el cálculo de la temperatura radiante media de un sujeto expuesto a la radiación de un algoritmo...

7/27/2019 El clculo de la temperatura radiante media de un sujeto expuesto a la radiacin de un algoritmo generalizado solar

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Building and Environment 40 (2005) 367375www.elsevier.com/locate/buildenv

The calculation of the mean radiant temperature of a subject exposed tothe solar radiationa generalised algorithm

Maria La Gennusaa, Antonino Nucarab, Gianfranco Rizzoa,*, Gianluca ScaccianoceaaDipartimento di Ricerche Energetiche ed Ambientali, (D.R.E. AM.), Universitdegli Studi di Palermo, Viale delle Scienze, 90128 Palermo, Italy

bDipartimento di Informatica, Matematica, Elettronica e Trasporti, UniversitMediterranea di Reggio Calabria,

Feo di Vito, 89060 Reggio Calabria, Italy

Received 6 January 2004; received in revised form 5 May 2004; accepted 3 June 2004

Abstract

The thermal sensation experienced by a subject in a confined environment is significantly affected by the radiative heat exchangebetween the human body and the surrounding surfaces: it contributes as far as 30% of the whole thermal exchanges of the subject.

Besides, the presence of high-intensity radiation sources like, for example, the sun, may appreciably modify the radiantfield to which people are exposed. As a consequence, this could alter notably the comfort conditions.

In order of properly taking into account this issue, a simple analytical method is introduced in this work, that allows theeasy evaluation of the thermal radiant field induced by the presence of the solar radiation.

An application to a typical thermal comfort computation is finally presented. 2004 Elsevier Ltd. All rights reserved.

Keywords: Mean radiant temperature; Thermal comfort; PMV; PPD; Radiative heat exchange

1. Introduction

People usually spend a relevant part of time in confined

environments, where an artificial climate is supposed to

be present. This is generally induced by mechanical

equipments that govern the indoor condi-tions of

buildings in terms of thermal, hygrometry and quali ty of

air parameters. With the increasing of the life-style

levels, the performances required by people from the

buildings (both envelope and climatisation system) are

becoming more advanced. In turn, methods forevaluating the behaviours of microclimate parameters of

buildings need to suitably match these requisites.

As far thermal sensations of people are in question,

the modelling of four objective parameters (air tem-

perature, mean radiant temperature, air velocity, rela -

*Corresponding author. Tel.: +39-091-236210; fax: +39-091-

484425.

E-mail address:[email protected] (G. Rizzo).

0360-1323/$ - see front matter 2004 Elsevier Ltd. All rightsreserved. doi:10.1016/j.buildenv.2004.06.019

tive humidity) and two subjective parameters (metabolic

rate, thermal resistance of clothing) should be ensured in

a suitable way [1]. Among them, one of the most

difficult parameter to be analysed is the mean radiant

tempera-ture, provided that it should take into account

not only the thermal radiation coming from low-

temperature surfaces (i.e. walls, windows,), but also the

thermal radiation hitting the human body from high-

intensity sources. The solar radiation constitutes an

important example of this kind of radiation flows, since

it generally contributes in a relevant way to the thermalbalance of people living in confined environments.

Among the methods for the evaluation of the mean

radiant temperature it is possible to distinguish the

measuring methods and the calculation methods.

First methods determine the mean radiant tempera-

ture utilising black globe thermometers, two-sphere

radiometers or constant-air-temperature sensors [2].

The calculation methods, on the contrary, derive the

mean radiant temperature from the knowledge of
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368 M. La Gennusa et al. / Building and Environment 40 (2005) 367375

T4

r

the absolute surface temperature of the surroundingsurfaces, Ti; and the angle factors between the personand the surrounding surfaces, Fp~i [2]

1/4 T41Fp!1 T42Fp!2 ~ ~ ~ T4

i Fp!i

~ ~ ~ T4NFp!N: 1

In this equation the angle factor between the personand a rectangular surface can be computed as a functionof width, a, and height, b, of the surface and as afunction of the distance, c, between the person and thesurface, by means of the following equation:

Fp~i 1/4 Fmax1/21 e a=c=r]

1/21 ~ e-b=c=1; (2)

where

r1/4 A Ba=c;

y 1/4 CDb=c Ea=c: 3

The coefficientsFmax

; A, B, C, D and E assume differentvalues for seated or standing postures of the person, forknown or unknown orientation of the person with respectto surrounding surfaces and for vertical or horizontalsurface [3].

