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Renewable Energy 75 (2015) 210e223

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Renewable Energy

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Modeling of cool roof heat transfer in tropical climate

Kishor T. Zingre a, Man Pun Wan a, *, Shanshan Tong a, Hua Li a, Victor W.-C. Chang b,Swee Khian Wong c, Winston Boo Thian Toh c, Irene Yen Leng Lee c

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, Singapore 639798, Singaporec Building Research Institute, Housing and Development Board HUB, 480, Lorong 4 Toa Payoh, Singapore 310480, Singapore

a r t i c l e i n f o

Article history:Received 10 April 2014Accepted 24 September 2014Available online

Keywords:Cool coatingSolid roof heat gainHeat transfer modelTropical climate

* Corresponding author. Tel.: þ65 6792 5498; fax:E-mail address: mpwan@ntu.edu.sg (M.P. Wan).

http://dx.doi.org/10.1016/j.renene.2014.09.0450960-1481/© 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

Cool roof is gaining popularity as a passive building energy saving solution. A concise and easy-to-applymathematical model is essential for building designers to evaluate the impact of cool coating on heattransfer and indoor thermal comfort. A novel cool roof heat transfer (CRHT) model was developed usingthe spectral approximation method. The CRHT model was verified against the conduction transferfunction method and was validated against experiments performed in two identically configuredapartments with concrete roofs in Singapore. The model predictions show that on a sunny day, a coolcoating (solar reflectance of 0.74) reduces the peak roof temperature, indoor air temperature and dailyheat gain by up to 14.1 �C, 2.4 �C and 0.66 kWh/m2 (or 54%), respectively through the concrete roof. Themodel predictions match with experimental measurements with reasonable accuracy. Further modelpredictions suggested that significant daily heat gain reduction can also be achieved by cool coating ongalvanized steel (metal) roofs. The daily heat gain reduction brought by the cool coating drops as the roofexposes to higher wind speeds. The proposed CRHT model largely simplifies the calculation of heattransfer of cool roofs, compared to existing methods, and is generally applicable to opaque solid surfaces(roofs and walls).

© 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Energy plays an important role in Singapore's economic growth,however, the ‘air-conditioned nation’ as quoted by Singaporeanauthor Cherian George [1], lacks natural energy resources for theproduction of electrical energy and relies on the import of fossilfuels from foreign countries [2]. The building sector consumesabout 57% of the total electrical energy production in Singapore [3].Air-conditioning of buildings alone guttle about 60% of the elec-trical energy consumed by the building sector [4]. This suggeststhat about 34% of the country's total electrical energy production isbeing consumed for air-conditioning of buildings alone [4]. Build-ing energy savings has become a huge concern in the city state.

In the tropical region, opaque envelope surfaces receive abun-dant solar irradiation throughout the year [5]. Chua & Chou [6]conducted computational simulation in a high-rise (12-storey),air-conditioned residential apartment building in Singapore. Theyreported that the heat gains through the opaque envelope surfaces

þ65 6792 4052.

constitute about 30% (including 19% through walls and 11% throughroof) of the total power consumption for air-conditioning of thebuilding [6].

A building surface exposed to solar irradiation is heated up byabsorbing the radiation energy. Part of the absorbed thermal energyis stored in thematerial due to its thermal storage capacity and someother part is lost to outdoor by thermal emission and convection. Theremaining is conducted into the building. The heat gain into build-ings can be reduced by reflecting off more of the solar irradiationduring day time and emitting off the stored heat in the opaquematerial to outdoorwhen the sky is clear [7]. The cool coating,whichfeatures high solar reflectance (r> 0.65) andhigh thermal emittance(ε > 0.75) provide passive cooling [8] based on such principle.

The potential economic and environmental benefits of coolcoating [9,10] have attracted attention over the last few decades. Anumber of studies conducted in Europe and the U.S. [11e16]showed that cool coating contributes significantly in reducingheat gain through opaque envelope surfaces in these climate zones.It is hypothesized that the performance of cool coating would bemore prominent where solar irradiation is abundant since coolcoating works on the principle of high solar reflectance when it isexposed to solar irradiation. The tropical climate [17] of Singapore

K.T. Zingre et al. / Renewable Energy 75 (2015) 210e223 211

receives abundant annual-averaged solar irradiation of 1680 kWh/m2 compared to other locations [10e19], as shown in Fig. 1. Air-conditioning of buildings is also sought throughout the year inthe tropics, suggesting that the potential heating penalty [9] of coolcoating does not exist in tropical climate applications. Cool coatingis often applied on roofs, which are commonly referred as “coolroof”.

