INTERCOMPARISONS OF EXPERIMENTAL

CONVECTIVE HEAT TRANSFER COEFFICIENTS

AND MASS TRANSFER COEFFICIENTS OF URBAN SURFACES

AYA HAGISHIMA1,*, JUN TANIMOTO1 and KEN-ICH NARITA2

1Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1,Kasuga-koen, Kasuga-shi, 816-8580, Fukuoka, Japan;

2Department of Engineering, Nippon Institute of Technology, Japan

(Received in final form 10 January 2005)

Abstract. The convective heat transfer coefficient (CHTC) of an urban canopy is a crucial

parameter for estimating the turbulent heat flux in an urban area. We compared recentexperimental research on the CHTC and the mass transfer coefficient (MTC) of urban surfacesin the field and in wind tunnels. Our findings are summarised as follows.(1) In full-scale measurements on horizontal building roofs, the CHTC is sensitive to the

height of the reference wind speed for heights below 1. 5 m but is relatively independent of

roof size.(2) In full-scale measurements of vertical building walls, the dependence of the CHTC on

wind speed is significantly influenced by the choice of the measurement position and wall

size. The CHTC of the edge of the building wall is much higher than that near the centre.(3) In spite of differences of the measurement methods, wind-tunnel experiments of the MTC

give similar relations between the ratio of street width to canopy height in the urban

canopy. Moreover, this relationship is consistent with known properties of the flow re-gime of an urban canopy.

(4) Full-scale measurements on roofs result in a non-dimensional CHTC several tens of timesgreater than that in scale-model experiments with the same Reynolds number.

Although there is some agreement in the measured values, our overall understanding of theCHTC remains too low for accurate modelling of urban climate.

Keywords: Convective heat transfer coefficient, Intercomparison, Mass transfer coefficient,

Urban canopy model, Wind-tunnel experiment.

Symbols:

a: thermal diffusivity [m2 s)1];Cm: transfer coefficient Cm ¼ hD=U;cp: specific heat of air at constant pressure [J kg)1];D: diffusivity [m2 s)1];FX: scalar flux of substance X [kg m)2 s)1];

* E-mail: aya@cm.kyushu-u.ac.jp

Boundary-Layer Meteorology (2005) 117: 551–576 � Springer 2005DOI 10.1007/s10546-005-2078-7

H: canopy height [m];h: convective heat transfer coefficient (CHTC) [W m)2 K)1];hD: mass transfer coefficient (MTC) [m s)1];Lfl: incident longwave radiation [W m)2];Nu: Nusselt number Nu=hx/k;Pr: Prandtl number Pr=m/a;q: sum of the convective and radiative heat gain of building surfaces

[W m)2];QE: turbulent latent heat flux [W m)2];QG: conductive heat flux of the ground surface [W m)2];QH: turbulent sensible heat flux [W m)2];Q*: net radiation [W m)2];Re: Reynolds number Re=Ux/m;Sc: Schmidt number Sc=m/D;Sh: Sherwood number Sh=hDx/D;St: Stanton number St ¼ h=qcpU;Sfl: incident solar radiation [W m)2];

Tair: air temperature [K];Ts: surface temperature [K];Te: sol-air temperature [K] (It is a technical term used in building science.);DT: Ts � Tair;U: wind speed [m s)1];Ud: wind speed at d metres above the target surface [m s)1];W: width of street of urban canopy [m];x: representative length [m];a: solar absorptivity;e: emissivity;q: density of air [kg m)3];qair,X: concentration of substance X in the air [kg m)3];qs,X: concentration of substance X adjacent to the surface [kg m)3];k: heat conductivity [W m)1 K)1];m: coefficient of kinematic viscosity [m2 s)1];kp: plan area density of obstacles

1. Introduction

The temperatures and winds in an urban canopy directly affect the health andcomfort of the city’s inhabitants, and consequently much effort has gonetowards gaining a greater understanding of urban climate. In particular,improving the calculation accuracy of the thermal balance in urban areas isan important goal of urban mesoscale modelling. As a result, several surfaceschemes, hereafter urban canopy models (UCMs), have been established for

AYA HAGISHIMA ET AL.552

use in mesoscale modelling (e.g., Kondo and Liu, 1998; Ashie et al., 1999;Masson, 2000; Kusaka et al., 2001). This paper focuses on an importantparameter in UCMs: the convective heat transfer coefficient (CHTC).

UCMs have become established because, unlike the one-dimensional heatconduction treatment in the previously used slab models, they can be used toprecisely estimate the effects of various urban conditions on the flow struc-ture and turbulent flux in the urban canopy. Thus, we consider only UCMshere. Figure 1 shows the basic features of single-layer and multilayer UCMs.Both types commonly include sub-models that treat certain aspects of radi-ative heat transfer, convective heat transfer, and the hydrodynamic effects ofthe buildings. The focus of our paper is on that part of the models that treatsthe convective heat transfer between the atmosphere and urban surfaces. Theimportant, yet still poorly understood, parameter for this transfer is theCHTC parameter.

In addition to urban climatology studies, research on the CHTC of urbansurfaces has been carried out in the fields of building science and heat transferengineering. For example, full-scale measurements of the CHTC for buildingsurfaces have been made in the field of building science to accurately estimatethe air-conditioning load. Also, wind-tunnel experiments of the CHTC forsurfaces with urban-like roughness have been carried out in the field of heattransfer engineering. Such studies do not have the aim of contributing toknowledge about urban climate. Nevertheless, despite some differences inscale and method among the various studies, all relevant studies of theCHTC can contribute to knowledge about the role of urban surfaces inUCMs. For this reason, we believe it is important to review and analyze thesevarious experimental studies on the CHTC of building surfaces and surfaceswith urban-like roughness. In addition to the CHTC, we also analyze severalprevious experiments on the mass transfer coefficient (MTC) of urban-likecanopy surfaces because mass transfer follows analogous equations to heattransfer.

GT

cTWT

RZ

aZ(a) (b)

dZT +

canopyHQ ,

streetHQ ,

wallHQ ,

roofHQ ,

HQ

RT

airTairT

GT

WT

RZ

aZHQ

airT

RT

Single-layer model Multi-layer model

Figure 1. Basic processes in urban canopy models (Kusaka et al., 2001). Ta is the air tem-perature at reference height Za, TR is the building roof temperature, Tw is the building walltemperature, Tc is the air temperature in the canopy, and TG is the road temperature.