In the case of small differences between the tempera-ture of the surfaces of the enclosure, the equation for thecalculation of the mean radiant temperature can besimplified in the following way:

Tr 1/4 T 1 Fp!1 T 2 Fp! 2 ~ ~ ~ TiFp!i

~~ ~ TNFp!N: 4

The mean radiant temperature may be also calculatedfrom the plane radiant temperature, tpr;i and the projectedarea factors fp;i of a person in six directions: up, down,left, right, front and back.

The resulting equation is the following:

P6 i1/41tpr;ifp;it r 1 / 4 ; (5)

i1/41 fp;i

where the values of the projected area factors aredifferent for seated or standing postures of the person.Unfortunately, the present available methods for thecomputation of the mean radiant temperature do notproperly take into account the contribution of the solarradiation on the human body.

After all, this limitation is an important constraint forthe evaluation of thermal sensations in different points ofa room and for the definition of the useful thermal zonesof the building.

This paper is an attempt in providing a contribution inthis field, by introducing a new generalised equation forthe computation of the mean radiant temperature in aconfined environment where solar radiation (both directand diffuse) is present in a given point of the floor.

The new algorithm will be derived starting from theanalysis of the radiative heat exchanges between

geometric elements and, then, by applying the properrepresentative equations to the exchanges betweenorthogonal surfaces and human body.

2. Radiative exchanges between concentric elements

Let consider two concentric grey bodies that exchangethermal energy only by radiation.

JI and JO denote respectively the radiosity, and GI andGO are the radiations incident upon the inside and theexternal body, respectively (see Fig. 1).

By supposing that the inside body is convex, the netradiative flux, QI; interesting its surface is equal to

QI 1/4 AIJI ~ AIGI; (6)

where AI denotes the external surface of the insideelement.

We can also write that

AIGI 1/4 FO!IAOJO (7)

where FO!I is the angle factor between external and insidebodies, and AO is the external surface of the body. Forthe reciprocity relationship [4] we can put

FO!IAO 1/4 FI!OAI (8)

being FI!O the angle factor between the inside and theexternal body.

By replacing Eqs. (7) and (8) in Eq. (6), we obtain

QI 1/4 AIJI ~ FI!OJO: (9)

Besides FI!O =1 for the closing property of the view

factors; as that

QI 1/4 AIJI ~ JO: (10)

The thermal flow exchanged between the inside and theoutside body can be now written as

QI2O 1/4 FI!OAIJI ~ FO!IAOJO 1/4 AIFI!OJI ~ JO

(11)

or (since FI!O =1)

QI2O 1/4 AIJI ~ JO: (12)

Fig. 1. Radiative thermal exchanges between two concentric bodies.


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M. La Gennusa et al. / Building and Environment 40 (2005) 367375 369

QbS

QdSQ A S

Q 0 S

Starting from Eqs. (10) and (12), it can be easilyassessed that the net flux leaving the inside body is equalto the thermal flux exchanged for radiation among thetwo bodies. That is

QI 1/4 QI.-.O. (13)

3. Radiative exchanges between confined environmentand human body

Relationship (13), that has been obtained in thegeneral case of two concentric bodies, can be usefullyapplied for appraising the thermal exchanges betweena human subject and a surrounding confinedenvironment.

For doing this, one must consider all the involvedradiative thermal exchanges.

3.1. Net radiative energy flux by the human body

When the environment in which the subject is placeddoes contain surfaces showing different values of thetemperature and when the subject is exposed to the solarradiation, the net energy lost by the human bodyevaluated as the difference between the emitted flow,Q0S, and the absorbed share of the thermal flow thatreaches the subjectis a function of the thermalradiation coming from the surfaces of the environment,

QA!

S,

and is also a function of the diffuse, Qd!S, and ofthe direct, Qb!S, solar radiation entering the room throughthe glazed surfaces (see Fig. 2).

That is

3.1.1. Emitted radiation, QOSIn Eq. (14) the radiative heat flow emitted by the

subject can be written as

QOS 1/4 seSArT4

(15)cl

where s (=5.67~10~8 Wm~2 K~4) is the StefanBoltz-

mann constant, eS is the emissivity of the human body,Aris the effective area of the human body and Tcl is themean temperature of the surface of the clothingensemble. The effective area is defined as the area of thesmallest convex surface that contains the body.

