Italian <~tandards' \{5.'8 W/m2l<h the difference ranges from 27% (for a north-facing win'dow) to '37% (for" a s:Quth-facing' window). Similar calculations have been performed assuming the shielding' of 'the' wil,'idow ,£r'om ':9, PM to 7 AM; in this Case, an average reduct­ion of the effe.ctive U-value of' ab,out 8%' COlI!pared "to ,the unshielded window has been observed.

CONCLUSIONS

The parametric analysis has shown the ~nad~quacy:,'"of ',the,:SHTC' 'in representing surface heat transfer for varying indoor and ,outdoor 'condi'tiql1s: ,The' SRT,q~"is rai," from ,being an invariant, and, moreover, its behavior becomes quite l1npredictahle, ,311,1, disp(n{tInuous 'wtH:~n' high radiation fluxes are present. The analysis of the correspondin'g ':heat:,'f1~iXj£~)3', ,an~ "~~,tYiIcr:('t~mpe'ratures ,~hows. on the contrary. rather regUlar and predietable, behavio~.;'~', --'r:his"'f,~,~,t --may ,su~~'est ,a 'method to treat $lIT in more accurate, albeit simplified, calculations':--'a reference flux: could be' calculated using standard values of, SHTC. and a corrective heat Hux, depending ori if!.door and outdoor conditions, could be added to it. Further developments of ,this rEi:search will ,aim at the definition of such methods.

When simplified long-term' energy calculations ar'e performed, monthly or seasonal average effect­ive U-values should be adopted~ as shown for Torino in the previous section. It must be stressed that the method of analysis presented itt this paper, is aimed at' evaluating transmission heat losses and does not take into account free heat from solar radiation. This method can therefore be used in conjunction with those simplified energy calculation methods taking into account free heat (e.g., modified degree-days).

188

REFERENCES

1. D.C. Hittle and C.O. Pedersen, "Calculating Building Heating Loads Using the Frequency

Re_sponse ot Multilayered Slabs." ASHRAE Transactions 87 (1981).2:545.

2. '1'. Kwwd:l. "Thermal Respons(' Factors [or Multi-Layer Structure of Various Beat Cunduction Systems. It ASHRAf<: Transactions 75 (1969). I; 246.

3. M. Cali, V. Ferro, G~ Fracastoro, M. MasoeTo. and C. Vannelli. "Experimental Analysis of a Test Room Unsteady-State Thermal Behavior," Proceedings of the Second CIB Symposium on Energy

Conserv<ltion in Built Environment (Copenhagen: Danish Building Research Institute. 1979), 4:241.

4. N. Ito, K. Kimura, and J. Oka. IIA Field Experiment Study _on the Convective Heat Transfer Coetficient on Exterior Surfaces of a Building,"-ASHRAE Transactions 68. 1972, p. 184.

5. ASHRAE Handbook--1977 Fundamentals Volume. Chapter 26, "Fenestration,-" p. 26.10.

6. Centre Scientifique et Technique _du Batiment, Regles Th--Titre I Characteristiques Thermiques Uti1es des Parois de Construction (Paris: Cahiers du CSTB no. 1478. November 1977), p. 74.

7. ASHRAE Handbook--1977 Fundatnentals Volume. Chapter' 26~ p. 26.9.

8. K.Y. Kondratyev. Radiative Heat Exchange in the Atmospqere (New York: Academic Press, 1969).

9. R.J. Cole, "The Longwave Radiative Environment Around Buildings." Building and Environment II (1976), p. 3.

10. J. Duffie and lv. Beckman, Solar Engineering of Thermal Processes (New York: J, Wiley. 1981).

11. P. Petherbridge, "Transmission Characteristics of Window Glasses and Suncontrol 11 (Garston,

U.K.: !lui Iding Ih-senreh Station. 1967 BRS Research P<lpers 72 ).