INTERCOMPARISONS OF EXPERIMENTAL RESEARCH 553

2. Definition of CHTC

The heat balance of a thin urban surface with zero heat capacity can bewritten

Q� ¼ QH þQE þQG; ð1Þwhere Q* is the net radiation, QH is the turbulent sensible heat flux, QE is theturbulent latent heat flux, and QG is the conductive heat flux at the groundsurface. The turbulent sensible heat flux from the urban surfaces can beexpressed using the convective heat transfer coefficient h as

QH ¼ h Ts � Tairð Þ; ð2Þwhere Ts is the surface temperature and Tair is the air temperature. Theturbulent sensible heat flux can also be expressed using the Stanton numberSt as

QH ¼ qcp Stð ÞU Ts � Tairð Þ; ð3Þ

where cp is the specific heat of air at constant pressure, q is the density of air,and U is the wind speed.

In UCMs, the surface temperature Ts is usually defined as the spatiallyaveraged surface temperature of the building walls, roofs, and streets.The definition of the air temperature Tair depends on the type of UCM; insingle-layer models, the air temperature in the urban canopy is represented asthat at the height of the roughness length. In multi-layer models, the verticaldistribution of area-averaged air temperature is considered.

In the same way, the scalar flux of a substance X can be expressed by themass transfer coefficient hD and transfer coefficient Cm as

FX ¼ hD qs;X � qair;X

� �; ð4Þ

FX ¼ CmU qs;X � qair;X

� �; ð5Þ

where FX is the scalar flux of substance X, qair,X is the concentration ofsubstance X in the air, and qs,X is the concentration of substance X imme-diately adjacent to the surface.

Heat transfer engineering studies use many dimensionless formulae to de-scribe the features of heat and mass transfer. For example, the empirical rela-tions for the Nusselt number and Sherwood number as a function of Prandtlnumber, Reynolds number, and so on have been presented for various exper-iments (e.g., Johnson and Rubesin, 1949). However, because of the difficultiesin defining a representative length and wind velocity, it is unclear how to applythese equations to the complex geometry of urban surfaces.

In the field of building science, the CHTC of building surfaces is also animportant parameter because it affects both the building thermal load and the

AYA HAGISHIMA ET AL.554

optimum size of the air-conditioning system. In this field, empirical rela-tionships between the CHTC and wind speed for a small flat plate in the windtunnel are used. One of the commonly used sets of equations is by Jurges(McAdams, 1954). These sets are based on fits to the CHTC for a heatedcopper square plate, 0.5-m on a side, which was oriented perpendicular to auniform air flow in a wind tunnel. In regard to such empirical treatments,Cole and Sturrock (1977) pointed out several problems with results fromwind-tunnel experiments using cube arrays. First, the CHTC of the surfacesof a cube depends on wind direction and differs from the CHTC of a flatplate; second, the local CHTC depends on the velocity profile at the pointinvestigated. Also, the area-averaged CHTC depends on the length of sur-face. Hence, the measured CHTC of a small flat plate cannot be applied tofull-scale building surfaces.

To overcome these problems, many experimental studies have been madeto determine the CHTC for particular types of building surfaces. For a givenstudy, this surface will be called the target surface. Such studies have sug-gested new empirical relations between the CHTC and the wind speed.However, few studies consider how the CHTC depends on the particularexperimental condition, such as the thermal stability, the flow structurearound the buildings, and the size of the target surface. Thus, there stillremains no reliable method that can be used as a sub-model in a UCM.

3. Full-Scale Measurements on Building Surfaces

3.1. HORIZONTAL ROOF

It is difficult to observe the detailed flow structure around an actual buildingbecause one generally cannot install sufficient instrumentation in an urbanstreet. Nevertheless, full-scale measurements can provide us with usefulinformation of the CHTC under natural conditions. We now discussfull-scale measurements of CHTC on horizontal roofs; the studies and theirmeasurement conditions are listed in Table I. All CHTC values discussedhere were obtained as the residual of the heat balance in which the netradiation and conductive heat fluxes were either directly measured or esti-mated. Hereafter, we call this method the thermal balance method. Althoughthe CHTC was originally known to be dependent not only upon wind speedbut also the temperature difference between surface and air, DT, the studiesof Table I do not provide sufficient information on the relationship betweenCHTC and DT. The most empirical relations between CHTC and wind speedare therefore approximate curves based on results obtained under conditionsof various thermal stability.

INTERCOMPARISONS OF EXPERIMENTAL RESEARCH 555

TABLE

I

BuildingparametersfortheCHTC

measurements

onthehorizontalroof.

Number

ofstoreys

Surface

finish

Roofsize

(m2)

Measurement

methoda

Condition

Heightofthe

reference

wind

speed(m

)

Uranoand

Watanabe(1983)b

4/coveringmortar

4.6

·10.9

DDT<

0,DT>

00.6

Kobayashi(1994)c

3/coveringmortar

45

·25

SDT>

010,1.5

Kobayashiand

Morikawa(2000)c

3/coveringmortar

45

·25

SDT<

0

U10<

2.5

ms)

1,

U1.5<

2.0

ms)

1

10,1.5

Hagishim

a

andTanim

oto

(2003)d

2/asphaltsheetroofing

22.2

·15.3

DDT>

15

�C0.13,0.6

Clearet

al.(2003)

1/asphaltsheetroofing

2940

DDT>

03

Clearet

al.(2003)

1/asphaltsheetroofing

2370

DDT>

03

a‘D

’indicatesdirectmeasurementmethod.‘S’indicatesSAT

meter

method.Thesize

oftheSATmeter

is12.9

m·

13.1

m.

bThereisaparapet

withtheheightof0.24m

aroundtheroof.

cThereisaparapet

withtheheightof1.2

maroundtheroof.

dThereisaparapet

withtheheightof0.25m

aroundtheroof.

AYA HAGISHIMA ET AL.556

By plotting the results in Figure 2, the CHTC is most sensitive to theheight of the reference wind speed; both the value of the CHTC and the slopeare larger for a lower reference height. To simplify the discussion, a referencespeed at height x above a target surface will be called S+x. For example, theslope of the uppermost curve from Hagishima and Tanimoto (2003) withS+0.13 m is significantly steeper than the other curves. Since the CHTCs ofKobayashi (1994) with S+1.5 m and S+10 m are almost equal, the refer-ence height of 1.5 m is assumed to be above the local boundary layer on theroof. The measured CHTCs under unstable conditions are in good agreementat wind speeds below 1 m s)1; in particular, their intercepts range within 6.4–8.7. In contrast, at wind speeds below 2 m s)1, the measured CHTC ofKobayashi and Morikawa (2000) under stable conditions is significantly lessthan the other measurements.

The curves of Urano and Watanabe (1983) and Hagishima and Tan-imoto (2003) for S+0.6 m agree well in spite of the differences in roof size.This agreement suggests that the CHTC is relatively independent of roofsize, but is inconsistent with the former remarks based on indoor experi-ments (e.g., Cole and Sturrock, 1977). In addition, this tendency is alsoinconsistent with the modelling of the local Nusselt number of a flat roof byClear et al. (2003). The effect of the parapets around the target roofs is apossible factor. Nevertheless, since most of the real roofs have parapets, thedependence of CHTC on roof size should not be treated as the same as theresults of indoor experiments using simple cube models. Nevertheless, asmost real roofs have parapets, the roof-size dependence of the CHTC isprobably not exactly the same as the analogous size dependence in cubic-array models.

