Energy and Buildings 76 (2014) 392–401

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Energy and Buildings

j ourna l ho me pa g e: www.elsev ier .com/ locate /enbui ld

Thermal performance of concrete-based roofs in tropical climate

Shanshan Tonga, Hua Lia,∗, Kishor T. Zingrea, Man Pun Wana, Victor W.-C. Changb,Swee Khian Wongc, Winston Boo Thian Tohc, Irene Yen Leng Leec

a School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singaporeb School of Civil and Environmental Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798 Singapore, Singaporec Building Research Institute, Housing and Development Board Hub, 480 Lorong 4 Toa Payoh, 310480 Singapore, Singapore

a r t i c l e i n f o

Article history:Received 9 October 2013Received in revised form 15 January 2014Accepted 25 February 2014

Keywords:Transient heat transferCFFT modelCool roofPassive roofing technologiesConcrete roof heat gain

a b s t r a c t

In this work, an analytical Complex Fast Fourier Transform (CFFT) method is used and modified to pre-dict the transient roof temperature and transmitted heat flux through the multilayer roofs of naturallyventilated rooms. A field experiment is carried out on two full-scale roofs to validate the CFFT model.The mean bias error (MBE) and cumulative variation of root mean square error (CVRMBE) in the ceil-ing temperature prediction using CFFT model are found less than 4% during both sunny and rainy days.After validation, a parameter study is conducted to investigate the impacts of rooftop surface solar reflec-tivity (from 0.1 to 0.9) and thermal resistance (from 0.1 to 2.5 m2 K/W) on the thermal performance oftwo types of concrete-based roofs, namely the unventilated and ventilated roofs. Compared to the roofswith solar reflectivity of 0.1, increasing the solar reflectivity by 0.1 reduces the daily heat gain by 11%in both the unventilated and ventilated roofs during a typical weather day in Singapore. Compared withthe unventilated roofs, the individual uses of roof ventilation and 2.5-cm expanded polystyrene (EPS)foam insulation reduce the daily roof heat gain by 42% and 68% respectively, and the daily roof heat gainreductions increase to 73% and 84% in the ventilated roofs incorporated with 2.5-cm EPS foam and radiantbarrier respectively.

© 2014 Elsevier B.V. All rights reserved.

1. Introduction

Nowadays the building sector has become the largest energyuser and it accounts for 30–40% of world energy use [1]. Among thevarious building services, heating, ventilation, and air-conditioning(HVAC) systems account for nearly 50% of total building energy usein the developed countries [2]. During summer periods or in trop-ical areas, the energy use for air-conditioning in buildings reachesto a particularly significant portion, for example, 28% in Taiwan[3], 40% in Hong Kong [4], and 40–50% in Singapore [5]. Moreover,the economic growth and increasing demands for indoor comfortpredict an upward trend of air-conditioning use in the future. How-ever, the heavy use of air-conditioning puts enormous burden onthe electricity demand during the peak summer hours and causesseveral environmental issues, such as global warming and urbanheat island effect.

Since a major part of the air-conditioning load comes from thesolar heat gain of building envelope, the thermal performance ofbuilding envelope is widely studied in recent years, in order to

∗ Corresponding author. Tel.: +65 6790 4953; fax: +65 67924062.E-mail address: LIHUA@ntu.edu.sg (H. Li).

improve the indoor thermal comfort or curb the air-conditioningload. Improvement on the building envelope is often independenton the external mechanical or electrical devices, which is cate-gorized into passive technology. A technical review was done bySadineni et al. to discuss the energy savings of applying passivetechnologies on the various building envelope components, suchas the wall, roof, window and door [6]. Among these envelopecomponents, the roof is most exposed to the overhead solar radi-ation. In general, the common passive roofing technologies thatcontribute to cooling load reduction include the cool paint, roofventilation, green roof, and mass/reflective insulation. In terms ofconcrete roofs, Parker and Barkaszi studied the energy savings pro-vided by cool paint through nine concrete-roofed houses in thesummer of Florida [7], and concluded that the electricity use byair-conditioners was decreased by 19% on average after applyingthe cool paint with a solar reflectivity of 0.73 on the residentialroofs, and the peak cooling load reductions ranged from 12% to 38%in the nine houses. The cool paint was applied on a 700 m2 concreteroof in Sicily of Italy, in which the roof exterior surface temperaturewas reduced by up to 20 ◦C, the indoor operative temperature wasreduced by 2.3 ◦C, and the cooling energy demand was reduced by54% during the cooling season [8]. Dimoudi et al. studied the ben-efits of using roof ventilation during the summer period in Greece,

http://dx.doi.org/10.1016/j.enbuild.2014.02.0760378-7788/© 2014 Elsevier B.V. All rights reserved.

S. Tong et al. / Energy and Buildings 76 (2014) 392–401 393

Nomenclature

E solar radiation intensity (W/m2)hc convective heat transfer coefficient at exterior roof

surface (W/m2 K)he overall heat transfer coefficient at exterior roof sur-

face (W/m2 K)hi overall heat transfer coefficient at the ceiling

(W/m2 K)i complex argumentk thermal conductivity of roofing material (W/m K)L thickness of the roof material (m)N total number of roof layersqo overall convective and radiative heat flux between

roof exterior surface and outdoor environment(W/m2)

qr net radiative heat flux in Eq. (12) (W/m2)QC daily roof heat gain (W h/m2)t time (s)Tn(x,t) roof temperature at distance x within the nth layer

(K)To outdoor air temperature (K)Ti indoor air temperature (K)Tsky the sky temperature (K)V outdoor wind speed (m/s)zn dimensionless distance within the nth roof layer