Heat transfer through roof/wall is a mixed-mode heat transferphenomenon. The roof/wall surface heat exchanges mainly consistof the radiation component (solar heat gain and thermal emission)and the convection component (heat exchanging with surroundingair). Cool coating affects the radiation component by providing highsolar reflectance and high thermal emittance. The cool coating layeradds resistance to the heat conduction through the roof/wall, whichis coupled with the surface heat exchanges. In order to quantita-tively analyze the impact of cool coating on the roof/wall heattransfer phenomenon, a robust heat transfer model is essential.

Over the years, numerous analytical methods, such as responsefactor (RF) and conduction transfer function (CTF), and numericalmethods, such as Finite Difference (FD) and Finite Element (FE)have been developed. These methods have been implemented inbuilding energy simulations programs, such as EnergyPlus [5],TRNSYS [9,10], eQUEST [12], BEopt [20], roof/wall savings calcula-tors [21,22], building load calculation software [23e25], as well asRF and CTF coefficient calculators [26]. In these implementations,RF method requires long series of history temperatures or heat fluxdata. CTF method requires a set of pre-calculated coefficients[27e29] which are tabulated for certain types of roof/wall assem-bly, building materials and certain climate conditions, limiting itspotentials for general uses. FD and FE methods overcome thedrawback of RF and CTF methods. However, for discretization of thetransient heat conduction equation, FD and FE methods use low-order polynomials, and require small grid size in the slab materialand small time step (15 min or less) to achieve sufficient accuracy[20]. This leads to heavy demand of computational resources. Dueto the need for discretization, these methods resolve the detailedtemperature distributions within the slab material which is un-necessary for air-conditioning load calculations.

Spectral approximation method [30e32], on the other hand,uses orthogonal functions or higher-order (trigonometric) poly-nomial to solve the partial differential equation for heat conduc-tion. This leads to the system of equations that are very easy-tohandle and substantially reduces the complexity of calculations[33]. It does not require a set of pre-calculated coefficients, historyheat flux data or the use of tables. At the same time, it does notrequire small grid size in the slab material (hence no need to

0

500

1000

1500

2000

Humidcontinental(Toronto)

Humidsubtropical

(Hong Kong)

Marine westcoast (London)

Mediterranean(Crete)

Wet tropical(Singapore)

Arid(California)

Ann

ual-a

vera

ged

sola

r ir

radi

atio

n (k

Wh/

m2 )

Fig. 1. Annual-averaged solar irradiation at different locations [10e19].

calculate the detailed temperatures within the slab material) and atime step of 1 h can be used [34]. Also, previous studies [35e39]showed that spectral approximation method is best suitable forthe problems involving mixed mode heat transfer such as thebuilding roof/wall applied with cool coating.

Despite the numerous advantages of the spectral approximationmethod, it has not yet been explored to develop a heat transfermodel for the analysis of heat transfer through building envelopesurfaces. This study proposed a novel cool roof heat transfer (CRHT)model for solid roofs (no air-gap between roof layers) applied withcool coating on the roof surface based on the spectral approxima-tion method. It should be noted that the CRHT model is alsoapplicable to opaque wall surfaces. The CRHT model can handletransient outdoor and indoor boundary conditions as experiencedby naturally ventilated buildings. The CRHT model is advantageousover other existing building energy simulation models since thefinal solution of the CRHT model is very concise and, therefore,much easier to apply.

The CRHT model is verified against CTF method [26e29,40] andis further validated against real-scale measurements on a testbuilding with concrete roof under the tropical climate conditions ofSingapore, though the CRHT model is a general model that isapplicable to other climate conditions and roof/wall materials.

2. Methodology

2.1. Cool roof heat transfer (CRHT) model

Building roofs experience transient heat transfer as the intensityof solar irradiation and ambient air temperature vary continuously.In a naturally ventilated building, the indoor air temperature alsovaries with the changing environments and the internal heat loads.In this derivation, it is assumed that the roof material has constantthermophysical (conductivity, specific heat capacity) and radiationproperties (solar reflectance, thermal emittance). The roof materialis homogeneous with constant material property (mass density). Incase of multi-layered roof, good contacts between different layersof the roof material with negligible interfacial resistance areassumed. The indoor air is assumed to be well-mixed and there areno internal heat sources inside the apartments. Hourly-averagedvalues of overall (combined convection and radiation) indoor heattransfer coefficient (hi) for ceiling and overall outdoor heat transfercoefficient (ho) for roof are used [14,19] in this study since the in-puts are hourly-averaged values.