3.1.2. Low frequency radiation, QA!S

The radiation coming from the surfaces of the indoorenvironment may be computed by means of therelationship

N

XQA!S 1/4 Fi!SAiseiT4i riGi, (16)

i1/4

1

where Fi!S is the angle factor between the ith internalsurface of the envelope and the subject, e i is itsemissivity,Ai is the area of the interested surface, Ti thetemperature, ri the reflection coefficient of the ithsurface and Gi the radiation reaching the ith internalsurface.

For the reciprocity relationship of the view factors, wecan write

Fi!SAi 1/4 FS!iAr (17)

being FS!i the angle factor between the subject and the ithsurface of the envelope.

Since the internal surfaces of the building can beconsidered as black bodies, characterised by ei=1 andri=0, the Eq. (16) can be rearranged in the followingform:

QS 1/4 Q0S ~ aSQA!S Qd!S Qb!S, (14) N

where aS is the absorptivity of the human body. XQA!S 1/4 sAr FS!iT4i .

(18)

In the following, all the terms appearing in Eq. (14)will be analysed indetails.

Fig. 2. Typical radiative exchanges between the confined environmentand the human body.

3.1.3. Diffuse radiation Qd!S

In the hypothesis that the diffuse radiation enteringthe room through the glazed surfaces follows theLamberts law, we can say that the solar radiation thatreaches the subject can be described by the followingexpression:

M

XQd!S 1/4 Fj!SAjId,j, (19)j1/41

where Fj ! S represents the angle factor between theglazed surface and the human body, Aj the area of thetransparent (glazed) surface and Id,j the diffuse radiationentering the room.

By applying again the reciprocity relationship:


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Fj!SAj 1/4 FS!jAr (20)


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XMQd!S1/4Ar

j1/41

FS!jId;j (21) XseSArT4 cl ~ aS sAri1/41

XFS!iT4i Arj1/41

FS!jId;j

MX

Arj1/41

[1 ~ eS=eS 1 ~ eA=eA] ~ Ar=AA 1;

e S aS Ap Ib

A reSs

PNaS i1/41FS!iT

4i

PMairr;d j1/41FS!j Id;jFS!i T4 i

airr;bfp Ib eSse S s

4

~Tr1/ Xi1/4

we can put Eq. (19) in the form ment, and by utilising Eqs. (23) and (25), we obtain:

3.1.4. Direct radiation Qb!S

The contribution of the direct radiation to the humanbodys thermal balance is

Qb!S 1/4 Ap Ib; (22)

whereAp is the projected area of the subject onto a plainnormal to the direction of the solar beam andIb is thedirect radiation that strikes the subject.

Finally, by introducing Eqs. (15), (18), (21) and (22)in Eq. (14), we can write

N

XQS 1/4 seSArT4 cl ~ aS sArFS!iT4ii1/41

!FS!jId;j Ap Ib 233.2. Thermalflow exchangedfor radiation between

subject and environment

Let now suppose that the thermal flow interesting asubject is coming from a black enclosure with anuniform temperature Tr; let also suppose that thetemperature of the human body is equal to the mean

temperature of the clothed surface of the human body,Tcl: In these hypotheses (that are typically assumed inthe indoor environment evaluations) the thermal flowexchanged by radiation between a subject and thesurfaces of the surrounding confined environment isgiven by

QS-.A 1/4 sArT4cl ~ ~T

4r

(24)

where eS and eA are respectively the emissivities of thehuman body and of the surfaces of the environment and

theAA is the whole area of the surface of the envelope.Finally, when the human body may be considered as

small with respects to the environment, the ratio Ar/AAcan be neglected: as that, Eq. (24) can be replaced by thefollowing:

QS-.A 1/4 AreSsT4cl ~ ~T

4r: (25)

4. Mean radiant temperature

By applying Eq. (13) to the case of the radiative heat

exchange between the human body and the environ-

! Ap Ib 1/4 AreSsT

4

cl ~ ~T

4

r 26

that can be usefully rearranged in thisform

eSsaSj1/41FS!jId;j

PM

1/4 ~T4

r:

Since the value of the temperature of the external

surface of the body is close to the value of the indoor1

temperature (and by using the Kirchoffs law), we canput aS=eS in the first term of the previous equation. Onthe contrary, this hypothesis cannot be imposed to thesecond and third terms of Eq. (27), because the sunrepresents a high intensity source and is characterisedby a temperature significantly higher in comparisonwith the mean temperature of the human body. In thiscase we indicate the absorption coefficient with thesymbol airr; since it must be referred to thetemperature of the source. Moreover the absorptioncoefficients for the direct and diffuse radiation should

assume different values. The ratio Ap/Ar; appearing inEq. (27), represents the projected area factor,fp:

All these considerations lead to the following expres-sion for Eq. (27):

(28)

that provides the value of the uniform temperature of ablack enclosure in which a subject would exchange thesame heat flow by radiation as in the actual environ-

ment. In other words, this represents the mean radianttemperature.