Greek letters˛ thermal diffusivity (m2/s)! solar reflectivity of rooftop surfaceε thermal emissivity of rooftop surface# Stefan–Boltzmann constant,

# = 5.67 × 10−8 W/m2 K$ dimensionless time

Subscripts and superscriptsn layer numberj Fourier transform coefficient

and reported that a 6-cm ventilated air gap reduced the daily heatgain of a flat concrete roof by 56% during the daytime, and the addi-tional use of radiant barrier increased the heat gain reduction to 68%[9]. The U-values of ventilated roof prototypes incorporated withradiant barrier were measured in laboratory environment by Changet al. [10], in which an optimum air gap height of 10 cm was sug-gested for the ventilated roofs with 30–90◦ inclinations. Green roofswere also implemented on the concrete roofs. For example, Zhouet al. reported that a rooftop lawn reduced the peak air temperatureinside a concrete building by 3–4 ◦C in the summer season of Japan[11]. Sfakianaki et al. observed a maximum indoor temperaturereduction of 0.6 ◦C after planting the vegetation on a concrete roof inGreece [12]. Halwatura and Jayasinghe studied the impact of insu-lation (polyethylene) thickness and concluded that adding a 2.5-cmthick polyethylene insulation on the scaled concrete roof reducedthe peak roof soffit temperature from 42 to 33 ◦C in the tropicalclimate of Sri Lanka [13]. Alvarado et al. measured the thermal per-formance of concrete-based roof prototypes with different types ofinsulations in laboratory, and found that the combined applicationof aluminum reflector and polyurethane insulation offered a notice-able heat flux reduction of 88% compared with the un-insulatedroof prototypes [14]. Regarding the implementation of these pas-sive roofing technologies, cool paint is compatible with most roofsand can be easily applied on both the newly built and retrofittedroofs. Structural issue associated with cool paint is minimal, making

cool paint suitable for both lightweight and heavyweight roofs.However, the implementations of other passive technologies onthe building roofs require careful design considerations. For exam-ple, for ventilated roofs, the secondary roof could neither be tooheavy so that it exceeds the load bearing capacity of main roof, norbe too light to resistant the wind force.

Singapore is a tropical country located at 1 ◦C north of the equa-tor having hot and humid tropical climate throughout the year, andthe incident solar radiation reaches 1000 W/m2 on the most cloud-less days [15]. With 100% of its population urbanized, the city-stateplaces major concern on the indoor thermal comfort and spacecooling energy savings. The majority of Singaporeans live in theconcrete-built and high-rise residential blocks. A typical design ofroofs in these residential blocks consists of a concrete main roof, aferrocement secondary roof, and an air gap between the two solidroofs. As far as the thermal comfort in these buildings is concerned,it is desirable to evaluate the thermal performance of current roof-ing system and estimate the potential benefit of integrating variouspassive technologies in these residential roofs.

According to the work by Wang and Chen [16], the existing spacecooling/heating load prediction methods were classified into fourcategories: periodic (harmonic), response factor (RF), conductiontransfer function (CTF), and numerical methods. Periodic meth-ods solve the transient heat conduction problem with periodicboundary conditions, in which the transient outdoor solar radi-ation and air temperature are approximated by finite number ofFourier series. The periodic methods were proposed by Mackey andWright to predict the transmitted heat flux across walls and roofs[17,18], and then improved by other researchers [19–21]. The RFmethods approximate the transmitted heat flux across the buildingenvelope as a linear function of the infinite series of history tem-peratures at the exterior and interior building surfaces, in whichthe coefficients were calculated by Laplace and Z-transforms [22],state space method [23], or the analysis in frequency domain usingFourier transform [24]. In order to reduce the potentially long seriesof response factors, the CTF method was proposed by Mitalas andStepheson to predict the heat flux using finite series of history tem-peratures and heat fluxes [25]. The RF and CTF methods are widelyimplemented in the building energy simulation programs, such asDOE-2 [26], TRNSYS [27], EnergyPlus [28] and BLAST [29]. How-ever, both RF and CTF methods require history temperatures orheat fluxes of the evaluated types of building walls and roofs asinput. Numerical methods approximate the wall and roof temper-atures using finite difference or finite element methods, in whichthe numerical accuracy depends on the nodal number, selectedtime-step, and solution methodology. Compared with the analyt-ical methods, the numerical methods are conceptually simple butcompute-intensive and time-consuming. Moreover, the tempera-ture calculations at nodes within the multilayer walls or roofs areoften unnecessary.

As well known, the Complex Finite Fourier Transform (CFFT)technique [21] as a periodic method can well predict the transientroof temperature and transmitted heat flux across the concrete-based multilayer roofs. The CFFT method doesnot require thehistory temperature and transmitted heat flux data as well as heavycomputational efforts, which are required by RF, CTF or numericalmethods. However, the CFFT method was seldom used. A few exam-ples of its application include the estimation of the total equivalenttemperature difference values for multilayer walls and roofs withconstant indoor temperatures [30], and the optimization of insula-tion thickness for multilayer walls in Tunisian [31].

In order to evaluate the thermal performance of multilayer roofsof naturally ventilated rooms, the CFFT method is used in this paperto predict the transmitted heat flux across multilayer roofs withperiodic boundary conditions at both the exterior and interior roofsurfaces. The CFFT model is validated by a field experiment carried

394 S. Tong et al. / Energy and Buildings 76 (2014) 392–401

Fig. 1. Schematic representation of a multilayer roof.

out on two full-scale multilayer roofs. Furthermore, the validatedmodel is employed to predict the impacts of rooftop surface solarreflectivity and thermal resistance on the ceiling temperature anddaily roof heat gain. The potential benefits of applying the coolpaint, roof ventilation, expanded polystyrene (EPS) foam and radi-ant barrier on the concrete-based roofs are also evaluated.