2.1.1. Problem formulation and boundary conditionsConsider an opaque solid roof applied with a cool coating (or

“cool roof”) having its top surface exposed to solar irradiation asshown in Fig. 2. The incident radiation includes short waves in thewavelength range of 250 nme3500 nm (SWin, i.e., insolation andthe radiation reflected by other objects on the earth surface) andlong waves with wavelength >3500 nm (LWin, i.e., thermal radia-tion emitted by clouds and other objects on the earth surface). Theoutgoing radiation includes SWout (i.e., reflected radiation by theroof surface during day time) and LWout (i.e., thermal radiationemitted by the roof surface to the sky and other objects on the earthsurface). The radiation balance at the cool roof surface is given asfollows:

Absorbed radiation by the cool roof surface (Iabs) ¼ Incidentradiation on the cool roof surface (Iin ¼ SWin þ LWin) e Outgoingradiation from the cool roof surface (Iout ¼ SWout þ LWout).

The diurnal heat transfer through the cool roof is assumed to beone-dimensional, i.e., in the direction perpendicular to the exposedsurface. Assuming that the coordinate direction perpendicular to

Fig. 2. Schematic diagram showing heat transfer processes at cool roof (not-to-scale).

K.T. Zingre et al. / Renewable Energy 75 (2015) 210e223212

the roof surface is y as shown in Fig. 2, the governing differentialequation for conduction heat transfer within the cool roof yields.

vTvt

¼ a*v2Tvy2

(1)

where a* ¼ k�r*C

The homogeneous-linear partial differential Eq. (1) can besolved using an initial condition in time and two boundary condi-tions in space. The Neumann boundary condition on the cool roofsurface (y ¼ 0) is

qðy¼0;tÞ¼�k�vTvy

�y¼0

¼ Iina�hoðTR�ToÞ� εIIR

¼hoIinaho

�hoðTR�ToÞ�hoεIIR

ho¼ho

�Iinaho

�ðTR�ToÞ� εIIR

ho

�

¼ho

�Iinaho

þTo� εIIR

ho�TR

�¼ho

�Tesol�air�TR

�(2)

where

Tesol�air ¼Iinaho

þ To � εIIR

ho; ho ¼ ho;conv þ ho;r$

TR � TskyTR � To

(2a)

and the Neumann boundary condition on the cool ceiling surface(y ¼ L) is

qCðy ¼ L; tÞ ¼ �k�vTvy

�y¼L

¼ hiðTC � TiÞ (3)

and initial condition is steady state solution of Eq. (1) at t ¼ 0.

2.1.2. Solution method for the CRHT modelSpectral approximation method [30e39] is a useful numerical

method to solve partial differential equations. The solution of apartial differential equation using spectral approximation method

is given as summation of product of higher-order polynomial ororthogonal function with time dependent coefficients.

An approximate solution of the governing differential Eq. (1) isgiven by

Tðy; tÞ ¼X∞m¼0

FðyÞ$qðtÞ (4)

Tðy; tÞ ¼X∞m¼0

ham cos

�mpyL

�þ bm sin

�mpyL

�i$qðtÞ (5)

To find the expression for qðtÞ, partial derivatives of Eq. (5) aretakenwith respect to t and y and substituted in Eq. (1), it gives Eq. (8)

vTðy; tÞvt

¼X∞m¼0

vqðtÞvt

$ham cos

�mpyL

�þ bm sin

�mpyL

�i(6)

v2Tðy; tÞvy2

¼X∞m¼0

qðtÞ$�m2p2

L2am cos

�mpyL

�

�m2p2

L2bm sin

�mpyL

�(7)

X∞m¼0

vqðtÞvt

$ham cos

�mpyL

�þ bm sin

�mpyL

�i

¼X∞m¼0

�a*m2p2

L2$qðtÞ$

ham cos

�mpyL

�þ bm sin

�mpyL

�i(8)

Re-arranging Eq. (8), it becomes

X∞m¼0

�vqðtÞvt

þ a*p2m2

L2qðtÞ

�$ham cos

�mpyL

�þ bm sin

�mpyL

�i¼ 0

(9)

K.T. Zingre et al. / Renewable Energy 75 (2015) 210e223 213

Since the functionsnam cos

�mpyL

�þ bm sin

�mpyL

�o∞m¼0

are

orthogonal, Eq. (9) can be simplified to the ordinary differentialequation

vqðtÞvt

þ a*p2m2

L2qðtÞ ¼ 0 (10)