12. ASHHAE fhmdhook--1977 Fundamentals V{~lume, Chapter 26. p. 26.2.

13. ASHRAE Handbook -1977 Fundamentals Volume. Chapter 26, p. 26.3.

14. M.N. Unsworth and J.L. Monteith, "Longwave Radiation at the Ground," Quarterly Journal of the Royal Meteorological Society 101 (1975), p. 13.

15. Ito, Kimura, and aka, p. 185.

16. F. Kreith, Principles of Heat Transfer (New York: Intext Education H?11, 3rd Edition 1973).

17. J.P. Holman, Heat Transfer (New York: McGraw-Hill, 4th Edition 1976).

18. B. Carnahan, H.A. Luther. and J.~. Wilkes. Applied Numerical Methods (New York: J._ W-iley, 1969).

19. Cow-d)',1 in N:n:ioll:IiL' dd Ie i{iet'rdw. Dati <:1 imatid per "1<1 ~Prog('ttazi()n(' Ed} 1(' ('d Imp-iant_i.stic<;l

(Mi Llno. Italy: PBC Bditrice. 1982).

189

lij

'-M"M"~~~

TABLE 1

U-yalue,.inside SHTe, and outside SHTe for 'a single glazing as a function of outdoor air temperature, solar' radiation flux (IT). and inside wall temperature (T2)

assuming wind speed V=O. cloud cover CC~O, and ~s= 0.2

U-VALUE

. -----------------------------~-------------- ,,--------.....,-------------------------------~W{ ~m"'f~*K») INSIDE SHTC (W/(", .. m*l-<n

1 1 I

OUTSIDe SHTC -(loll (m*,(>f,K))

--------------------~-------------------------------------------------------.---------------------~-- ._--------------------1 1 1

1 I 1 1

1 1 1

1 t OuTDOOR-Te~PERATURE (DEG~C) OUTDOOR TEMPERATURE (DEG.C) -. o 5

OUTDOOR TEMPERATURE (PEG. C)

10 -10 -s o • 10 1 1 IT 12 -10 5 10

1 1 1 1 -10 -5 o

--------------------------------------------------------------------------------------------------------------------------1, ' , , . I 1 16 1

o J 20 1

4.5

4.8

5.1

4.5

4.9

5.2

4.6

S.O

5.'

4.7

•• 2

S."

1 4.9 J 7.~

1 5.8 J 8.S

t

7.3

S.4

9.7

~.'1 0.4

8.2 8.0

9.8 ~O.l

5,7 1 B.4 12~:; 14.0 Hf • .(l. 4.J.4 1

7. 7 ~ 11.2 12.0 13.2 1,5.,9 ,24 • .6

10.9 1 J1.1 11.7 12..7 14 .. 5 19.0 I 1 24

1

0.7 J 9.7 I

-------~---------------------------------------------------------------,..--:,.--"'-----_ ... _-------1

4 • .,1 I 1

7 .. 2 I 1

12.6.. 1 I

I 1 1 1 200 1 1

3.7

4.(l

4.3

3.' 3.?

4.3

3.3

3.S

4.3

3.0

3 ••

4.2

7.2

a.4 9.7

6 ••

S.2

9.S

6.3 5.5 7.7

7.9 7',6. 7,.8

1'0.1 10,.7 7.9

7.S

7.7

7.'

7.2

7.4

7.6

6.7

7.0

7.3

'.7 6..2

6.7

1

1 1 J 16. 1 I 1 I 20 1 1 1 I 24 I 1 1

I 2.4 1

I 3.3: J

1 4.3 I

1 --------------_ .. - ---------------------------------------~---... ~-----'-------------------------------1

1 1 1 1 I 14 1 2.'S' 1 1 1 14ooJ2o.l 3.2 1 1 1 J I 24 1 :;.5

2.0-

3.0

3.4

2.1

2.0

3.1

1.4

2.1

2."