2. CFFT model

Considering a roof consisting of N parallel layers as shown inFig. 1, the exterior roof surface is exposed to the transient outdoorsolar radiation E(t) and dry-bulb air temperature To(t). At the inte-rior roof surface, the heat gain due to indoor human activity orequipment as well as the radiative heat transfer between roof andthe walls or floor is assumed negligible, such that the convectiveheat transfer between roof and the indoor air is considered only. Lnis the thickness of the nth roof layer, and the transient temperatureat distance x within the nth roof layer is denoted as Tn(x,t). Tn(x,t)is a function of roof properties, including the roof layer thickness(L), thermal conductivity (k), thermal diffusivity (˛) and exteriorsurface solar reflectivity (!), as well as the transient indoor andoutdoor environmental conditions. Two assumptions are made tosimplify the transient conductive heat transfer across the multi-layer roofs. One assumption is that the length and width of roofare much larger than the thickness, such that heat is transferred inthe direction perpendicular to roof surface only. The other is thatroof is made up of homogenous material layers with constant ther-mal properties in each layer. Therefore, the heat transfer across the

roof is governed by the following one-dimensional heat conductionequation,

∂2Tn

∂x2n

= 1˛n

∂Tn

∂tfor 0 < xn < Ln, and 1 ≤ n ≤ N (1)

The boundary conditions on the upper and lower surfaces of eachroof layer are given by

−kN∂T1

∂x1= (1 − !)E(t) − [he(T1 − To) + qr] at x1 = 0 (2)

−kn−1∂Tn−1

∂xn−1

!!!!xn−1=Ln−1

= −kn∂Tn

∂xn

!!!!xn=0

(2 ≤ n ≤ N) (3)

hi[TN − Ti(t)] = −kN∂TN

∂xNat xN = LN (4)

T |xn−1 = Ln−1 = T |xn=0 for 2 ≤ n ≤ N (5)

The periodicity condition Tn(x, t) = Tn(x, t + p) (p = 24 h) isimposed in Eqs. (1)–(5). By CFFT method [21], a general periodicsolution of the transient roof temperature is obtained in the formbelow

Tn(zn, $) =j=M"

j=−M

Tn,j(Zn) exp(iωj$) (6)

where zn = xnLn

, $ = t−1224 , ωj = 2'j

and

Tn,j(zn) =# 1/2

−1/2Tn(zn, $) exp (−iωj$)d$ (7)

In this work, the indoor air temperature Ti(t) is also transformedinto dimensionless form following the same treatment for the out-door solar radiation E(t) and air temperature To(t), in order topredict the transmitted heat flux across the roofs of naturally ven-tilated units. A direct solution for the transient roof temperature isobtained as

Tn,0(zn) = Anzn + Bn for j = 0; (8)

Tn,j(zn) = Cn,j sinh (!n,jzn) + Dn,j cosh (!n,jzn) for j /= 0; (9)

where !n,j = (1 + i)$

ωjen

2 , en = L2n

˛np and An, Bn, Cn,j, Dn,j are the

coefficients determined by Eqs. (1)–(5). The transmitted heat fluxinto the building interior becomes

q(t) = hi[TN(zN = 1, t) − Ti(t)] (10)

Fig. 2. Shots on the experimental roofs.

S. Tong et al. / Energy and Buildings 76 (2014) 392–401 395

Fig. 3. Schematic diagram of experimental setup.

and thus the daily roof heat gain per unit area is

QC =24"

t=1

q(t) × (t (11)

3. Model validation by field experiment

3.1. Experimental setup

Field experiment is carried out on a 12-storey residential build-ing to validate the CFFT model. Two naturally ventilated andside-by-side vacant units located on the top floor are selected forthe experimental study. The existing building roof consists of fourlayers, which are placed from top to bottom as a 3-cm thick ferroce-ment slab, a 22-cm thick ventilated air gap, a 15-cm thick concreteslab and a 0.5-cm thick cement plaster. On one of the two roofs,cool paint with high solar reflectivity is applied on the top surfaceof ferrocement slab, as shown in Fig. 2. The experiment lasted forthree weeks in the February of 2012, due to the approved access toresidential units and rooftop during this period.

The schematic of experimental setup is shown in Fig. 3. Theroof surface temperatures are measured by resistance temperaturedetectors (RTDs) with errors within ±0.25 ◦C, and the tempera-ture data is collected by data loggers placed inside the units. Thesurface temperatures of upper ferrocement slab (T1), lower ferroce-ment slab (T2), upper concrete roof (T3), and ceiling plaster (T4) aremeasured by RTDs. The global solar radiation is measured by thealbedometer (Kipp and Zonnen CMA11) installed at 1.5 m abovethe rooftop. The outdoor dry-bulb air temperature and humidityare measured by a weather station (WeatherHawk 916) installedon the rooftop. The indoor air temperature and humidity are mea-sured and recorded by the temperature and relative humidity datalogger (TransiTemp). All the parameters are measured at 1 mininterval. In addition, the solar reflectivity (!) and thermal emis-sivity (ε) of the ferrocement surface are measured by the portablesolar spectrum reflectometer (Devices and Services ER 6) and emis-someter (Devices and Services AE1). After applying the cool paint,the solar reflectivity of ferrocement surface increases from 0.36 to0.72, and the thermal emissivity slightly changes from 0.87 to 0.84according to the measurement. The cool paint layer applied on theferoocement surface is on average 0.5-mm thick with the thermalconductivity of 0.045 W/m K.