The solution of Eq. (10) is

qðtÞ ¼ A$e�l2mt (11)

where l2ma*p2m2

L2 and A is an arbitrary constant.Substituting the value of qðtÞ in Eq. (5), it becomes

Tðy; tÞ ¼X∞m¼0

ham cos

�mpyL

�þ bm sin

�mpyL

�i$A$e�l2mt (12)

where coefficients am and bm are

Tsol�air;n ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 112

X24t¼1

Tesol�air$cosðnwtÞ!2

þ

112

X24t¼1

Tesol�air$sinðnwtÞ!2

vuut; tanðjnÞ ¼

ð 112P24

t¼1 Tesol�air$sinðnwtÞÞ

ð 112P24

t¼1 Tesol�air$cosðnwt

�Þ:

am ¼ 2L

ZL0

ðc1yþ c2Þ$cos�mpy

L

�dy and

bm ¼ 2L

ZL0

ðc1yþ c2Þ$sin�mpy

L

�dy:

(13)

Applying the initial (steady state) condition to Eq. (1), it yields

Tðy;0Þ ¼ c1yþ c2 (14)

where c1 and c2 can be obtained by considering an arbitrary uni-form temperature field [41]. Hence the final solution of Eq. (1)which satisfies the Neumann boundary conditions at the roof andceiling surfaces and the initial condition is given as

ðTiÞcool ¼ðhiÞcool

"ðTCÞcool þ

Pwall

Twall þ Tfloor

#þ P

windowUwindow þ x

!To

ðmÞcool

�"hi$

TC þ

Xwall

Twall þ T floor

!þ X

window

Uwindow þ x

!$To � Ti$ðmÞ

#cool

$e

�tLir

*air

Cair

ðmÞcool(18)

T�y; t�¼"�

B$cos�mp$y�� D$sin

�mp$y��

L L

$�E$

yL� G$

�1� y

L

��#e�l2mt

(15)

where B ¼P∞m¼0

h 2m2p2 ðTðL;0Þ � Tð0;0ÞÞðcosmp� 1Þ

i,

D ¼P∞m¼0½

2mp

$TðL;0Þ$ðcosmp� 1Þ�

26 hi$Ti

37

E ¼ 64 k4L$TðL;0Þ þ

4hip2k

$ðTðL;0Þ � Tð0;0ÞÞ75;

G ¼

2664

hok$Tssol�air

4L$TðL;0Þ þ

4hop2k

$ðTðL;0Þ � Tð0;0ÞÞ

3775:

(15a)

Tssol�air in Eq. (15a) is a function of outdoor conditions (solarirradiation, outdoor air temperature and wind speed, as shown inEq. (2a)). Ts

sol�air can be mathematically expressed as Eq. (16)

Tssol�air ¼ Tsol�air;M þXNn¼1

Tsol�air;n$cos�nwt � jn

�(16)

where

Ti in Eq. (15a) is calculated using the heat balance in indoorenvironment, as given by Eq. (17).

Lir*airCair

�dTidt

�¼ hi½TC � Ti� þ

Xwall

hi½Twall � Ti�

þX

window

Uwindow½To � Ti� þ hihTfloor � Ti

iþ x½To � Ti�:

(17)

where x ¼ ðachÞLir*airCair3600�VOLi

.

By solving Eq. (17) with steady state initial condition, it gives

where m ¼ hi þPwall

hi þPwall

Uwindow þ x

In order to analyze the cooling impact (of applying a coolcoating) on the indoor air temperature, a simplified Eq. (18a) isderived by subtracting (Ti)cool from (Ti)org. In Eq. (18a), F1 < 1 entailspositive cooling impact or reduction in the indoor air temperature,F1 > 1 implies negative cooling impact or increase in the indoor airtemperature and F1 ¼1 implies no cooling impact on the indoor airtemperature by applying a cool coating.