1 .0. I 6.e t>.2:

1 1.0 1 8.2 7.9

I 2.1 J 9.& 10..1

5.4 :.s:.9 .0. 1 . 1

7.4 7~'l' 6.0 J t

10..7 1'2.8 «~4 1 I

s .•

'5.4

,.7

4.' 4.9

'.2

3.6

4.1 .. ~ '.3

3.0

3.6

.0

1.2

2.3

1 1 1 1

1 1

___ ""; ____________ ~ ____________ ,_.,... _________________________________________ -7"'---------------------1 1 I 16. I 1 1

2.1

2.'5

2.$

1.7

2.1

2.5

1.0

1.5

2.1

-.1 -2.1 J 6.2 5.4 1

.6 -1.0. 1 7.9 7.b 1

1~4. .1 1 10.1 10..7

3.9 -.3- 129.4 I 1

7.1 6..0. 7.7 1 1

12.8 46..6. - .. 3. I I

3..3

3.7

4.0

•• S

2.9

3.3

1 ••

2.0

2.5

-.2 -2.1

.7 -.9

1.5 .2

1

1 1;'.9 I

1 7.8 J

1 4.1 1

1

bOO 1 20. I 1 1 I 24 1 1 1 __________________ ... _____________________________ ...-c-. ________________________ -------------------------------

I 1 1 I SOo. 1 1

1.4

1.7

2.1

.a -.0

1.2 •• 1.7 1.1

.1 '~1.4 -4.1 I 5'.4-

1 -.e. -'3.1 I 7.f,

1 .1 -2.l 1 10..7

3.9

7.1

12.7

-.3 119.6.

6..0 7.7

41.4 -.0

1.9 1.1 -.0. -1.4 -3.2

2.3 1.S .'5 -.6 -2.3

2.7 1.' 1.1 .1 -1.4

1 16 1

1 20 1

1 24 1

1 1 1 --------------------~ ~----------------------------------------------------------------------------------------------------

~' .. ~ -~.-•. ---.--.,-.• ---~~-------- ---'-----

§

TABLE 2 U-value, inside SHTC, and outside SHTe for a single glazing

as a function of out4oor air temperature, solar radiation flux (IT), and inside wall temperature (T2) assuming'wind speed V=5, cloud cover CC=O, and 0. =,0.2 s

-----------, -- ---- - ._---------------------------------------------------'_ .. _-----------------------------------------

U-\i'lLUE (W( (m_m*IO} INSIDE SHTC o.U (m-l'm_"'> t OUTSIDE SHTC (W/(ffl"*m*K))

----------------------------------------------------------------------------,----------------------------------------------1 I 1 1

! ! !

OU1DOOR TEMPERATURE (OEG.C) OUTDOOR TEMPERATURE (DE~.C)

-10 -. o • OUTDOOR TEMPERATURE (DEG~C)

10 -10 ..,. o • 10 1 IT T2 -10 • 10 -. o ---------------------------------------------------------------------------~---------------------------------------------! 1.

o 20

24

'.7

•• 1

•• 4

••• •• 1

•••

••• •• 1

•• 7

'.5 •• 2

7.0

1 5.3 J e-,o 7.7

1 6..5 I B,a •••

1 7.7 1 9.7 9.7

1

7.2

••• '.7

6..7 5.e

8.1 7.9:

9.9 10.3:

21.2 22.B 25.7 32:.7 72.$ 1 1

20.7 22.1 2:4.3 28.9 43.9 I 1

20.4 21.5 23..2 26..4 34.1 J 1

---------------------------------------------------------------------~------------------------------------1 1

13.2: I 1

13.8 I I

14.1 1 I

1 I 1. I 1200120 1 1 I I 24

5.1

5.4

S ••

4.' •• 3

5.'

4.7

'.2

•••

4.3

S.O

•••

1 3.6- 1 7.e-

I 4.8 I S.7

! 6-.0 I 9.7

I

7.'