0

5

10

15

20

25

0 2 4 6U [m s-1]

hW[

m2-K

1-]

Figure 2. Measured convective heat transfer coefficient h for horizontal building roofs atvarious wind speeds U. The grey thick line marks results from Urano and Watanabe

(1983). Thick solid and broken lines mark results of Kobayashi (1994) for measurementsdone under unstable conditions with S+1.5 m and S+10 m, respectively. Thin solid andbroken lines are from Kobayashi and Morikawa (2000) for measurements done under sta-

ble conditions with S+1.5 m and S+10 m, respectively. The lines with white and black cir-cles are from Hagishima and Tanimoto (2003) with S+0.13 m and S+0.6 m, respectively.Further details of these studies are in Table I.

INTERCOMPARISONS OF EXPERIMENTAL RESEARCH 557

Unfortunately since the measurement data for various roof sizes and thesame height of the reference wind speed are not sufficient, the dependence ofCHTC on roof size is only imprecisely known. In addition, there are insuf-ficient measurements under stable conditions (Figure 3).

3.2. VERTICAL WALLS

Cole and Sturrock (1977) pointed out that the CHTC of surfaces of anisolated cube varies with the wind direction, mainly because the wind speednear a wall varies with the wind direction, even for a constant wind speedabove the canopy. However, Ito et al. (1972) made full-scale measurements,suggesting that the wind speed 0.3 m from the target surface can be used forthe CHTC under various wind speeds and directions. To clarify the use of theCHTC for vertical walls, we now compare various measurements of CHTCfor vertical building walls. The studies and their measurement conditions arelisted in Table II.

First, we compare the results of Loveday and Taki (1996) and Sharples(1984), where the height of the reference wind speed for both studies is 1 m(Figure 4a). (In this paper, we use the term ‘height above a surface’ to meanthe distance away from the surface in the direction normal to the surface.)These two studies involved the measurement of the CHTCs of the walls ofhigh buildings, which had few roughness elements such as eaves or verandas,based on the SAT meter method (the SAT meter method is described in theAppendix A). The measurement method and stability conditions of these twostudies are assumed to be almost the same, though the size of the test plates(SAT meters) is different. In these studies, the effect of the wind direction on

0

10

20

30

(a) (b)

0 1 2 3U 1 [m s-1]

hW[

m2-

K1-]

Windward (L) Leeward (L)Windward,18E (S) Leeward,18E (S)Windward,6c (S) Leeward,6c (S)

0

10

20

30

40

0 1 2U 0.13, U 0.3 [m s-1]

hW[

m2-K

1-]

3

S+0.3m(N) S+0.13m(H)

S+0.3m (I)

U1-h U0.13, U0.3 -h

Figure 3. Measured convective heat transfer coefficient of vertical walls on buildings at var-ious wind speeds. ‘18E’ indicates data observed at the edge of the wall of 18th floor and

‘6c’ indicates the data observed at the central wall of the 6th floor. (H), (I), (L), (N) and (S)indicate the data of Hagishima and Tanimoto (2003), Ito et al. (1972), Loveday and Taki(1996), Narita et al. (1997) and Sharples (1984), respectively.

AYA HAGISHIMA ET AL.558

TABLE

II

BuildingparametersfortheCHTC

measurements

ontheverticalbuildingwall.

Storeysof

building

Sizeandshape

ofthetarget

surface

Positionin

thetarget

surface

Measurement

methodSize

oftest

plate

aThermalcondition

Heightofthe

reference

windspeed(m

)

Itoet

al.(1972)

6H

18m

with

few

roughness

Centreofwall

at4th

floor

C 0.3

·0.3

m

Nighttime,

DT>

0b

0.3

Sharples(1984)

18

W36m

·H

78m

Centreandedgeof

wallat6th

and18th

floor

C 0.25

·0.25m

Nighttime,

DT>

01

Loveday

andTaki(1996)

8W

9m

·H

28m,

withfew

roughness

7th

floor

H 0.8

·0.5

m

Nighttime

DT>

0b

1

Narita

etal.(1997)

8–9

W73m

·H

31.3

m

surrounded

byveranda

Window

surrounded

bytheveranda

at7th

floor

E 0.71

·0.71m

)8�C

<DT<

5�C

0.3

Hagishim

aand

Tanim

oto

(2003)

12.4

·2.4

m,sm

ooth

Centre

DDT>

15�C

0.13

a‘C’,‘D

’,‘E’and‘H

’indicate

thecoupledheatedSAT

meter

method,directmeasurementmethod,evaporationmethodwithfilter

paper

and

heatedSATmeter

method.

bAlthoughtheinform

ationaboutDTisnotmentioned

intheoriginalpaper,DTisassumed

tobeabovezero

because

ofthemeasurementmethod.

INTERCOMPARISONS OF EXPERIMENTAL RESEARCH 559

the CHTC is small. However, the dependence of CHTC on wind speed issensitive to the measurement position. Sharples’s (1984) results indicate thatthe CHTC at the edge of the building wall is much higher than that near themiddle. The particular choice of target building also significantly affects theCHTC. If the SAT meter size affected the measured value, the CHTC ofSharples (1984) should be greater than that of Loveday and Taki (1996).However, Figure 4a indicates the opposite tendency: the CHTCs of Lovedayand Taki (1996) are higher than those of Sharples (1984) under the same windspeed. This discrepancy is probably because the target building wall ofLoveday and Taki (1996) was so narrow that the depth of the local boundarylayer above the measurement point was smaller. The flow near a buildingwall edge is more complex than that of the inner part of the walls because ofthe separation vortex; this interpretation is supported by the results ofSharples (1984) in that the CHTC of the edge part of the building wall islarger than that of the centre part. Thus, wall size and shape are likely toinfluence the measured CHTC. In contrast, the effect of the wind direction onthe CHTC is small, which is consistent with Ito et al. (1972).

Next, we discuss three results where the heights of the reference windspeed are under 0.3 m; they were obtained for both windward and leewardconditions. All measurements were made near the centre of the wall (Fig-ure 4b). The CHTC of Narita et al. (1997) is half that of Ito et al. (1972) eventhough the same height for the reference wind speed was used. The reason forthe discrepancy may be the different size of the test plates, although themeasurement conditions were also different. Hagishima and Tanimoto (2003)found that the vertical-wall CHTC and its slope with wind speed are largerthan those for the horizontal roof even though both measurements used thesame method and height of reference wind speed. Since the size of the targetvertical wall in their study was about one-tenth of that of the horizontal roof,the different slopes are likely due to the different surface sizes.