In order of better characterising the features of thesolar radiation, we introduce here two morecoefficients: the daynight coefficient Cdn (equal to 1 inthe daytime period and equal to 0 in the night period)and the shading coefficient CS (equal to 1 when thesubject is directly hit by the solar beam and equal to 0in the other cases).


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1This assumption refers to the so-called moderate thermal environ-ments,

where thermal comfort conditions can be reached by means of HVAC

systems.


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N,4 + Cdn

FS-i 1 iESs

M4

airr,di=1 j=1

In this way, a more general expression of the meanradiant temperature equation can be derived, that is

Tr =

)FS!jId,j+ CSairr,bfp Ib.(29)

5. An application

The usefulness of such relationship for the calculationof the mean radiant temperature in a given enclosurewhere a subject is irradiated by the solar radiation will beillustrated in the following by means of a numericalexample.

Eq. (29) is here utilised for evaluating the meanradiant temperature, the predicted mean vote, thepredicted percentage of dissatisfied and a long timeindex through the 24 h of 21 December in a parallele-piped room, located in Palermo (38 07'N, 13 21' E),town characterised by a Mediterranean mild climate.

The analysis has been lead for a seated subject facingthe north direction and subsequently placed in the pointsof the grid reported in Table 1.

The building module (600 x 400 x 300 cm3) isequipped in the south wall with a glazed surface (200 x120 cm

2), as shown in Fig. 3.

The hourly direct and diffuse components of the solar

radiation incident on the external side of the glazedsurface have been determined by means of the Liu andJordan method [5], starting from the knowledge of themonthly average of the solar radiation on the horizontalsurface for the site [6]. The entity of the attenuation ofthe value of the solar radiation through the glazedsurface has been evaluated by means of the SHGFprocedure of ASHRAE [7]. The angle factors betweenthe window and the subject have been analyticallyassessed [3].

Table 1

Co-ordinates of the points in the building module utilised for the

evaluation of the comfort conditions

Point X(m) Y(m) Z(m)

1 1.00 1.00 0.602 1.00 2.00 0.603 1.00 3.00 0.60

4 3.00 1.00 0.605 3.00 2.00 0.606 3.00 3.00 0.60

7 5.00 1.00 0.608 5.00 2.00 0.60

9 5.00 3.00 0.60

Fig. 3. Sketch of the considered environment.

Regarding the coefficients contained in Eq. (29), theparameter Cdn has been evaluated with reference to theduration of the day, h:

h = 12 arccos(- tan 9 tan S) - 180(30)

15

being 9 the latitude of the site and S the solardeclination for the day under examination; the coeffi-cient CS has been determined by means of a relation-ships introduced by some of the authors in a previouswork[8].

The values of the diffuse and direct solar radiationfalling on the south fac-ade, along with the values of thedaynight and of the shading coefficients in the daytime

period of the selected day are reported in Table 2.The projected area factors fp have been computed [9]

only for the hours in which the subject is reached by thedirect solar radiation (see Table 3).

The behaviour of the mean radiant temperature for apeople irradiated by the sun and placed in the points ofthe grid of the building module is reported in Fig. 4. Forthe sake of simplicity, the temperature of the internalsurface of the walls has been here assumed equal to20C.

The changes of the mean radiant temperature over thetime allow the determination of the comfort conditions

through the analysed day. The predicted mean vote(PMV) and the predicted percentage of dissatisfiedindexes [1] are reported in Figs. 5 and 6 under thesubjective and physical conditions shown in Table 4.

It is interesting to note that the entering the room by thesolar radiation in the central hours of the day brings thesensations felt by people from the comfort (-0.5XPMVX + 0.5) to the heat discomfort (PMV> +0.5) conditions. This situation occurs at different times,depending on the points in which the analysis isconducted.