••• '.7

4.'1' 4.2 5.0 1 15.3 15.2 15.0 14.5 I

8.2 7.'1' 7.'5 I 15.4 15.2 15.0 14.4 I

'1'.8 10.1 10.9 I 15.4 15.3 15.1 14.8 I

I -----------------------------------------------------------------------------------------------------------------------I

3.6. I 1

7.1 1 1

12.5 I 1

'00

1 1 1. I I 20 1

4.~ '.2 ••• 4 ••

5.2 S.1

3 •• 3.1

'.3 3.' '.9 •• 7

I 1.9 1

1 3.1 I

1 4.3 I

1

7 ••

••• '.7

7.1 •• S S •• 11.3

•• 3 •• 1 7.7 11.4

'.7 ••• 10.4 Jl.B

10.5

10.8

11.2

9.2

••• 10.2

7.3

•• 2

•••

4.0

5 ••

••• I 2. I --.. ----------------------------.~------------------------------------~----------------

I ,. 3.8

6-00 I 2:0 4-.2

2' 4 .•

3.' 3.' •••

2.' 3.' '.1

2 ••

2.7

3 ••

1 .2 I 1.3-

I 1.4 I 8.4 , 2.7 J 9.7

I

4.8 6-.0 4.4 .7 I 8.4 ]

8.2: 7.9 7.4 4.4 I 8.S 1

9.8 10.2 1l.3 19.9 I 9.1 I

7.3

7.' •• 2

'.7 ••• 7.0

3.' 4.' S.'

.3

1.' 3.3

-----------------------------------------------------------------------------------------------------------------------I 1 1 18 .. I 1

1. 20

24

3.2

3 ••

4.0

2.7

3.2

3.7

2.0

2 ••

3.2

•• 1 ••

2.'

1 -1.4 I

1 -.2: I

1 1.3 1

I

7.0

'.3 •••

•• 4 5.3

•• 0 7 ••

10.0 10.7

2.9 -14.5

6.9 -'1'.1

1"3.8 -15.6.

•• 3

•• 7

7.1

S.O

'.S •• 0

3.3 1.2 -1.6

4.1 2.2 -.2

'.7 3.1 1.2

1 .. ----------------_. ------------------------------------------------------_._----------------------------------------

:;; '"

TABLE 3

as a function of

U-value, inside SHTC, and outside $HTC for a single glazing outdoor, ,air temperature, solar radiation fl,ux (IT) 1 and inside wall

assuming wind speed V=O, cloud c6ver CC ... S, and a- -0.2

temperature (T2)

•

~------------------- -----------------------------------~--------------~~------------------------------------------------1 1 1

OUTSIDE SHTC (W/(m.~.-K)) <i.I( Cm*/tI.-K)-) INSIDE ~HTC'\ (WI (JTli'kIll*K)) 1

1 1

u-vALUE ---,--------------------------------------------------------'-------------'- -----------------------------------

1 1 J OUTDOOR TEMPERATURE <DEO.C)

------------------~-.------~---------------------~----------------------------------------------~--------------------1 I

, 1 1

J 1(>, I ••• 3,,8' 3-_4 3.2 2.'6- I 7.' 7 •• ••• ,.7 ,.3 1 •• 7 6.' 6.3 7.7 60.4 1

I I 1 I

1

o 1 20 I •• 3 •• 2 ••• ••• 3.' 1 $.4 ••• 6.0 7.7 7.2 I 6.& 6 •• &.3 7 •• t;..S 1

1 I I 1 I

4~5 •• S 4;:; 4~'S , '.7 ••• 10:.0 lO.S 12.3 1 8.' •• 7 ••• ••• 7.2 1

1 1

-10 ... o • I •

1 DUTOOOR TEMPERATURE (DEG.C) 1 '1-10 -S 05 10

1 1 -10 -5 0 !5

,. 1 I 1 , 1 I 1 IT 1 T2

OUTDOQR TEMPERATURE (DEG~C)