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

0 2 4 6 8 10 12row number from windward

h Dh/

Dfo

the

mos

twod

nstr

eam

rod

roof H/W=0.5 (N)

roof H/W=1 (N)

windward wall H/W=0.5 (N)

windward wall H/W=1 (N)

leeward wall H/W=0.5 (N)

leeward wall H/W=1 (N)

street H/W=0.75 (B) ex.A

street H/W=0.75 (B) ex.B

Figure 4. Variation of mass transfer coefficient of 2-D canopy with fetch.

AYA HAGISHIMA ET AL.560

4. Scale-Model Experiments

It is well known that the flow structure in the roughness sublayer of anurban-like canopy can be divided into three groups according to the arealdensity of the roughness elements, hereafter roughness density. These areskimming flow, wake interference, and isolated flow (Oke, 1987). Thus, it isgenerally assumed that the CHTC for an urban surface depends strongly onthe flow regime and the roughness density. To clarify the relation between theCHTC and the flow structure of an urban canopy, scale-model experimentsshould be a valuable tool because one can easily change the measurementconditions, such as the model shape, street pattern, and wind direction. Inaddition, if measurements are made in a wind tunnel, not only the CHTC butalso the detailed flow structure around the models can be obtained simul-taneously, a task that is almost impossible in full-scale measurements. Forexample, Meinders et al. (1998) found a relation between the flow pattern andthe distribution of CHTC values on a three-dimensional (3-D) canopy, arelation that is greatly affected by the canopy shape. We compare the formerscale-model experiments on the CHTC and the MTC of an urban canopy inthis section.

4.1. EFFECT OF FETCH

Barlow et al. (2004) used the naphthalene sublimation method to investigatethe effect of fetch on the MTC of a 2-D canopy with H/W=0.75. The 2-Dcanopy of their experiment consisted of nine rods of square cross-sectionplaced on the floor of the wind tunnel to simulate nine rows of buildings.They clarified that the MTCs downstream of the second or third row werenearly equal regardless of variations of the vertical profile of the approachingflow. In spite of the differences of the measurement method, model size, andupstream condition, the results of Narita et al. (2000) based on the evapo-ration method with filter paper show a similar tendency (Figure 4). TheMTCs decreases significantly from the first row to the third row. Fluctua-tions in the MTC behind the fourth row are relatively small; the MTC ratiosfor the fourth row to that of the last row are generally 0.9–1.1. This tendencyis consistent with the well-known fetch effect in the flow characteristic ofroughness sublayers, as pointed out by Barlow et al. (2004).

4.2. EFFECT OF CANOPY GEOMETRY

The effect of an approaching flow on the MTC of the canopy can be negli-gible downstream of about the fourth row, as mentioned in the previous

INTERCOMPARISONS OF EXPERIMENTAL RESEARCH 561

section. Also, the effect of canopy geometry on the MTC becomes dominantin these regions. Here we compare two experiments that reveal the rela-tionship between the MTC of a 2-D canopy surface and the model geometry.Figure 5 shows the relationship between the normalised MTC of a 2-Dcanopy and H/W, the ratio of model height to street width. Narita et al.(2000) confirmed that the relations between MTC and H/W have a similartendency for wind speeds of 2, 4, and 6 m s)1, and adopted their average.Barlow et al. (2004) obtained the Stanton number from five cases with windspeeds ranging between 4 and 13 m s)1. For H/W<0.6, where the flow re-gime is assumed to be isolated flow or wake interference, the values for theroof decrease with an increase ofH/W. ForH/W>1.0, where the flow regimeis likely to be skimming, the values are roughly without change. According tothe former wind-tunnel experiments on a sparse canopy, it is expected thatthe canopy with lower density has a larger area of separation and reverse flowabove the roof top. Hence, the mass transfer should be greater with smallervalues of H/W. For a dense canopy with skimming flow, the flow above theroof has little separation or reverse region, as shown by Brown et al. (2000).The smooth flow around the roof may cause a small effect of H/W on MTC.The value of MTC from Narita et al. (2000) is nearly the same as that fromBarlow et al. (2004).

The measured MTCs of a street are below 0.7, as found by Barlow et al.(2004), the only known study of the MTC for a street. Under conditions ofwake interference (H/W=0.6), the MTC of the street is close to that of theleeward side of the building. On the other hand, the MTCs of a street underconditions of skimming flow (H/W=1 and 2) are larger than those of theleeward wall. We will make another comparison of the MTC of a street by

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3H/W

ronm

aliz

edh D

roof(N) leeward(N) windward(N)roof(B) leeward(B) windward(B)street(B)

Figure 5. Measured mass transfer coefficients for various values of height to width ratios

H/W. (N) marks data of 2-D canopy 18H downstream of the edge of canopy arrangementby Narita et al. (2000). (B) is the data of 8th row by Barlow et al. (2004). The MTCs arenormalised by the results in each case for the roof with H/W=1.

AYA HAGISHIMA ET AL.562

Barlow et al. (2004) with the measured distribution by Narita et al. (2000) inthe next section.

The MTCs of the vertical windward wall from two experiments generallydecreases with increasing H/W. In addition, the normalised MTC of thevertical windward wall by Narita et al. (2000) is close to 0.9 for the range ofH/W=0.8–1.0. The relation betweenH/W and MTC of the windward wall ofNarita et al., (2000) is similar to that of Barlow et al. (2004). However, mostMTC values of Barlow et al. (2004) are larger than those of Narita et al.(2000) under the same H/W. The difference of these two experiments isespecially large under the condition of H/W=2.

The MTCs of the leeward wall for two experiments decreases withincreasing H/W for H/W below 0.3 and above 0.7, related to regimes ofisolated flow and skimming flow, respectively. The MTC values for a leewardwall of Barlow et al. (2004) are smaller than those from Narita et al. (2004 )under the sameH/W. This tendency is reversed from that of a windward wall.The difference between these two experiments is particularly large under thecondition of H/W=2. The reason why the wall MTCs from the two exper-iments do not agree is possibly connected with the differences in model size,reference wind speed, surface roughness, and coefficients of molecular dif-fusion. The reason why the molecular diffusion coefficients are differentcomes from the fact that Narita et al. (2000) used water evaporation, whereasBarlow et al. (2004) used naphthalene sublimation.

4.3. DISTRIBUTION OF TRANSFER COEFFICIENT ON EACH SURFACE

OF THE ROUGHNESS ELEMENTS

In this section, we compare the following three experiments on the distri-bution of CHTC and MTC of canopy surfaces.