K.T. Zingre et al. / Renewable Energy 75 (2015) 210e223214

Tcooling impacti ¼ ðTcÞorg

�him

�org

$ð1� F1Þ (18a)

where F1 ¼ ðTcÞcoolðTcÞorg and assuming ðmÞorgyðmÞcool

Substituting Eq. (15) in Eq. (3) and re-arranging, the surfacetemperature of cool ceiling can be obtained as given by Eq. (19)

ðTCÞcool¼"hi$

Xwall

TwallþTfloor

!þ X

window

Uwindowþx

!$To�

hi$

TCþ

Xwall

TwallþT floor

!þ X

window

Uwindowþx

!$To$�Ti$ðmÞ

!#cool

$

�1�U

hi

�cool

þ"Uhi$

Tsol�air;Mþ

XNn¼1

bnTsol�air;n cos�nwt�jn�4n

�!#cool

(19)

In order to analyze the cooling impact on the ceiling tempera-ture, a simplified equation Eq. (19a) is derived by subtracting (Tc)coolfrom (Tc)org. In Eq. (19a), F2 < 1 implies positive cooling impact orreduction in the ceiling temperature, F2 > 1 implies negativecooling impact or increase in the ceiling temperature and F2 ¼ 1implies no cooling impact on the ceiling temperature by applying acool coating.

Tcooling impactC ¼

Tsol�air;Mþ

XNn¼1

bnTsol�air;ncos�nwt�jn�4n

�!org

$

"�Uhi

�org

��Uhi

�cool

$F2

#

(19a)

where

F2 ¼

Tsol�air;M þPN

n¼1 bnTsol�air;n cos�nwt � jn � 4n

�!cool

Tsol�air;M þPNn¼1 bnTsol�air;n cos

�nwt � jn � 4n

�!org

where

1Ucool

¼ 1hi

þ 1ho

þ Lkþ lcoatingkcoating

(19b)

Substituting Eq. (15) in Eq. (2) and re-arranging, the surfacetemperature of cool roof can be obtained as given by Eq. (20)

ðTRÞcool ¼

0BBB@Tsol�air;M þPN

n¼1 Tsol�air;n cos�nwt � jn

��1þ 1

n

� þ

Ti

�1� U

hi

�þ

ð1þ

where n ¼ hiLk

In order to analyze the cooling impact on the roof temperature, asimplified equation Eq. (20a) is derived by subtracting (TR)cool from(TR)org. In Eq. (20a), F3 < 1 implies positive cooling impact orreduction in the roof temperature, F3 > 1 implies negative coolingimpact or increase in the roof temperature and F3 ¼ 1 implies nocooling impact on the roof temperature by applying a cool coating.

Tcooling impactR ¼ �Tssol�air

�org$

1�

1þ 1n

�org

� F3�1þ 1

n

�cool

!

þ ðTcÞorg$

1ð1þ nÞorg

� F1ð1þ nÞcool

!

(20a)

where F3 ¼ ðTsol�air;M þPNn¼1Tsol�air;n cosðnwt � jnÞÞcool

ðTsol�air;M þPNn¼1Tsol�air;n cosðnwt � jnÞÞorg

The transient heat flux through cool roof can be obtained asgiven by Eq. (21)

qcool ¼ ðUð1þ nÞÞcool�Tssol�air �

Ti

�1� U

hi

�þ Uhi$Tsol�air;M

�cool

(21)

In order to analyze the cooling impact on the heat flux byapplying a cool coating, a simplified equation Eq. (21a) is derived bysubtracting qcool from qorg. In Eq. (21a), F4, F5 < 1 implies positivecooling impact or reduction in the heat flux, F4, F5 > 1 impliesnegative cooling impact or increase in the heat flux and F4, F5 ¼ 1implies no cooling impact on the heat flux by applying a coolcoating.

qcooling impact ¼ ðUð1þ nÞÞorgh�Tssol�air

�org$

�1� F4

�� ðTcÞorg

$�1� F5

�i(21a)

where F4 ¼ ðUð1þ nÞTssol�airÞcoolðUð1þ nÞTs

sol�airÞorg, F5 ¼ ðUð1þ nÞTcÞcool

ðUð1þ nÞTcÞorgThe CRHT model, i.e., Eq. (21), is a generalized heat transfer

model that can be applied to solid roofs/walls in any climate

Uhi$Tsol�air;M

nÞ

1CCA

cool

(20)

K.T. Zingre et al. / Renewable Energy 75 (2015) 210e223 215

condition. For validation of the CRHTmodel, an experimental studywas carried out.

2.2. Experimental setup for validation of the CRHT model

An experimental study was carried out in a high-rise (12-storey), naturally ventilated residential building with a 100-mm-thick concrete (plus 10-mm-thick plaster on the ceiling) solid flatroof in Singapore. The experimental study was performed on asunny day (with clear sky) in February, 2012. The selected resi-dential building is one of the public housing buildings developed bythe Singapore government. In Singapore, about 86% of the totalpopulation resides in public housing buildings [42,43], inwhich themajority are high-rise apartment buildings.