1 1

'.2 2.7 .3

J 24 1 ••• 1 1

1 ---------------~-------.. -----------------------------------~- ---------------------------------1 1 1 1 1 J6-"J 3.2 2.8 ' 2.' 1.7 .2 , 7.0 .. ' 5.' •• 3 ".7 1 ••• '.2

1 , 1

1 1

1 200 I 20 I 3.' 3.2 2.' 2.3 1.2 1 •• 2 '.0 7.7 7.2 •• 2 1 '.1 5.' •• 7 3.' I.' 1 1 1

1 ,

1 1 24 I 3.6 3 •• 3 •• 3.0 2.' I ••• 10.0- 10.5 12.2 31.2 I •• 3 ••• '.1 ••• Z.'!'

1 I 1 1

, --------------------------------------------------------------------------------------------------------------------------1 , I 1 1. 2.' I.' 1 '.3 .2 -1.9 •• S •• 1 ••• .. .**** 3.' 3 •• 1 •• .2 -2~('I I

1 1

1

1400120 2.1 2.3 1 •• .s -.6 •• 0 7.7 7.2 •• 3 7 •• '.2 ••• 2.' 1.0 -.e I

I 1

1

1 1 2' 3.1 2.7 2.3 1 •• .3 10.0 10.!S 12.1 26-.9 -1.2 ••• '.6 2.' 1.7 .21

1 1

1

__ ----"lI' _________ . ____________________________________________ --------------------------------------

1 ,

1 ,. 1.7 1.1 .2 -1.2 -4.0 1 •• 7 ••• 1.1 -59.1 14.4 2.' 1.' .> -1.2 -3.1

1 1

600 I 20 2.0 1.' • 7 -.. -2.'9 1 7.1 7.3 ••• 7.' 7 •• 2.7 1.' •• -.' -2.2

1 1

I 2. 2.3 1.' 1.' •• -1.'!' 1 10.4 11.9 22.8 -2.3 ••• 3.1 2.' 1.' •• -1.3

1 1

------------------ ,-------------------------------------------- -- ------------------------------------

:!:

TABLE 4 U-value, inside SHTe, and outside SRTe for a single ,glazing

as a function of outdoor air temperature,solar radiation flux (IT), and inside wall temperature (T2) assuming wind speed V=O, cloud cover CC=O, and Cis =0.1

IT T2

1 , 1 16- I 1 ,

o I 20 1 1 1 I 24 I , ,

1 , 1 1 200 1 t 1

1 1 1 I 400 1 1 1

I I I 1 6.00 I 1 I

1 1 1. t 1 20 1 , .. t

1 1 1 16, 1 1 I t20I 1 • 1 J 24 1 1 1

1 I 1 I'b 1 I I I 20 J I 1 1 24 1 1 1

U-vALUE HH(rn*",*"O)

OUTDOOR TEMPERATURE (DEG.C)

-10

'.5 '.a '.1

'.1 ••• '.7

3.7

'.0 4~3

3.3

3.' 3 ••

-. •• 5

••• 5.2

'.0 • •• •• S

3.5

3.' •• 3

3.1

3 ••

3 ••

u

••• '.0 ~.:;

3.' ••• ..S

3.3

3 ••

'.3

2.7

3.2

'.7

• '.7 S.2

5 ••

3 ••

••• '.0

3.0

3.' '.2

2.2

2 ••

3.S

INSIDE SHTC (W/(m*II1*K;J.I

, J 1 1

OUTDOOR TEMPERATURE <DEO.C) 1 1 1 1 10 -10

1 4.9 J 7.6.