3.2. Discussion on experimental data

3.2.1. Determination of the overall heat transfer coefficientsIn order to qualify the overall convective and radiative heat

transfer between building envelope and the outdoor or indoorenvironment, the overall heat transfer coefficient is used at the

exterior or interior building surface (he or hi). For the non-metallicflat roofs, the building thermal code in Singapore suggests he andhi to be 16.2 and 6.2 W/m2 K respectively [32], and the ASHRAEhandbook suggests that the typical he and hi were in the rangesof 16.7–33.3 W/m2 K and 5.0–8.3 W/m2 K respectively [33]. In thiswork, the value of hi = 6.2 W/m2 K from Singapore building ther-mal code [32] is adopted for the model validation. However, thereis a discrepancy in the given values of he between the Singaporebuilding thermal code [32] and the ASHRAE handbook [33].

In order to obtain a more accurate estimation of the overall heattransfer between roof and outdoor environment, the overall heatloss per unit area (qo) at the exterior roof surface is correlated to thetemperature difference (T1 − To) between the exterior roof surfaceand outdoor air, given by

qo = he(T1 − To) + qr (12)

where he is the overall heat transfer coefficient (W/m2 K) at roofexterior surface, and qr is a net radiative heat flux (W/m2). The val-ues of he and qr are obtained based on interpolation of experimentaldata, as detailed below.

The overall heat loss per unit area (qo) includes the convectiveheat flux (qconv) from roof to outdoor air, and the radiative heatflux (qrad) from roof to the sky. The overall heat loss per unit areaat exterior roof surface is thus rewritten as

qo = hc(T1 − To) + #ε(T14 − T4

sky) (13)

where he is the outdoor convective heat transfer coefficient atexterior roof surface, # is the Stefan–Boltzmann constant of5.67 × 10−8 W/m2 K4, ε is the emissivity of rooftop surface, and Tskyis the sky temperature defined as the temperature of a black hemi-sphere absorbing the same radiative flux as the sky. In terms of theoutdoor convective heat transfer coefficient, a correlation proposedby McAdams gives [34]

hc(W/m2 K) = 5.7 + 3.8V (14)

where V is the wind velocity. According to the average wind speedgiven by Singapore National Environment Agency (NEA) [35], hcbecomes 16.2 W/m2 K.

For the radiative heat transfer from roof to the sky, the empiricalcorrelation for the sky temperature suggested by Swinbank [36]gives

Tsky = 0.0552To1.5(K) (15)

The overall heat loss qo at the exterior roof surface is thus calcu-lated by Eqs. (13)–(15) based on the To, T1 and ε obtained from thefield measurement. The calculated qo is plotted against the tem-perature difference (T1 − To) to figure out the values of he and qr inEq. (12), as shown in Fig. 4. The he and qr found with the R-squaredvalue of 0.999 are 21.5 W/m2 K and 65 W/m2, respectively.

3.2.2. Indoor thermal comfortSince the experimental units are located on the top floor and

not air-conditioned, they are naturally hotter and more humid thancomfortable under the tropical climate of Singapore. The measuredair temperatures and relative humidities under both the uncoatedand coated residential roofs are presented in Fig. 5. The comfort-able indoor temperature is in the range of 25.5–28 ◦C according tothe study conducted in the neighboring tropical country Malaysia[37]. The measured air temperatures fluctuate from 25 to 30 ◦Cinside both units, indicating that it is sometimes too hot and air-conditioning is needed, especially during the sunny afternoons.However, it is also observed that the application of cool paintcontributes to reduce the indoor temperature and makes it lessuncomfortable during most of the period. The relative humiditiesinside two units are quite close to each other and fall into the

396 S. Tong et al. / Energy and Buildings 76 (2014) 392–401

y = 21.517x + 65.01R² = 0.999

0

100

200

300

400

500

-5 0 5 10 15 20 25

Ove

rall

outd

oor h

e at f

lux

q o, W

/m2

Temperatur e di fferenc e (T1-To), oC

Fig. 4. Correlation between the heat flux qo and temperature difference (T1 − T0).

range of 60–86%. However, it is still beyond the comfortable relativehumidity range of 30–60% recommended by ASHRAE [38].

3.3. Comparison between measured and modeled results

The CFFT model with adapted overall heat transfer coefficientand modified boundary conditions at the roof interior surface isimplemented in Matlab environment [39]. In order to validate themodel, the transient temperatures of both uncoated and coated res-idential roofs are predicted using CFFT model, and comparisons aremade between the predicted and measured results.

The variations of outdoor solar radiation and air temperatureduring the entire experimental period are presented in Fig. 6. Twoextreme weather days, namely one sunny day with the maximumpeak solar radiation and one rainy day with the minimum peak solar

radiation, are selected for model validation. The hourly solar radi-ation, outdoor temperature and indoor temperature during thesetwo days are used as model inputs. Other inputs such as the prop-erties of roofing materials are listed in Table 1. The model is runfollowing the procedures described in Section 2, and computingconvergence is achieved when the change in the calculated rooftemperature in Eq. (6) is smaller than 10−3 with 50 sequences intotal.

The hourly T1 and T4 of the coated and uncoated roofs are sim-ulated using CFFT model, as presented in Figs. 7 and 8, for thecomparisons between simulated and measured results during thesunny and rainy days respectively. It is found that the CFFT modelwell predicts the roof temperature amplitudes as well as the occur-rence time of peak temperatures in both roofs during the twoextreme weather days.

In order to provide a quantitative evaluation for the compu-tational accuracy of CFFT model, two indicative parameters areintroduced [40]. One is the mean bias error (MBE), and the otheris the cumulative variation of root mean square error (CVRMSE),which are calculated by the following formulae One is the meanbias error (MBE), and the other is the cumulative variation of rootmean square error (CVRMSE), which are calculated by the followingformulae [41]

MBE =%24

i=1(Mi − Si)%24i=1Mi

(16)

CVRMBE =

$%24i=1((Mi − Si)

2/24)

%24i=1Mi/24

(17)

where Mi and Si are the hourly roof temperatures during a dayobtained from the field experiment and model prediction, respec-tively.