Two identically configured, side-by-side, unoccupied apart-ments located on the top most storey were used for the experi-ments. Each of the two test apartments had the same roof area ofabout 90m2.White-color cool coating (0.50-mm-thick when dried)was applied on the roof surface of one of the two apartments whilethe other apartment's roof was uncoated (original) as the referencefor comparison. Fig. 3 shows the schematic diagram of the exper-imental set up. The cool coating thickness was measured using acoating thickness gauge (Elcometer, A456CSFI1) which was cali-brated to an accuracy of ±1% reading using the zero offset cali-bration method compatible with ISO 19840 [44]. In the calibrationprocess, the thickness gauge probe was initially placed on theoriginal roof surface and the thickness was set to zero (as refer-ence). Then a set of calibration standard samples (provided withthe instrument) were placed on the original surface and measuredby the thickness gauge. The offset between the thickness gaugereadings and the actual thicknesses of the calibration standardswas adjusted to match with the calibration standards. The coolcoating thickness measurements were made at five locations bydirectly placing the calibrated thickness gauge on the coated roofsurface. The cool coating thickness homogeneity of these five lo-cations was ±0.01 mm.

The solar irradiation received by the roof surfaceswasmonitoredby a pyranometer (Kipp and Zonen, CMP 11) facing upwards

Fig. 3. Schematic diagram showing the experimental set u

(towards the sky) mounted at 1.5 m above the roof surface. Thepyranometer was factory calibrated to an accuracy of ±1.4% reading.The detailed calibration procedure of CMP 11 pyranometer can befound in Ref. [45]. The surface temperatures of the roof and theceiling were monitored by surface-type resistance temperaturedetectors encapsulated in stainless steel probes of 4mm in diameterand 25 mm in length (Omega, 4 wire RTDs). The calibrated RTDswere installed at five points (to check the homogeneity) of the eachroofand the ceiling surfaces such that the sensorportionofRTDswascovered with an insulation tape followed by another reflective tapeon top. The reflective tape and insulation tape prevented the sensortip from being affected by solar irradiation such that the sensor tipmeasured the actual temperature of the surfaces. The RTDs werecalibrated to an accuracy of ±0.5 �C prior to the experiment using astirred silicon oil bath thermal calibrator (Tempsens Instruments (I)Pvt. Ltd, Calsys �40/200) for the temperature range of 15 �Ce65 �C(as experienced by the concrete roof on a sunny day). In the cali-bration process, the silicon oil bath was controlled to the calibrationtemperature in the thermal calibrator. The RTD sensors wereinserted into the silicon oil bath. The temperature readings by theRTD sensors were compared against the oil bath temperaturereading from the thermal calibrator to produce a calibration curvefor each RTD sensor. The outdoor air temperature and wind speedwere monitored using a wireless weather station (Scientific SalesInc., WeatherHawk 916) installed at the roof of the experimentalbuilding. The weather stationwas factory calibrated to the accuracyof ±0.5 �C temperature and ±0.3 m/s wind speed. The detailedspecifications and calibration procedure of WeatherHawk 916weather station can be found in Ref. [46].

Inside each apartment at the center point, a standalone indoorair temperature and relative humidity (RH) recorder (MadgeTech,TransiTemp-II) was installed at a height of 1.4 m above the floor tomeasure the indoor RH and air temperature. The recorder wasfactory calibrated to the accuracy of ±0.5 �C temperature and ±3.5%RH. The detailed specifications and calibration procedure ofTransiTemp-II recorder can be found in Ref. [47].

The solar reflectance and thermal emittance of both the roofsurfaces were measured using a portable solar spectrum

p for original and cool concrete roofs (not-to-scale).

Fig. 4. (a). Hourly-averaged solar irradiation, outdoor air temperature and solar-air temperature measurements (with Fourier series simulations). (b). Hourly-averaged wind speed(V) and ho for original and cool concrete roofs. (c). Hourly-averaged hi and ho,r for original and cool concrete roofs and ho,r for original roof (Oliveti et al. [55]). Error bars show 1standard deviation of the 1-minute measurements in each hour.