One experiment, by Aliaga et al. (1994), involved the CHTC of a 2-Dcanopy using the thermal balance method. In that study, ribs with a height of25 mm were arranged on the wind-tunnel floor under the conditions ofH/W=0.09 and 0.25. The Reynolds numbers based on the rib height areabout 78,000 and 52,000. The second experiment, by Chyu and Goldstein(1986), involved the MTC of a 2-D cavity using the naphthalene sublimationmethod. The depth of the cavity was 6.35 mm and the Reynolds numberbased on the cavity depth is about 15,000. During the measurements, theentire surface inside the cavity and the floor around the cavity was coatedwith naphthalene. The third experiment, by Narita et al. (2000), involved theMTC of a 2-D canopy using the evaporation method (using filter paper).They measured the distribution of the MTC of a 2-D canopy with a modelhaving ribs of height 60 mm. The Reynolds number based on the rib height isabout 15,000. The MTC for the 2-D canopy was measured using filter paper

INTERCOMPARISONS OF EXPERIMENTAL RESEARCH 563

60-mm wide and 10-mm long. The filter paper’s position on the model sur-face was changed for every measurement. Hence, the boundary condition ofmass transfer of Narita et al. (2000) is not analogous to that of Chyu andGoldstein (1986).

First, we discuss the data for the 2-D canopy of Narita et al. (2000);Figure 6 shows that the MTC for the roof is nearly independent of positionand H/W. The MTC of the street under the condition of H/W=2 is muchsmaller than that of the wall and roof. Conversely, the MTC of the street islarger on average than that of the leeward wall for H/W=0.5–1. Also, theMTC on the street peaks at a distance of 0.5H from the windward verticalwall. On the leeward wall, the MTC values depend on H/W; for H/W=2, theMTC is larger for higher positions. In contrast, the MTC peaks at a height of0.4H when H/W=1.

Next, we discuss the differences between Narita et al. (2000) and Chyu andGoldstein (1986). In general, the trends are similar in both studies, but theMTC of Chyu and Goldstein (1986) is more sensitive to position than that ofNarita et al. (2000). For example, for H/W=0.5 and 1, the MTC values inthe street have peaks at about the same position for both studies. However,the peak values of Chyu and Goldstein (1986) are larger than those of Naritaet al. (2000). The windward wall shows the same features. Such a tendency islikely to be caused by the difference in the boundary condition of mass

C

D E

B

A

street

windward

leeward

roof

0

0.5

1

1.5

2

2.5

3

3.5

0 1 2 3 4 5

x/H

MT

C/

vaer

gade

MT

Cof

stre

et,

/H

W=1

H/W=0.5 (C) H/W=0.5 (N)H/W=1 (C) H/W=1 (N)H/W=0.67 (N) H/W=2 (N)

streetleeward windward roofA DCB E

Figure 6. MTC measurements from models of Narita et al. (2000), marked (N), and Chyuand Goldstein (1986), marked (C). Reynolds numbers based on the model height are about1.5 · 104 for both studies.

AYA HAGISHIMA ET AL.564

transfer between the two experiments. Narita et al. (2000) used filter paperwith a length of H/6 and a width of H. Hence, the measured MTC was notaffected by advection from other source areas. On the other hand, in Chyuand Goldstein’s experiments, the entire model surface was coated withnaphthalene. Therefore, some of the naphthalene sublimed from the uppersurfaces would be blown into the bottom of the windward wall and also intothe street near the leeward wall, thus causing the air near these regions tohave a higher density of naphthalene and thus a smaller sublimation rate.

The spatial average of the multipoint data of the MTC for a street fromNarita et al. (2000) can also be compared with the results of Barlow et al.(2004), as presented in Figure 5. The data of Barlow et al. (2004) in Figure 5were obtained by measuring the weight change of naphthalene, which wascoated on the street surface. Thus, the resulting value is the spatially averagedMTC. Both studies were for MTCs of a 2-D canopy that had a sufficientnumber of rows on the windward side. Thus, the approaching flows in thewind tunnel are likely very similar for both cases. In brief, the MTC of a streetby Barlow et al. (2004) forH/W=2 is overestimated and that forH/W=0.5 isunderestimated, compared with the results of Narita et al. (2000). Forexample, the MTC of a street of Narita et al. (2000) is smaller than that of aleeward wall for H/W=2. The reverse tendency is observed forH/W=0.5. Incontrast, the MTC for the street in Barlow et al. (2004) is larger than that forthe leeward wall for H/W=2, and is almost the same as that of the leewardwall for H/W=0.5. For H/W=1, the results of both studies are similar. Thedisagreements are likely caused by the differences in the boundary conditionof mass transfer. Narita et al. (2000) used the same source size for measure-ments under various H/W conditions, which have different street widths, andtherefore Reynolds number based on the size of wet filter paper is constantunder various H/W. In contrast, Barlow et al. (2004) measured the MTC ofthe naphthalene-coated street under various H/W conditions with the samevalue ofH. Therefore, the Reynolds number based on the street source size ofnaphthalene differs from H/W. Therefore, the MTC of Barlow et al. (2004) isunderestimated compared with that by Narita et al. (2000) for small H/W,where the street size is large, due to the effect of advection. Accordingly, infuture measurements of MTC and CHTC of an urban-like canopy, it shouldbe required to discuss both the effect of geometry and source size separately.

For the case of a sparse canopy, measurements of MTC in one study havea different dependence on position (Figure 7). For H/W=0.09, Aliaga et al.(1994) confirmed that, based on visualization using yarn tufts, the flow re-gime is an isolated flow. The peak of the CHTC of Aliaga et al. (1994) is adistance of 5H from point B, which was consistent with the observed point ofreattachment from the flow visualization. Also, the CHTC increases rapidlyat a distance of 11H from point B; this result is connected with the separationpoint, which was observed at a distance of 10H from point B.

INTERCOMPARISONS OF EXPERIMENTAL RESEARCH 565

The CHTC of Aliaga et al. (1994) for H/W=0.25, a flow regime that wasobserved to be wake interference, increases monotonically from point B topoint C. In contrast, the MTC of Chyu and Goldstein (1986) has a sharppeak near point C. Since the MTC of Narita et al. (2000) for H/W=0.5 inFigure 6, which is also in the wake interference regime, has a similar ten-dency, the difference in measurement methods and Reynolds number mayhave caused the difference in results between Aliaga et al. (1994) and Chyuand Goldstein (1986).