0102030405060708090100

2526272829303132333435

Indo

or te

mpe

ratu

re (o C

)

Coated roofUncoated roof

Relativ e hu mid ity

Indoor temperature

Rela

tiveh

umid

ity (%

)

Feb 02 03 04 05 06 07 08 09 10 11 12 13 Date

Comfort zone for indoor temperatu re

Comfort zone for relati ve hu midi ty

Fig. 5. Measured indoor air temperature and relative humidity.

Fig. 6. Measured outdoor solar radiation and air temperature.

S. Tong et al. / Energy and Buildings 76 (2014) 392–401 397

Table 1Thermal properties of roofing materials.

Material Conductivity (W/m K) Conductance (W/m2 K) Thermal diffusivity (m2/s)

Cement plaster 0.533 3 × 10−7

Concrete 1.442 7.5 × 10−7

22-cm air cavity without radiant barrier 5.01b 1.9 × 10−5

22-cm air cavity with radiant barrier 2.04b 1.9 × 10−5

Ferrocement 0.836 5.2 × 10−7a

Expanded polystyrene 0.037c 1.01 × 10−6c

All property values are taken from Singapore code on envelope thermal performance for buildings [32], except:a Greepala et al. [43]b Naouel et al.c Estimated.

In all the case studies presented in Figs. 7 and 8, the MBEs in theprediction for T1 and T4 are less than 7% and 4% respectively, andthe CVRMBEs are less than 9% and 4% respectively. The discrepancymay arise from the experimental error, as well as the differencebetween the actual and adopted values of roofing material proper-ties or overall heat transfer coefficients (he and hi). However, theaccuracy at this level is sufficient to characterize the temperaturevariation and daily heat gain of various roofs.

4. Parameter study

After validation, the CFFT model is employed to study theimpacts of rooftop surface reflectivity and thermal resistance onthe thermal performance of concrete-based roofs subjected to thetropical climate in Singapore.

4.1. Typical Singapore climate

In order to acquire the typical climate characteristics as modelinput for the parameter study, the history meteorological data ofSingapore is obtained and analyzed by following the proceduresbelow.

1) Obtain the long-term meteorological data from NEA, whichincludes the hourly dry-bulb air temperature from 0:00 to 24:00during the period of 1985–2009 and the hourly solar radiationfrom 5:00 to 18:00 during the period of 1990–2003.

2) Generate two typical meteorological years (TMYs), one for thedry-bulb air temperature, and the other for the solar radiation.Each TMY consists of 12 calendar months, and each calendar

20

25

30

35

40

45

50

55

60

0 4 8 12 16 20 24Day hours

T1 measuredT4 measuredT1 si mul atedT4 si mul ated

Tem

pera

ture

(o C)

(a)

20

25

30

35

40

45

50

55

60

0 4 8 12 16 20 24

T1 measuredT4 measuredT1 si mul atedT4 simulated

(b)

Day hours

Tem

pera

ture

(o C)

Fig. 7. Comparisons between the measured and simulated T1 and T4 on the (a) uncoated and (b) coated roofs during a sunny day.

20

24

28

32

36

40

0 4 8 12 16 20 24

Tem

pera

ture

(o C)

Day hours

(a)

T1 measuredT4 measuredT1 si mul atedT4 si mul ated

20

24

28

32

36

40

0 4 8 12 16 20 24

Tem

pera

ture

(o C)

Day hours

(b)

T1 measuredT4 measuredT1 simulatedT4 si mul ated

Fig. 8. Comparisons between the measured and simulated T1 and T4 on the (a) uncoated and (b) coated roofs during a rainy day.

398 S. Tong et al. / Energy and Buildings 76 (2014) 392–401

Fig. 9. Hourly (a) dry-bulb air temperature and (b) solar radiation during each month in the TMY and TWD.

month is chosen from the long-term meteorological data usingFinkelstein–Schafer statistical method [42].

3) Generate the monthly profiles of dry-bulb air temperature andsolar radiation based on TMY data. For each month in the TMY,the hourly dry-bulb air temperature or solar radiation duringthe same hour is averaged to represent the weather conditionsin this month, as shown in the first 12 curves in Fig. 9(a) and (b)for the dry-bulb air temperature and solar radiation respectively.

4) Generate two typical weather days (TWDs), one for the dry-bulbair temperature, and the other for the solar radiation. The TWDsare generated by averaging the 12 monthly profiles in TWYs, asshown in the last curves in Fig. 9(a) and (b) respectively.

As shown Fig. 9(a), the hourly dry-bulb air temperature in TMYvaries within the range of 27–31 ◦C in the hottest month (May) andwithin the range of 25–29 ◦C in the coolest month (December). Asshown Fig. 9(b), the peak solar radiation is the highest at 803 W/m2

in May and the lowest at 506 W/m2 in November. The monthlychanges in both the dry-bulb air temperature and solar radiationare insignificant during the 12 months in TMYs. Moreover, in thetwo TWDs, the lengths of error bars standing for 95% confidenceinterval are less than 1 ◦C for the dry-bulb air temperature, andless than 100 W/m2 for the solar radiation intensity. It is thus rea-sonable to neglect the monthly changes and take the outdoor airtemperature and solar radiation on a single TWD to represent thetypical climate in Singapore. In addition, the hourly indoor air tem-perature used in parameter study is produced by averaging theair temperature inside two units during the entire experimentalperiod.