These computations, that are of crucial importance inorder of suitably designing the climatisation equipment,


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PPDlimit

Table 2Diffuse solar radiation on the south exposure and direct solar radiation on the beam direction; daynight and shading coefficients for each selectedpoint of the environment in the daytime period (Palermo, 21st December)

Time (h) Ib,out(Wm2) Id,out(Wm2) Cdn CS1 CS2 CS3 CS4 CS5 CS6 CS7 CS8 CS9

7.30 6 8 1 0 0 0 0 0 0 0 0 0

7.45 86 20 1 0 0 0 0 0 0 0 0 08.00 173 35 1 0 0 0 0 0 0 0 0 08.15 239 52 1 0 0 0 0 0 0 0 0 08.30 288 68 1 0 0 0 0 0 0 0 0 08.45 325 84 1 0 0 0 0 0 0 0 0 09.00 353 100 1 0 0 0 0 0 0 0 0 09.15 374 115 1 0 0 0 0 0 0 0 0 09.30 392 128 1 0 1 0 0 0 0 0 0 09.45 405 141 1 0 1 0 0 0 0 0 0 010.00 416 153 1 1 1 0 0 0 0 0 0 010.15 425 163 1 1 1 0 0 0 0 0 0 010.30 433 172 1 1 1 1 0 0 0 0 0 010.45 438 180 1 1 1 1 0 0 0 0 0 011.00 443 186 1 1 1 1 0 0 0 0 0 011.15 446 192 1 1 1 0 0 0 0 0 0 0

11.30 449 195 1 1 1 0 0 0 0 0 0 011.45 450 197 1 0 1 0 1 0 0 0 0 012.00 450 198 1 0 0 0 1 1 0 0 0 0

12.15 450 197 1 0 0 0 1 1 0 0 0 012.30 449 195 1 0 0 0 1 1 0 0 0 012.45 446 192 1 0 0 0 1 1 0 0 0 0

13.00 443 186 1 0 0 0 1 1 1 0 0 013.15 438 180 1 0 0 0 1 1 1 0 0 013.30 433 172 1 0 0 0 1 1 0 0 0 013.45 425 163 1 0 0 0 1 1 0 0 0 114.00 416 153 1 0 0 0 1 1 0 0 0 114.15 405 141 1 0 0 0 0 1 0 0 0 114.30 392 128 1 0 0 0 0 0 0 0 0 114.45 374 115 1 0 0 0 0 0 0 0 1 115.00 353 100 1 0 0 0 0 0 0 0 1 1

15.15 325 84 1 0 0 0 0 0 0 0 1 015.30 288 68 1 0 0 0 0 0 0 0 0 015.45 239 52 1 0 0 0 0 0 0 0 0 016.00 173 35 1 0 0 0 0 0 0 0 0 016.15 86 20 1 0 0 0 0 0 0 0 0 0

16.30 6 8 1 0 0 0 0 0 0 0 0 0

can be only derived from the knowledge of the timechanges of the mean radiant temperature and from the

evaluation of the effects induced by the presence of thesolar radiation.In order of better analysing this aspect of the

problem, a new long term index is here introduced: it issimply selected among those introduced by the lastdraft of the ISO 7730 Standard [10], but it is herecomputed in terms of the PPD index rather than interms of the PMV parameter. It can be evaluated bymeansof thefollowingexpress

ion:

N

>I=i=1


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where PPDi is the predicted percentage of dissatisfiedvalued in the ith period of time, Dti, and PPDlimit is set to10% (limit of the comfort conditions).

The calculation of this index in the points of the gridof Table 1 has lead to the results reported in Figs. 7and 8.

It is noticeable that highest values of the index

match with the points 1, 2, 4 and 5, which are theclosest to the window; on the contrary the indexshows a null value only for the point 7, which is neverhit by the direct solar radiation in the considered dailyperiod.

Starting from these results, it must be considered thatEq. (24) does allow the evaluation of the space changesof the thermal comfort conditions. In fact, the mean


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radiant temperature depends on the view factors, on theprojected factor and on the daynight and shadingcoefficients: all these parameters show a spatial depen-

Table 3Projected area factors for the human subject in the solar beam

direction

Time (h) Azimuth angle() Altitude angle() fp (-)

9.30 143.7 19.2 0.2299.45 146.9 20.9 0.223

10.00 150.3 22.4 0.21610.15 153.7 23.8 0.21010.30 157.2 25.0 0.205

10.45 160.8 26.1 0.19911.00 164.5 27.0 0.194

11.15 168.3 27.7 0.19011.30 172.2 28.2 0.18511.45 176.1 28.5 0.18212.00 180.0 28.6 0.179