K.T. Zingre et al. / Renewable Energy 75 (2015) 210e223216

reflectometer (Devices and Services, SSR-6) compatible with theASTM standard C1549 [48] and a portable emissometer (Devicesand Services, AE1-RD1) compatible with the ASTM standard E408[49], respectively. Both instruments were calibrated using the fac-tory suggested calibration procedures prior to the experiment. Thereflectometer was calibrated to an accuracy of ±0.001 using the setof calibration standard samples (a black-body cavity, mirror andceramic tiles) supplied with the instrument. In the calibrationprocess, the reflectometer was powered on to warm up forapproximately half an hour. The calibration standard samples werethen placed alternately on the reflectance head to measure theirsolar reflectance values. The offset between the solar reflectancereadings and the actual solar reflectance of the calibration stan-dards was adjusted using the electronic module until the reflec-tometer readings matched with the calibration standards. Thereflectance head of the calibrated reflectometer was then directlyplaced on the original and cool roof surfaces to measure their solarreflectance values.

Table 1Parameters involved in solar-air temperature calculations for various roof materials.

Roof Solar reflectance(r)

Thermal emittanc(ε)

Original concrete 0.30 0.84Cool concrete 0.74 0.90Original galvanized steel (metal) 0.60a 0.30a

Cool galvanized steel (metal) 0.74 0.90

a Radiation properties are taken from Refs. [52,56].

The emissometer was calibrated to an accuracy of ±0.01 usingthe two calibration standard samples, a high thermal emittancestandard (ε ¼ 0.88) and a low thermal emittance standard(ε ¼ 0.06), supplied with the instrument. The slide method, whichis commonly used to measure thermal emittance of the materialsthat cannot be placed on the heat sink and the materials with lowthermal conductivity, was used to measure the thermal emittance.In the calibration process, both the high and low thermal emittancestandard samples were placed side-by-side on the roof surface. Inorder to ensure that both the standard samples were at the samesurface temperature, several drops of water were put on the surfacebefore placing the standard samples. The detector head, which hadbeen switched on and warmed up for approximately half an hour,was placed alternately on both standard samples to get the thermalemittance readings. The gain and the offset of the emissometerwere adjusted until the thermal emittance readings matched withboth standard samples. In the slide method, the detector head ofthe calibrated emissometer was directly placed on the roof surface

e Tsol�air;M(�C)

Tsol�air;n (�C) jn (Radian)

n ¼ 1 n ¼ 2 n ¼ 1 n ¼ 2

31.6 18.4 10.3 3.5 0.724.9 7.6 3.8 3.6 0.826.3 9.9 5.2 3.6 0.824.9 7.6 3.8 3.6 0.8

Table 2Thermophysical properties of various materials.

Roof material Thermal conductivity(W/m-K)

Thickness(mm)

Conduction resistance(m2-K/W)

Density(Kg/m3)

Specific heat capacity(J/kg-K)

Air [7] 0.025 e e 1.27 1008Plaster [7] 1.5 10a 0.007 600 750Polystyrene [41] 0.09 e e 1050 1300Concrete [56] 0.85 100a 0.111 2350 675Galvanized steel [56] 15.3 8 0.001 4800 500Cool coating 0.045a 0.50 0.011a 1053a 0 (assumed)

a Thermophysical properties are taken from the manufacturers.

K.T. Zingre et al. / Renewable Energy 75 (2015) 210e223 217

and allowed about a minute for the detector reading to reach a nearsteady value. Then the detector was slid several inches across theroof surface to a different spot without breaking contact with thesurface. Solar reflectance and thermal emittance measurementswere made at five locations on each roof to check the homogeneity.The readings difference obtained at these five locations for bothsolar reflectance and thermal emittance were within ±0.02 units.Themass density, specific heat capacity and thermal conductivity ofthe roof materials were not measured on-site but were obtainedfrom the manufacturers or literature [7,41,50].

Solar irradiation, surface temperatures, indoor RH, indoor airtemperature, outdoor air temperature and wind speed weremonitored at 1-min intervals. Fig. 4(a) and (b) show the hourly-averaged values and standard deviations of these measurementsthat were estimated from the 1-min raw data. The measured solar-air temperatures, shown in Fig. 4(a), were estimated (using Eq. (2a))from the measurement data of solar irradiation, solar reflectance,thermal emittance, outdoor air temperature and wind speed.Estimating from the instrumentation errors of the pyranometer,reflectometer, emissometer and weather station, the error of themeasured solar-air temperatures was ±0.9 �C. The measured solar-air temperatures were approximated using Fourier series (Eq. (16))with two harmonics (N¼ 2), which were required as an input to theCRHT model. The parameters involved in the solar-air temperatureestimations are shown in Table 1. The solar reflectance and thermalemittance of the original and cool concrete roofs were obtainedfrom the measurements.