4.4. COMPARISONS BETWEEN FULL-SCALE AND SCALE-MODEL EXPERIMENTS

Previous heat-transfer engineering studies have found that the Nusseltnumber for a flat plate under turbulent forced convection can be expressed as

Nu ¼ CRemPrn; ð6Þwhere Nu is the Nusselt number, Pr is the Prandtl number, and Re is theReynolds number; C, m and n are empirical parameters. Johnson andRubesin (1949) showed that C=0.0296, m=4/5, and n=2/3 under the con-dition of turbulent flow with 0.5<Pr<5. Assuming the similarity of masstransfer and heat transfer, the Sherwood numbers can be expressed as

Sh ¼ CRemScn; ð7Þwhere Sc is the Schmidt number, and Sh is the Sherwood number. ThusSherwood number and Nusselt number can be compared directly, via

Nu.Prn ¼ Sh

.Scn ¼ CRem: ð8Þ

0

0.5

1

1.5

2

2.5

3

0 2 4 6 8 10x/H

rona

mliz

eM

dT

C,C

HT

C

12

H/W=0.25 (A)

H/W=0.09 (A)

H/W=0.25 (C)

B C (H/W=0.25) C (H/W=0.09)

Figure 7. CHTC of a street in a 2-D canopy and MTC of a street of 2-D cavity. (A) areCHTC data from Aliaga et al. (1994). (C) are MTC data from Chyu and Goldstein (1986).CHTC and MTC are normalised by the area-averaged data. The Reynolds number based

on the model height of the data of Aliaga et al. (1994) for H/W=0.09 and 0.25 are 7.8 ·104 and 5.2 · 104, respectively. The Reynolds number based on the model height in Chyuand Goldstein (1986) is 1.5 · 104.

AYA HAGISHIMA ET AL.566

If similar scaling applies to full-size and scale-model experiments for urbansettings, one should be able to directly compare results from these two typesof experiments. To address this issue, we compare three scale-model exper-iments on the MTC and CHTC for the roof in an urban-like canopy with onefull-scale measurement on the CHTC of a building roof.

The scale-model experiment of Barlow et al. (2004) used a naphthalenesublimation method to study both the windward wall and roof of a 2-Dcanopy. The Reynolds number based on the canopy height of H=9.4 mmand the wind speed above the boundary layer is as high as 7000. The secondscale-model experiment, by Narita et al. (2000), uses the evaporation methodwith filter paper on a 2-D canopy under a turbulent boundary layer generatedby an L-shaped bar. The Reynolds number based on the rib height ofH=60 mm and the wind speed above the boundary layer is as high as 22,000.The last scale-model experiment, by Meinders et al. (1998), used the thermalbalance method. In that study, eight cubes 15-mm on a side, were scattered atregular intervals on a straight line in a wind tunnel of height 50 mm. Thereference wind speed was defined as the bulk speed of the wind-tunnel flow.

The full-scale study, by Kobayashi (1994), used measurements of theCHTC on a horizontal roof of a three-storey building; the thermal balancemethod was used and the thermal conditions were unstable. There were onlysmaller buildings in the vicinity, so we assume that the flow was isolated; theoriginal reference height of the wind speed was 10 m above the building roof(2H). To compare this study to the scale-model experiments, we assumed thatthe wind speed was proportional to the height to the power 0.25 and thentransformed Kobayashi’s measured wind speed to the value at 8H.

Figure 8 presents the CHTCs and MTCs normalised by non-dimensionalparameters under various Reynolds numbers. For a given Reynolds number,the non-dimensional CHTC from the full-scale study was found to be severalorders of magnitude larger than the values from all three scale-modelexperiments. We now discuss several reasons for the discrepancy between thefull-scale and scale-model results. The first reason is the difference in heightof the reference wind speed. Although the reference wind speeds of all theexperiments are defined above the surface boundary layer, the heights are notexactly equal. These differences may account for several tens of percent in theReynolds number. This discrepancy in Reynolds number is not large enoughto explain the measured discrepancy in non-dimensional CHTC. It is as-sumed that such an error is much smaller than the disagreement in ordinatevalue. The measured discrepancy might also be caused by the difference inshape between the scale models and the full-size building. However, this isunlikely to be the main cause for the following reasons: (1) Figure 2 indicatesthat the CHTCs of roofs at low wind speed are nearly independent of roofsize and shape. Thus, the error of the full-scale model should be small at

INTERCOMPARISONS OF EXPERIMENTAL RESEARCH 567

small Reynolds numbers. (2) H/W has relatively little effect on MTC of theroof (Figure 5). (3) The number of rows on the windward side can changeMTC by at most about 50% (Figure 4).

We also need to consider the possibility that MTCs are not exactly anal-ogous to CHTCs. However, the similarity between heat and mass transfer iswell established, so the differences between these processes is probably muchtoo small to explain experimental discrepancies exceeding a factor of ten.

Consequently, we believe that the most plausible reason for the discrep-ancy is that the representative length in the non-dimensional coefficients isnot applicable to both full-scale and scale-model sizes.

4.5. COMPARISONS OF STANTON NUMBER BETWEEN SCALE-MODEL AND

FULL-SCALE EXPERIMENTS

Here we investigate the differences of the transfer coefficient (hD/U) andStanton numbers (h/qcpU) between the scale-model experiments and afull-scale measurement. We compare the scale-model data on MTCs for theroof of a 2-D canopy from Barlow et al. (2004) and Narita et al. (2000) to thefull-scale results from Kobayashi (1994). We also examine the roof of anisolated cube under a turbulent boundary layer based on Narita et al. (2000).

1E+0

1E+1

1E+2

1E+3

1E+4

1E+3 1E+4 1E+5 1E+6 1E+7Re

hScS/

2(/3

) ,N

u/P

r2(

/ 3)

Figure 8. Scaled Sherwood numbers and Nusselt numbers for various Reynolds numbers

from measurements on 2-D scaled model and a full scale building. Empty circle and x aredata from a roof of a 2-D canopy with H/W=2 and 0.25, respectively. Diamond and triangleare data from a windward wall of a 2-D canopy with H/W=2 and 0.25, respectively. Thinlines are data of the eighth rib of the 2-D canopy by Barlow et al. (2004). Grey-filled circle

and diamond are data of 2-D canopy by Narita et al. (2000), which were measured 15Hdownstream of the leading edge of a 2-D canopy. Black squares are values from Meinderset al. (1998), which are the CHTCs for the roof of a cube in the fifth row. In their experi-

ments, six cubes were scattered at regular intervals on a straight line with H/W=1. Thick-solid and dotted lines are empirical equations for the CHTC on the roof of a three-storeybuilding from Kobayashi (1994) for wind speeds above 0.5 and below 0.5 m s)1, respectively.

AYA HAGISHIMA ET AL.568

First, we discuss the results of the scale-model experiments. The transfercoefficients for the roof are about three times greater than those for thewindward wall and both have little dependence on wind speed (Figure 9).The transfer coefficient of the roof of an isolated cube, based on Narita et al.(2000), decreases with increase of wind speed. Those for the roof of Barlowet al. (2004) also decrease with increase of wind speed. In contrast, most ofthe transfer coefficients of the windward wall of a 2-D canopy are aboutconstant with wind speed.