1 5.8 J 8.5

1 0.7 I .,,7

1

, 3.6. 1

I 4.5 I

1 5.4 J

I

2.3

3.3 .. , 1.1

2.1

3.1

1 1 1 t 1 1 1

7.' e ••

•• 7

7.2

• •• •• 7

7.0

•• 3

•• e

-5

7.3

••• '.7

7.1

..3 •. S

••• ..2 •• S

•• A

•• 1

•••

o • 10

6.9 6.4 5.1

8.2 6.0 7~7

9.8 10.1 10.6.

A.' •• 1

•••

A.3

7.' 10.1

••• 7 ••

10.3

•• 0

7 ••

10.3

'.5 7.'

10.7

••• 7.'

11.4

1 5.0 I

1 7.5 1

1 11 .2:

'.1 7.2

12.6

I 2.7 1

1 6..8- 1 ,

16..2 I I

OUTSIDE SHTC (Wf(m*m*K)) 1 1 I

OUTDOOR TEH.PERATURE (D£O.O) 1 1 1

-10 -5 o • 10 1

11.4 12.3 14.0 l&~O 41.4

11.2 12.0 13.2 15.9 24.6

11.1 11.7 12.7 14.5 1"'.0

••• • •• •••

7.7

7 ••

7.'

•• 3

A.' A.7

• •• • •• • •• 7.5

7.7

7 ••

5.' •• 1

•••

10.0

• •• • •• 7.2

7.' 7 ••

'.2 ••• 5.9

10.8

10.4-

10.2:

'.7 7.0

7.2

4.1

4 ••

5.1

1 13.4 I

1 U.8 I

1 10.'9 I

1

••• '.2

••• 1

2.0 I 1

3.1 I I

4-.0 J I

--~---------------~--~---------.. ------~------------------------------------------------------------------------------------, 1 ,

'1 800 1 I ,

, 1 lA I I 20 1 1 2' t

2.9

3.~

3 ••

2 ••

3.0

, .. 2.1

2.' 3.1

1.' 2.0

2.7

-.0

1.0

2.1

A.a

•• 2

•••

A.2

7.9

10.1

S.' 7 ••

10.7

3.' 7.1

12.E:I

-.0

•• 0 .... 5.2

5.' '.7

••• ••• '.2

s .•

'.1 '.S

2.2

2.9

3 ••

t -.0 I

1 1.2 I

1 2.2 I

1

TABLE 5 Percentage variations of li, hi' and ho for

V, IT, CC t OAT, T2 varying in the specified range

V IT CC OAT T2

RANGE OF 0 to 10 0 to 800 0 to 8 -10 to 10 16 to 24 VARIATION mls W/m2 °c 0(;

(1)

(2)

(3)

(4)

S

E/ll

N

U 38X -90% . , -20% 20% 18%

h. 4% (1)

- 3% _10%(2) , 35% , h 200% t -90% ~ -38% 100%(3) t _10%(4),

0

For T2 < 20 0 e, h. decreases with increasing IT as long as the global heat flui is outgoing. For T2 > 20"'C, h. increases with increasing IT. For high values of V, h. tends

1to stabilize ,

Except fefr TZ > 20 0 e

Only for IT ... 0 'iI/m2; for other 'values of IT h shows a var-i ab Ie negative gr adi en t

o

Only for IT = 0 w/trl; for IT'> 200 W/m2 gradient becomes pos~ itive and' increases with increasing IT

TABLE 6 Average values of Qlos s (W/m2), U (W/m2K), hi and ho (W/m2K)

for a single glazing in Torino (four orientations)

Oct Nov Dec Jan Feb Mar Apr Year

~loss 23.3 50.1 70.8 77.9 69.8 45.0 30.2 56.7

U 2.79 3.49 3.81 3.87 3.78 3.46 3.24 3.64

h. 7.57 , 7.80 8.02 8.09 8.00 7.86 7.71 7.97

h 4.51 6.46 7.43 7.62 7.34 6.34 5.73 6.82 0

~loss 30.4 57.0 78.3 85.5 76,4 49.9 32.0 63.1

U 3.63 3.97 4.21 4.25 4.14 3.83 3.39 4.05

h. 7.50 7.82 8.01 8.14 8.05 7.81 7.63 8.00 , h 7.23 8.27 9.05 9.14 8.75 7.71 6.25 8.44