4.2. Impact of solar reflectivity of rooftop surface

In order to investigate the impacts of solar reflectivity, thethermal performance of concrete-based roofs at different rooftopsurface solar reflectivities are predicted using CFFT model. Twotypes of roofs commonly found in the high-rise buildings inSingapore are studied. Type 1 is an unventilated roof consisting of15-cm concrete roof and 0.5-cm cement plaster. Type 2 is a ven-tilated roof consisting of 3-cm ferrocement slab, 22-cm air-gap,15-cm concrete, and 0.5-cm cement plaster.

The variations of ceiling temperature with the rooftop sur-face solar reflectivity varying from 0.1 to 0.9 under the TWD areshown in Fig. 10(a) and (b) for the unventilated and ventilatedroofs, respectively. The increase in solar reflectivity effectively coolsdown the ceilings of both roofs. The ceiling temperature reduces bya greater extent in the unventilated roofs than that in the ventilatedroofs. For example, the peak ceiling temperature reduces by 8.1 ◦Cin the unventilated roofs and 3.3 ◦C in the ventilated roofs, if thesolar reflectivity of rooftop surface increases from 0.1 to 0.9. It is alsoobserved that the peak temperature in the ventilated roofs appear3 h later than that in the unventilated roofs, due to the increase ofthermal capacity in the ventilated roofs.

The daily heat gains of the unventilated and ventilated roofs atdifferent rooftop surface solar reflectivities are predicted, as shownin Fig. 11. The daily heat gains of both roofs reduce linearly withthe increase in the rooftop surface solar reflectivity. Compared toroofs with the solar reflectivity of 0.1, every 0.1 increase in solarreflectivity cuts down the daily roof heat gains by 11% in both theunventilated and ventilated roofs. The application of the cool paintthat increases the solar reflectivity from 0.36 to 0.72 reduces the

S. Tong et al. / Energy and Buildings 76 (2014) 392–401 399

26

28

30

32

34

36

38

0 4 8 12 16 20 24

Tem

pera

ture

(o C)

Day hours

γ=0.1γ=0.3γ=0.5γ=0.7γ=0.9

26

28

30

32

34

36

38

0 4 8 12 16 20 24

Tem

pera

ture

(o C)

Day hours

γ=0.1γ=0.3γ=0.5γ=0.7γ=0.9

(a) (b)

Fig. 10. Hourly ceiling temperatures of the (a) unventilated and (b) ventilated roofs with different surface solar reflectivities.

0

100

200

300

400

500

600

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Dai

ly h

eat g

ain

(W h

/m2 )

Solar refl ectiv ity

Unventilated roof

Ventilated roof

Fig. 11. Daily heat gains of the (a) unventilated and (b) ventilated roofs with varyingsolar reflectivities.

daily heat gain by 234 and 135 W h/m2 in the unventilated andventilated roofs, respectively.

4.3. Impact of thermal resistance

The impacts of the thermal resistance on the thermal perfor-mance of concrete-based roofs are investigated in the 10 roofs listedin Table 2. The roofs (1)–(10) are designed with several passive roof-ing technologies, including the cool paint, 2.5-cm EPS foam, radiant

Table 2List of 10 investigated roofs.

No. Roof components

(1) 15-cm concrete + 0.5-cm plaster(2) 15-cm concrete + 2.5-cm EPS + 0.5-cm plaster(3) 3-cm ferrocement + air-gap + 15-cm concrete + 0.5-cm plaster(4) 3-cm ferrocement + air-gap + 15-cm concrete + 2.5-cm EPS + 0.5-cm

plaster(5) 3-cm ferrocement + air-gap + 15-cm concrete + radiant

barrier + 0.5-cm plaster(6) Cool paint + 15-cm concrete + 0.5-cm plaster(7) Cool paint + 15-cm concrete + 2.5-cm EPS + 0.5-cm plaster(8) Cool paint + 3-cm ferrocement + air-gap + 15-cm concrete + 0.5-cm

plaster(9) Cool paint + 3-cm ferrocement + air-gap + 15-cm concrete + 2.5-cm

EPS + 0.5-cm plaster(10) Cool paint + 3-cm ferrocement + air-gap + 15-cm concrete + radiant

barrier + 0.5-cm plaster

barrier, and roof ventilation that consists of 3-cm ferrocement andair gap. Based on whether cool paint is applied, the 10 roofs are cat-egorized into two groups, namely the uncoated roofs (1)–(5) andcoated roofs (6)–(10). The physical properties of roofing materialsare listed in Table 1 for the parameter study.

The ceiling temperatures of the 10 investigated roofs under TWDare predicted by the CFFT model, as shown in Fig. 12(a) and (b)for the uncoated and coated roofs respectively. Compared with theleast insulated roofs (1) and (6), the additional use of insulationmaterial in other roofs effectively reduces the ceiling temperaturesfrom 10 a.m. to 9 p.m. However, the roofs (1) and (6) achieve the

26

28

30

32

34

36

0 4 8 12 16 20 24

Tem

pera

ture

(o C)

Day hours

(1) UVR(2) UVR+2 .5-cm EPS(3) VR(4) VR+2 .5-cm EPS(5) VR+RB

26

28

30

32

34

36

0 4 8 12 16 20 24

Tem

pera

ture

(o C)

Day hours

(6) UVR(7) UVR+2 .5-cm EPS(8) VR(9) VR+2 .5-cm EPS(10) VR+RB

(a) (b)

UVR (unvent ilated roof)VR (venti lated roof)

UVR (unvent ilated roof)VR (v enti lated roof)

Fig. 12. Ceiling temperatures of 10 investigated (a) uncoated and (b) coated roofs.