Such a tendency should be caused by the differences in flow charac-teristics within and above the urban canopy. Above the roof top of a 2-Dcanopy consisting of uniform ribs, it is expected that there is almost noreverse flow, as reported by Brown et al. (2000). Therefore, the charac-teristics of mass transfer from a roof may be similar to that above a flatplate. The fact that the Stanton number of the roof is not constant withwind speed is consistent with the former nonlinear relation betweenSherwood number and Reynolds number on turbulent flow above a flatplate, as mentioned above.

In contrast, high turbulence within the canopy ensures the transfer coef-ficient of the windward wall is insensitive to wind speed. The large-eddysimulation of Kanda et al. (2004) supports this explanation, who pointed outthat the flow patterns around cubic-array models have large intermittencyand the stream patterns fluctuate instantaneously.

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0 2 4 6 8 10 12 14

wind speed U [m s-1]

hD/ U

fo s ca

led

-2D

c a

onnyp

nad

h/U

cp

o f

b u

dlin i

g

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

h D/U

foro

foo

fi s

loat

edc u

ebof

Nar

itae ta

l.(002

)0

Figure 9. Transfer coefficient and Stanton number for various wind speeds. + with thickline indicates the data of roof of isolated cube quoted by Narita et al. (2000). Circle and xindicate the data of roof of 2-D canopy with H/W=2 and 0.25, respectively. Diamond and

triangle indicate the data of windward wall of 2-D canopy with H/W=2 and 0.25, respec-tively. Plots with thin lines are data of eighth rib of 2-D canopy by Barlow et al. (2004).Grey plots are data of 2-D canopy by Narita et al. (2000), which are measured at 15H

downstream of leading edge of 2-D canopy. Black thick line indicates the data of roof ofthree-storey building based on Kobayashi (1994).

INTERCOMPARISONS OF EXPERIMENTAL RESEARCH 569

The transfer coefficient of the windward wall with H/W=0.25 for a windspeed of 4.4 m s)1 is greater than that for wind speeds above 5 m s)1.According to the data for a windward wall with H/W=2, all of the transfercoefficients are nearly independent of wind speed. Hence, the critical condi-tion when the effect of length scale and wind speed on transfer coefficientbecomes negligible is expected to depend on the roughness and the locationof the target surface.

Next we discuss the differences of Stanton number of a 2-D canopy be-tween Narita et al. (2000) and Barlow et al. (2004) under the condition of H/W=2. Unfortunately, the other experimental conditions are different; theseinclude different model dimensions, wind speeds, surface roughness, andmolecular diffusion coefficients. Therefore, it is difficult to evaluate preciselywhether their data are consistent or not. In short, we cannot concludewhether those two datasets are consistent by extrapolation or not.

Next, we compare the full-scale measurements to the scale-modelexperiments. The heat transfer coefficient of the full-scale measurementsdecreases with increasing wind speed, and the rate of decrease is greatest atthe lowest wind speeds. This tendency is similar to those for roofs in scale-model experiments. Also, for a given wind speed, the value of the heattransfer coefficient for the full-scale measurement is about 60% of theStanton number from the two scale-model experiments. The factors ofdisagreement between full-scale and scale-model experiments cannot beverified precisely due to differences in the measurement conditions,including the model shape, surface length, the use of CHTC or MTC, andthe reference height of the wind speed.

Consequently, a further systematic experiment under various conditions isneeded for clarifying the differences of the CHTC and MTC betweenscale-model and full-scale urban surface.

4.6. EFFECT OF THE DEVIATION OF THE ROUGHNESS ON THE MASS TRANSFER

COEFFICIENT

The characteristic of flow around a real urban-like canopy, which consists ofvarious building heights, has recently been investigated. For example, thewind-tunnel experiments of Cheng and Castro (2002) showed that the depthof the roughness sublayer with various block heights is larger than that forthe same size blocks having the spatially averaged height. Also, the large-eddy simulations of Kanda (2005 ) showed that the drag coefficient of a densecanopy increases with increasing standard deviation of the building heights.These results indicate that the inhomogeneity of building heights may greatlyinfluence the CHTC of urban surfaces. However, this has not been fullyexamined using scale models with blocks of varying height.

AYA HAGISHIMA ET AL.570

Here, we discuss the experiments of Narita et al. (1986), who used thesalinity measurement method. In this method, the tanks, which are filled withwater, are embedded in the target surface, and the level of the water and thetarget surface are identical (both of which constitute the inner floor of thewind tunnel in their study.) The water tanks are exposed under a constantflow condition for a fixed period of time. Then the evaporation rate and theMTC are obtained by determining the changes of the salinity of the watertank. In the wind tunnel, Narita et al. (1986) had a square water tank 0.6 mon a side, in which 36 rectangular blocks with bases 60 mm · 60 mm andvarious heights above the water surface were arrayed 0.1 m apart in a lattice.The plan area density kp was fixed at 0.36 and the ratio of street width to thespatially averaged blocks heights was fixed at 1.5. The spatially averagedMTCs of the streets in the 3-D canopy were measured with various devia-tions of the block heights.

Figure 10 shows that the normalised MTCs of the street increase with thenormalised standard deviation of the model heights r/H; the normalised dragcoefficients by Kanda (2005) are also plotted for comparison. The trend showsthat the value of hD and CD increase with r/H, and likely exceed 40% for r/Hgreater than 0.5. Their results suggest that non-uniformities in the buildingheights can change the flow from skimming flow to a more turbulent flow.

5. Conclusions

We compared past experimental studies on the CHTC and MTC of urbansurfaces, including both indoor and outdoor studies. The results are sum-marised as follows.

– In full-scale measurements on horizontal building roofs, the CHTC is mostsensitive to the height of the reference wind speed for heights below 1.5 m.In contrast, two CHTCs with different roof sizes but the same referencewind speed height are almost the same. This agreement suggests that theCHTC of a full-scale roof is relatively independent of roof size.

– In full-scale measurements of vertical building walls, the dependence of theCHTC on wind speed is significantly influenced by the choice of themeasurement position and wall size. The CHTC of the edge of the buildingwall is much higher than that near the centre. The effects of thermalstability and measurement method on the measured CHTC have not beensystematically studied.

– Two wind-tunnel experiments suggested similar relationships between H/Wand the MTC values of a 2-D urban-like canopy, despite the differences inmeasurement method. The relationships between MTC and H/W in thesestudies were consistent with current knowledge on the flow regime of urbancanopies.

INTERCOMPARISONS OF EXPERIMENTAL RESEARCH 571

– The MTC dependence on position from two experiments with differentmeasurement methods showed a similar tendency, but the sensitivity of thatdependence varied because of the difference in areas of the evaporatingsources (water in one case, naphthalene in the other).

– The non-dimensional CHTC of a full-scale building surface was muchlarger than that from three scale-model experiments with the sameReynolds number. The most plausible reason was that the representativelength used in the Reynolds number, the roof size, is not appropriate forboth full-scale and scale-model experiments.