0

Q _loss

34.5 59.5 80.4 88.0 79.7 54.7 37.4 66.4

U 4.12 4.15 4.32 4.37 4.31 4.20 4.01 4.26

h. 7.48 7.84 8.08 8.16 8.07 7.81 7.59 7.95 , -h 9.46 9.06 9.56 9.69 9.54 9,39 8.75 9.38

0

194

'u(t) y~t}

mml.·! pur:IUQcter~

y!tJ MOllEt;

net)

+

+ error: ---

Figure,l. Soheme of the identification process

AlJ,!M:~:NT

IUIOM!i

TEST

ROOM

ftUT~;llir.

ENV IIIUNMt:NT

n,,\,. '''''I'''I,;! '"'' U"i l

Pigure 3. Layout of the test room

'95

unceTtainty

,. P¥!- PROCESS ut outDI

I- I DllNTIFlCATION

, , , , PAMMETERS CALCULATION

-CONTROL

I , I

I I

Ii'

'-- CONTROLLeR reference ,i gnal

Figure 2. Scheme bf adaptive control

.,'.tW

Figure 4. Scheme of the da'ta acquisition unit

iii

Ul

'" § ... H

-'

~ " > .., ... j 2

I • I I I I I II

I I I I . I

OUTDOOR AIR TEMPERATURE

I I I i il§ .. I ~ "~'~'~"I 1~,I=I:5§~ ~

mllli;,',I'IIII~1 ~ ~ I ~ ~I~ 24 12 8 TIME (br8)

SOLAR RADIATION FLUX

I

."". ~,8,:~,': i" ,~, !ill~· ..... 1. ~ ;;0 ;;0 "". ""' II ... ;;0 !iO.. Ii·.· ~ ~ I'" il·I-' ~ ...... II! '" .. ~. ... 51a~~E§"~ m

~ E 5:l; =:.,&5, ~ !liS" '"' "'''' "" "" ... "" .... e~~~'=I§ ~E!e ~ g ~ ~ ~" ',15 ~ Ii I!!!C

~111=111=1111 ... 1~~!i~ 24 12 8 TIME (br8)

Figure 5. Typical statistica2 characceristics of the experimental data

• C-;) .., 0 C-• Il. E • ....

SIZI. llZ1lZ1. lSIZI. Time Choure)

,Figure 6. "

3S.

33. ~ .... In I 0RD-3 - STl)o • 85 I

31.

29.

27.

2S. IZI. SIZI. llZ1lZ1. '

Time Choure)

Fjgure 6. Comparison between SLS (64) and B£S (6b)" method results ,97

lSIZI.

.. 1 ... SElL

Figgre 7a

5.

.. I-++t~t±:!:;t++"i-+-++-"+ I I I I II I I I I I I I I I ~ ~~~~ __________ ~ __ ~_

.. 5.

1 ... 2E1L Figure 7b

IEIL 2E1L

SAMPLING STEP Flgor'e 7c

Figure 1. TYpical 'trends of Parameters aI_ a2' and a3 (Jrd order model) .. ,

SElL

SElL

1

a I- .5 en

1 2 3 4 5 6 7 OR DE R Figure Ba

• •

• •

10 50 100 Figure 8b

Figure B. STDS of tgpe-A identification/simulation results versus model order (~a) and sampling interval (8b)

199

.dT; (min)

35. r-----;;;;;::;::::;;::;;;l I'~~'-~'''I . 11t- •• h •. 33 •

• i 31.

1 27.

25. L--.l--:c'--,-~-:-::':--"""'-:-:' 0. 50. 100. 150.

1 ::: 27.