400 S. Tong et al. / Energy and Buildings 76 (2014) 392–401

0

100

200

300

400

500

0 0.5 1 1.5 2 2.5

Dai

ly h

eat g

ain

(W h

/m2 )

Thermal resistanc e (m2 K/W)

Uncoated roofCoated roof

(1)

(3)

(2)

(5)(4)

(6)

(8)(7) (9)

(10)

Fig. 13. Daily heat gains of roofs with varying thermal resistances.

lowest ceiling temperatures in their respective groups from mid-night to 8 a.m., when heat is transferred from indoors to outdoors.In both the uncoated and coated roofs, the peak ceiling temperatureis reduced by the largest extent through the combined use of roofventilation and radiant barrier, followed by the combined use ofroof ventilation and 2.5-cm EPS foam, the individual use of 2.5-cmEPS foam and the roof ventilation.

The daily heat gains of the uncoated and coated roofs with ther-mal resistance varying from 0.1 to 2.5 m2 K/W are evaluated aswell. As shown in Fig. 13, the daily heat gains of both uncoatedand coated roofs reduce gradually with the increase in thermalresistance, and the heat gain reductions become more significantin the less insulated uncoated roofs. When roof thermal resistanceincreases from 0.1 to 2.5 m2 K/W, the daily heat gain reduces from408 to 46 W h/m2 in the uncoated roofs, and reduces from 164 to18 W h/m2 in the coated roofs. Among the 10 investigated roofs, theleast insulated roofs (1) and (6) with the same thermal resistanceof 0.11 m2 K/W demonstrate the largest daily heat gains of 391 and157 W h/m2 in their respective groups. In both roof groups, com-pared with the least insulated roof (1) or (6), the individual usesof roof ventilation and 2.5-cm EPS foam reduce the daily heat gainby 42% and 68% respectively, and the individual uses of 2.5-cm EPSfoam and radiant barrier in the ventilated roofs increase the heatgain reductions further to 73% and 84%, respectively.

5. Conclusions

In the present work, the CFFT method is used to predict thetransient roof temperature and transmitted heat flux across themultilayer roofs of naturally ventilated roofs. A field experiment iscarried out on two roofs of residential units to validate the CFFTmodel, in which satisfactory agreement is obtained between themeasured and simulated results. The validated model is furtheremployed to study the impacts of the rooftop surface solar reflec-tivity and thermal resistance on roof thermal performance.

In the parameter study, the thermal performances of theconcrete-based roofs with varying solar reflectivities and thermalresistances under the TWD in Singapore are evaluated. It is con-cluded that the increase in solar reflectively cools down the ceilingduring 24 h, and the cooling effect is more significant during thedaytime in the less insulated unventilated roofs than that in theventilated roofs. Compared with the roofs with solar reflectivity of0.1, every 0.1 increase in the solar reflectivity cuts down the dailyroof heat gain by 11% in both the unventilated and ventilated roofs.The application of cool paint reduces the daily heat gain by 234 and135 W h/m2 in the unventilated and ventilated roofs, respectively.

The increase in roof thermal resistance contributes to cool down theceilings during the daytime, but the situation is reversed at night.Compared with the least insulated roofs, the individual uses of roofventilation and 2.5-cm EPS foam reduce the daily roof heat gainby 42% and 68% respectively, and the daily heat gain reductionsincrease to 73% and 84% if the 2.5-cm EPS foam and radiant barrierare integrated in the ventilated roofs. All the investigated passiveroofing technologies are very effective in reducing the daily heatgain of concrete-based roofs in tropical climate.

Acknowledgement

The authors highly appreciate the financial support from Hous-ing and Development Board Singapore (GRANT No. M4060819)for the experiment carried out, and the assistance from EnergyResearch Institute @ NTU.

References

[1] Energy Efficiency in Buildings: Lessons Learned from International Experience,United Nations Development Programme, Energy and Environment Group,New York, USA, 2009.

[2] L. Perez-Lombard, J. Ortiz, C. Pout, A review on buildings energy consumptioninformation, Energy and Buildings 40 (2008) 394–398.

[3] C.-m. Lai, J.Y. Huang, J.S. Chiou, Optimal spacing for double-skin roofs, Buildingand Environment 43 (2008) 1749–1754.

[4] J.C. Lam, C.L. Tsang, D.H.W. Li, S.O. Cheung, Residential building envelope heatgain and cooling energy requirements, Energy 30 (2005) 933–951.

[5] Singapore’s Second National Communication: Under the United NationsFramework Convention on Climate Change, National Environmental, Agency,Singapore, 2010.

[6] S.B. Sadineni, S. Madala, R.F. Boehm, Passive building energy savings: a reviewof building envelope components, Renewable and Sustainable Energy Reviews15 (2011) 3617–3631.

[7] D.S. Parker, S.F. Barkaszi Jr., Roof solar reflectance and cooling energy use: fieldresearch results from Florida, Energy and Buildings 25 (1997) 105–115.

[8] C. Romeo, M. Zinzi, Impact of a cool roof application on the energy and com-fort performance in an existing non-residential building. A Sicilian case study,Energy and Buildings 67 (2013) 647–657.

[9] P.-C. Chang, C.-M. Chiang, C.-M. Lai, Development and preliminary evaluationof double roof prototypes incorporating RBS (radiant barrier system), Energyand Buildings 40 (2008) 140–147.

[10] A. Dimoudi, A. Androutsopoulos, S. Lykoudis, Summer performance of a venti-lated roof component, Energy and Buildings 38 (2006) 610–617.

[11] N. Zhou, W. Gao, M. Nishida, H. Kitayama, T. Ojima, Field study on the thermalenvironment of passive cooling system in RC building, Energy and Buildings 36(2004) 1265–1272.