12.15 176.1 28.5 0.18212.30 172.2 28.2 0.18512.45 168.3 27.7 0.19013.00 164.5 27.0 0.194

13.15 160.8 26.1 0.19913.30 157.2 25.0 0.20513.45 153.7 23.8 0.21014.00 150.3 22.4 0.21614.15 146.9 20.9 0.22314.30 143.7 19.2 0.22914.45 140.7 17.4 0.23415.00 137.7 15.4 0.240

15.15 134.8 13.4 0.245

dence that enables the computation of PMV in each pointof a given room.

These analyses are also important in order of definingthe useful zones of a room and with the aim of correctlysizing the heating and cooling systems.

6. Conclusions

In this paper, it has been introduced a simple methodfor the evaluation of the mean radiant temperature for ahuman subject placed in a confined environment, andirradiated by solar radiation, direct as well diffuse.

The proposed relationship requires the knowledge of:(a) the temperature of the internal surfaces of theenvironment; (b) the intensity of the diffuse and directsolar radiation entering the room through the glazedsurfaces; (c) the angle factor between the opaque andglazed surfaces of the environment and the subject; (d)the projected area factor of the subject in the solar beamdirection.

Such detailed computation of the mean radianttemperature allows the evaluation of the time and spacechanges of the indoor thermal conditions. This kind ofinformation, in turn, can be utilised for suitably sizingthe HVAC systems and, finally, for a bettermanagement of the energy sources for climatisationpurposes.

Fig. 4. Mean radiant temperature for an irradiated subject placed in the points of Table 1.


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Fig. 5. Predicted mean vote for the irradiated subject placed in the points of Table 1.

Fig. 6. Predicted percentage of dissatisfied for the irradiated subject placed in the points ofTable 1.

Table 4Adopted parameters for the evaluation of the comfort conditions

Subjective conditions Indoor air conditions

Activity level (met) Thermal insulation of clothing (clo) Temperature C Relative humidity (%) Velocity (m/s)

1.0 1.1 22.0 50 0.10


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Longtimeindex

4. 0

2. 0

6 .0

5 .0

3. 0

0 .0

1. 0

.

.

.

5.40 5.34

.

.

.

.

1 2 3 4 5 6 7 8 9

Points

Fig. 7. Long-term index in the points ofTable 1.

Fig. 8. Distribution of the long term index in the points ofTable 1.

References

[1]Fanger PO. Thermal comfort. Copenhagen: Danish TechnicalPress; 1970.

[2]ISO 7726. Thermal environmentsinstruments for measuringphysical quantities. Geneva: International Standard Organiza-tion; 1998.

[3]Cannistraro G, Franzitta G, Giaconia C, Rizzo G. Algorithms forthe calculation of the view factors between human body andrectangular surfaces in parallelepiped environments. Energy andBuildings 1992;19:5160.

[4] Kreith F. Principles of heat transfer. New York: Intext Educa-tional Publisher; 1973.

[5] Liu BYH, Jordan RC. The interrelationship and characteristicdistribution of direct, diffuse and total solar radiation. SolarEnergy 1960;4(3):119.

[6] Rizzo G, Cannistraro G, Giaconia C, Pietrafesa M. Reducedweather data for building climatisation and application to 29European locations. EnergyThe International Journal1995;20(7):63746.

[7] ASHRAE. Handbook fundamentals. Atlanta, GA: AmericanSociety of Heating, Refrigerating and Air Conditioning Engi-neers, Inc.; 1791 Tullie Circle, N.E.; 1989.

[8] Marino C, Nucara A, Rizzo G, RodonG. Solar energy enteringglazed surfaces: computation of the abatement due to thebuilding envelope. Proceedings of EUROSOLAR Conference,sixth European Conference Solar Energy in Architecture and

Urban PlanningThe CityA Solar Power, Bonn, Germany,1215 September; 2000. p. 1447.

[9] Rizzo G, Franzitta G, Cannistraro G. Algorithms for thecalculation of the mean projected area factors of seated andstanding persons. Energy and Buildings 1991;17:22130.

[10]ISO/DIS 7730. Ergonomics of the thermal environmentanalytical determination and interpretation of thermal comfortusing calculation of the PMV and PPD indices and local thermalcomfort. Geneva: International Standard Organization; 1999.

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