To improve UCM modelling, we need a complete model of CHTC forurban areas, with investigations as follows.

– For the full-scale CHTC case, measurements with the same referenceheights from previous studies (e.g., 1 m) should include simultaneous flowmeasurements around the target surface and in the urban boundary layer.Similarly, determination of the impact of the thermal stability condition(e.g., bulk Richardson number between the surface and a reference height)on CHTC is needed.

– Studies with the same scales but using different methods, and studies withthe same method but different scales, are needed. Several studies adoptedhere for comparisons have different measurement methods and differentscales. For clarifying the effects of measurement method and model size onCHTC and MTC, systematic intercomparisons should be made that wouldhold all variables constant, and vary only one at a time.

– Scale-model experiments under various geometric conditions of roughness,such as the roughness density, street pattern, and heterogeneity in the

0.9

1.2

1.5

1.8

0 0.2 0.4normalized standard deviation

ronm

aliz

edh

Da

dnC

d

Figure 10. Measured MTC and drag coefficient. The values are normalised by those under

the condition of r/H=0. Grey circles indicate the normalised MTC of 3-D canopy withrectangular blocks kp=0.36 from Narita et al. (1986). This work was done using the salin-ity measurement method. Plots with line are the normalised drag coefficient of 3-D canopy

with rectangular blocks by Kanda (2005). x, triangle, and + indicate the value under thecondition of kp=0.11, 0.25 and 0.44, respectively.

AYA HAGISHIMA ET AL.572

obstacle shape are needed, in particular, experiments using 3-D, urban-likeroughness with sufficient fetch. In addition, because the length scale ofconvection around urban surfaces is not determined solely by the canopyheight or wall size, simultaneous measurements of both the CHTC and theturbulent flow structure in and above the urban canopy would be helpful.

– Scale-model experiments under various thermal conditions should beperformed, since most scale-model experiments have been performed in awind tunnel under neutral conditions. Therefore, the CHTC for real urbansurfaces, which have significant variations of surface temperature due toshady regions, has not been clarified.

Appendix A: Methods of measuring the CHTC

A.1. THERMAL BALANCE METHOD

A.1.1. Direct measurement methodThe directmeasurementmethod uses estimates ormeasurements ofQE,QG, andQ* in Equation (1) to estimateQH, and then usesmeasurements ofTs andTair inEquation (2) to obtain h (i.e., CHTC). To simplify the determination of heat fluxQH, the QE term is made negligible by using dry surfaces in the experiments.Then, the net radiation and conductive heat flux of the surface are measured todetermine QH. With QH and (Ts)Tair), Equation (1) is used to obtain h.

In this method, the conductive heat fluxes on the surfaces are usuallymeasured with a heat flow meter that consists of a thin plate with manythermocouples. To ensure uniform flow conditions, the outside surface of theheat flow sensor should be painted with a thin coat that has the same solarabsorption rate, emissivity, and roughness of the target surface. The netradiation is generally measured directly near the target surface. In thismethod, it is necessary that the view factor from the net radiometer to thetarget surfaces nearly equals one and the temperature of the surface is asuniform as possible. This method is mainly used for experiments with a largeflat building surface such as a horizontal roof. Measurement errors of Sfl, Lfl,Ts and Tair accumulate in the derived value of CHTC in this method. Inparticular, when both the net radiation and the temperature difference be-tween the surface and air are small, the experimental error is relatively large.Thus this method is ordinarily used only in daytime. The advantage of thismethod is that it can directly give the CHTC of the target surfaces because theflow around the heat flow sensor nearly equals that around the target surface.

A.1.2. SAT meter methodIn this method, a black-painted test plate consists of a heat insulator, here-after the SAT meter, and is mounted on the target surface. SAT is the

INTERCOMPARISONS OF EXPERIMENTAL RESEARCH 573

acronym for ‘sol-air temperature’, an effective outdoor temperature modifiedby solar radiation and longwave radiation. It is defined as

Te ¼ Tair þ1

h

�aS# þe

�L# �rT4

s

��; ðA:1Þ

where a is the solar absorptivity, Lfl is the incident longwave radiation, Sfl isthe incident solar radiation, e is the emissivity, and Te is the sol-air tem-perature, which is a technical term used in building science. The sol-airtemperature Te is used to estimate the cooling and heating load of thebuilding based on

q ¼ h Te � Tairð Þ; ðA:2Þwhere q is the air-conditioning heat flux that will be needed in the building insteady state.

A SAT meter consists of a thermal insulator covered with a thin copperplate painted black. If the solar absorption rate and emissivity of the paintedsurface are known, one can estimate the net radiation using the measuredvalue of incident solar radiation, longwave radiation, and surface tempera-ture of the SAT meter. Conductive heat flux into the surface is usually as-sumed negligible because of the thermal insulation. Therefore, the CHTC ofa SAT meter can be obtained using

h ¼aS# þeL# �erT4

s

� �

Ts � Tairð Þ : ðA:3Þ

If the thermal and hydrodynamic boundary layers of the building surfacesequal those of the SAT meter, we can assume that the measured CHTCequals that of the building surfaces.

This method is applicable even for actual building surfaces that have acomplex distribution of surface temperature caused by multiple coveringmaterials and surface irregularities. At nighttime, the uncertainty in h isrelatively large because both the denominator and the numerator are small.Thus, this method is ordinarily used in the daytime.

A.1.3. Other methodsSince the measurement error in both the direct measurement method and theSAT meter method is relatively large when the absolute value of DT is small,several methods have been used to overcome this problem. One, the ‘heatedSAT meter method’, uses the SAT meter with an embedded electrical heater.Another method, the ‘coupled heated SAT meter method’, uses two SATmeters with the same surface colour, both of which are heated with electricalheaters. The SAT meters are placed side by side on the target surface. Thequantity of supplied heat should be controlled to keep the surfaces of the twoSAT meters at different temperatures. Under such a condition, the CHTC of

AYA HAGISHIMA ET AL.574

both SAT meters can be deduced based on the thermal balance equation ofeach SAT meter. Since these methods can maintain a temperature differencebetween air and the surface of the SAT meter above a set value, measure-ments can be made even at nighttime.

In addition to these methods, there are those in which the measurementsof conductive heat flux and net radiation are designed according to the sitecondition. For example, Kanda and Katsuyama (2002) estimated the netradiation based on a 3-D numerical simulation using a Monte-Carlo methodin an outdoor scale-model experiment. This was done because of difficultieswith directly measuring the net radiation on the small surfaces of the concreteblock on the site.

Acknowledgments

This research was partially supported by Core Research for Evolution Sci-ence and Technology (CREST) of the Japan Science and Technology Agency(JST) and a Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Young Scientists (A), 14702047, 2002.

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