[12] A. Sfakianaki, E. Pagalou, K. Pavou, M. Santamouris, M.N. Assimakopoulos, The-oretical and experimental analysis of the thermal behaviour of a green roofsystem installed in two residential buildings in Athens, Greece, InternationalJournal of Energy Research 33 (2009) 1059–1069.

[13] R.U. Halwatura, M.T.R. Jayasinghe, Thermal performance of insulated roof slabsin tropical climates, Energy and Buildings 40 (2008) 1153–1160.

[14] J.L. Alvarado, W. Terrell Jr., M.D. Johnson, Passive cooling systems for cement-based roofs, Building and Environment 44 (2009) 1869–1875.

[15] National environment Agency, Singapore Weather, 2010, http://www.weather.gov.sg/online/loadNotesProcess.do (retrieved 5.06.12).

[16] S. Wang, Y. Chen, Transient heat flow calculation for multilayer constructionsusing a frequency-domain regression method, Building and Environment 38(2003) 45–61.

[17] C.O. Mackey, L.T. Wright, Periodic heat flow—homogeneous walls and roofs,ASHVE Transactions 50 (1944) 293–312.

[18] C.O. Mackey, L.T. Wright, Periodic heat flow—composite walls and roofs, ASHVETransactions 52 (1946) 283–296.

[19] R.C. Sonderegger, Dynamic models of house heating based on equivalent ther-mal parameters (Ph.D. thesis), Princeton University, New Jersey, 1977.

[20] D.C. Hittle, C.O. Pedersen, Calculating building heating loads using the fre-quency response of multi-layered slabs, ASHRAE Transactions 87 (1981)545–568.

[21] R. Yumrutas, M. Unsal, M. Kanoglu, Periodic solution of transient heat flowthrough multilayer walls and flat roofs by complex finite Fourier transformtechnique, Building and Environment 40 (2005) 1117–1125.

[22] D.G. Stephenson, G.P. Mitalas, Cooling load calculation by thermal responsefactors, ASHRAE Transactions 73 (1967) 1–7.

[23] K. Ouyang, F. Haghighat, A procedure for calculating thermal response factorsof multi-layer walls—state space method, Building and Environment 26 (1991)173–177.

[24] M.G. Davies, A time domain estimation of wall conduction transfer functioncoefficients, ASHRAE Transactions 102 (1996) 328–343.

S. Tong et al. / Energy and Buildings 76 (2014) 392–401 401

[25] D.G. Stephenson, G.P. Mitalas, Calculation of heat conduction transfer functionsfor multi-layer slabs, ASHRAE Transactions 77 (1971) 117–126.

[26] LBNL, DOE-2 Engineer Manual-Version 2.1A, LBNL, University of California,Berkeley, 1982.

[27] S.A. Klein, W.A. Beckman, J.W. Mitchell, TRNSYS-A Transient System SimulationProgram, Solar Energy Laboratory, University of Wisconsin–Madison, Madison,1994.

[28] EnergyPlus Engineering Reference, The References to EnergyPlus Calculations,U.S. Department of Energy, University of Illinois, 2013.

[29] BLAST, Building Loads Analysis and System Thermodynamics, Version 3, Uni-versity of Illinois, Urbana-Champain, Blast Support Office, IL, USA, 1986.

[30] R. Yumrutas, Ö. Kas ka, E. Yıldırım, Estimation of total equivalent temperaturedifference values for multilayer walls and flat roofs by using periodic solution,Building and Environment 42 (2007) 1878–1885.

[31] N. Daouas, Z. Hassen, H.B. Aissia, Analytical periodic solution for the study ofthermal performance and optimum insulation thickness of building walls inTunisia, Applied Thermal Engineering 30 (2010) 319–326.

[32] Code on Envelope Thermal Performance for Buildings, Building ConstructionAuthority, Singapore, 2008.

[33] American Society of Heating, Refrigeration and Air-Conditioning Engineers,Heat, air, and moisture control in building assemblies – material properties,in: ASHRAE Handbook: Fundamentals, Atlanta, USA, 2009 (Chapter 26).

[34] W.H. McAdams, Heat Transmission, 3rd ed., McGraw-Hill, New York, 1954.[35] Guide to Singapore’s weather, National Environment Agency, Singapore, 2007.[36] W.C. Swinbank, Long-wave radiation from clear skies, Quarterly Journal of the

Royal Meteorological Society 89 (1963) 339–348.[37] A.M.A. Rahman, Housing design in relation to environmental comfort, Building

Research & Information 23 (1996) 49–54.[38] American Society of Heating, Refrigeration and Air-Conditioning Engineers,

ANSI/ASHRAE standard 55-2010, in: Thermal Environmental conditions forHuman occupancy, Atlanda, USA, 2010.

[39] D.C. Hanselman, B. Littlefield, Mastering MATLAB 6: A Comprehensive Tutorialand Reference, Prentice Hall, New Jersey, 2001.

[40] P. Raftery, M. Keane, A. Costa, Calibrating whole building energy models:detailed case study using hourly measured data, Energy and Buildings 43 (2001)3666–3679.

[41] American Society of Heating, Refrigeration and Air-Conditioning Engineers,ASHRAE Guideline 14-2002, in: Measurement of Energy and Demand Savings,Atlanda, USA, 2002.

[42] A.L.S. Chan, T.T. Chow, S.K.F. Fong, J.Z. Lin, Generation of a typical meteorologicalyear for Hong Kong, Energy Conversion and Management 47 (2006) 87–96.

[43] V. Greepala, R. Parichatprecha, T. Tanchaisawat, P. Nimityongskul, SpecificHeat Capacity of Ferrocement Using Inverse Thermal Analysis, 2009, fromhttp://fscieng.csc.ku.ac.th/∼ce/images/stories/paper/vatwong rsid str10.pdf