25. L-~_-L_-"-_-'---"""~-:-::' 0. 50. 1 BI/J. 150.

25. L-_~_L...._~_.l-..,.,.~---J B. SII!. 11110. 150.

T j lI:\e (hour".)

35. r------;:;;;;;;~;:;::;l 1-'· .... ·"1 _ ttr ..... ,,, . 33.

i 31. 1 II 29.

! 27.

25. L-~~-'_~_-L_~_...J 0. 50. 1 I,m. 150.

Ti",. <hou,..)

35. r-------;:;;;;::;=;;;;=;;::;l 1_·"..· .. 1

Dr" •• 1 .. 33 •

• 31. ! ~ 29.

o ... 27.

25.L.l_~_.L.._~_.L.._~_.J

•• 5 •• lIZ10. 150.

3S'l---~-;;;;=;;;;::;:;l

1-· .... • .. 1 Of .... ," 33.

1,:: 27.

5 •• 10121. 150.

FigUre 9. Tgpe-B identification/simulation results for various model orders

ISS ISS III ... m---- III .. ...

"'5

Qi ~: •• il; ISS • • s .... II; ISS ... . s .... • L ... . -,

~ • L > 0 ~ " ..c 0 • 4 ~

..c " ~ '" • '" E • " -.. E '" ISS I- ' .. ~ III ISS I- • III • • " 0 "

" ~ " • <:

~ .S • • • oj III • ISS 4 III III ... . oj ~

~ (I) (I) N N N tti gj ... III " • (I) (I) N N N • .~n-:a.t) .... dw.! " .... n~D.J.dw·l § ," 4 • ~

ISS

l~ " • -" III

-~ • .--- ... "-§ III • .~ '" " ~~ ~1Il ~ :::: '" • • • • 4

" II: • II; ISS .1J s '" S ....

S .... ~ ... • ... • • L l 11. ~ ~ ~ 0 0 ~ ..c .L ~

~

C • • ~ E E • ' ..

m-'::: " . ISS I- 0

'" III III '" ~

·-d. ). • • ISS ISS .S

..: • .. .. sa s, tti !Ii m " III lSI lSI (I) (I) (1! N N N N ... ..... n~D ..... dUi·l • .... n":l-Cl..J.d ... ·l

201

(J) L J

+>

30.,-___________________________ --,

25. .' /\ /\ .

ORD-3- STD-5. 85 OT ... 68 min

~ 20. . / \. f\

I \ .. J '\/. \.. . / \ .. / I "-..---...... 'V (J)

a.. E (J)

.-....j

I- 15. .-1

(J) L J +> 0 L (J) a.. E (J)

I-

10. 0. 50. 100. 150.

Time (hours) Figure lia

5.

3.

1.

-1.

-3.

-5. -'

0. 50. 100. 150. Time (hours)

Figure lIb

Figure 11. Type-A i.dentification/simulation results using d]lIc-rL'llt: d<./td sets for simulation and identification

"'2

Discussion

J.W. Mitchell, Professo~. Univ. of Wisconsin, Madison: The large variation in surface conduc­tanCe for windows impl ies a large value of solar absor:p'tance f(lr the glazing and also that the difference between sol-air and air- temperature is 'large compared to the difference between room aqd outdoor air temperature. What is, the value 'of solar ahsorptance of glazing? Would the window U-value be constant If the measured heat flow were divided by the tQmperature difference between room and sol-air temperature?

M. Masoer-o: The results presented 'in the paper were obtained assuming a solar absorptance of 0.2, except .. 0. t .. e ~e~mlt8 at Tab .. 4, where-a value of 0.1 Was assumed. In the latter case, the surface conductancp and U-valup of the window stU,I ahow relevant variations with varying solar radiation. We have tried to calculate. 'U u's1ng the sol-air temperature as you suggpsted, but there is no evidence- that thtc' resulting value is less sensitive to radiation than using the outdoor air temperalOrf>.