Fig. 4(b) shows the hourly-averaged values of wind speed andoverall outdoor heat transfer coefficient ho. Eq. (22) shows that hocombines the effects of ho,conv and ho,r. The correlations for ho,conv istaken from Ref. [51] and for ho,r is taken from Ref. [52]. Eq. (22a) isapplicable for the estimation of ho,conv for any roof surface and is notsensitive to wind direction nor roughness of the roof surface. Incase of wind speed (V) < 4.88 m/s, ho,conv (Eq. (22a)) assumes aconstant value of 5.6 W/m2-K to represent the natural convectionportion of the total convection coefficient [51]. Eqs. (22b)e(22d) areused for the estimation of ho,r. The sky temperature [7] was esti-mated using Eq. (22d), as plotted in Fig. 4(a). The ho values for theoriginal and cool concrete roofs were estimated using themeasuredroof surface temperatures, outdoor air temperature, wind speedand thermal emittance. Estimating from the instrumentation errorsof the surface temperature sensors, weather station and emiss-ometer, the error of the measured ho was ±1.4 W/m2-K.

ho ¼ ho;conv

þ ho;r$TR � TskyTR � To

for a roof surface directly facing the sky;

(22)

where

ho;conv ¼ 5:6þ 4:0V for V < 4:88 m=s or

ho;conv ¼ 7:2V0:78 for V � 4:88 m=s; (22a)

ho;r ¼ ε$s$F_

R;sky

�T2R þ T2sky

�$

�TR þ Tsky

�; (22b)

F_

R;sky ¼ 0:5�1þ cos f

� �F_

R;sky ¼ 1 for a horizontal surface�;

(22c)

Tsky ¼ 0:0552ðToÞ1:5 for clear sky days or

Tsky ¼ To for cloudy sky days: (22d)

Fig. 4(c) shows the hourly-averaged values of overall indoor heattransfer coefficient hi for the original and cool concrete ceilings. Eq.(23) shows that hi combines the effects of hi,conv and hi,r [53]. The hivalues were estimated by Eqs. (23)e(23c) using the measuredceiling surface temperatures, floor surface temperatures, indoor airtemperatures and thermal emittance values. The correlation forhi,conv (Eq. (23a)) is applicable to the ceilings of naturally ventilatedbuildings [54]. The correlation for hi,r (Eq. (23b)) is based on theassumptions that the thermal emittance of all the indoor facingopaque surfaces (including ceiling, inner walls and floor) is thesame [53]. Accounting for the errors of the instruments used in thecurrent study, the accuracy in the measured hi was ±0.3 W/m2-K.

hi ¼ hi;conv þ hi;r (23)

where

hi;conv ¼ 0:704D0:601h

!$ðTC � TiÞ0:33 (23a)

hi;r ¼s$εi

4� ð2� εiÞ�1þ F

_

C;floor

��TC þ Tfloor

�3(23b)

F_

C;floor ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ L2i

W2

s� LiW

�F_

C;floor ¼ 1 for Li≪W�

(23c)

Fig. 4(c) also compares the trends of ho,r obtained in this studyand the experimental study by Oliveti et al. [55] for horizontal roofson a sunny day with clear sky. Eqs. (22b)e(22d) were used for thisanalysis. It can be observed (from Fig. 4(c)) that the ho,r profileobtained in this study closely matches (with a maximum discrep-ancy of ±0.2 W/m2-K) with that reported in Oliveti et al. [55]. Thisdiscrepancy may be due to the differences in outdoor air temper-atures and thermal emittance values of the horizontal roof surfacesbetween the two studies.

Fig. 5. Comparison of CRHT predictions with conduction transfer function (CTF)method for hourly-averaged roof temperature, ceiling temperature and conductionheat flux through original vs. cool concrete roofs.

Table 3CTF coefficients for the test building roof (U ¼ 2.44 W/m2-K).

CTF term index(j)

Exterior coefficient, Xj

(W/m2-K)Cross coefficient, Yj(W/m2-K)

Interior coefficient, Zj (W/m2-K) Flux, Qj

0 1.14Eþ01 9.91E�02 3.56Eþ01 01 �1.25Eþ01 5.02E�01 �3.04Eþ00 7.34E�012 1.91Eþ00 1.46E�01 2.26E�01 �3.99E�023 �1.96E�02 1.73E�03 �7.21E�04 1.33E�054 2.71E�06 1.57E�07 6.12E�08 �4.29E�125 �5.05E�13 1.87E�14 �6.41E�15 �9.92E�19aTotal

P5j¼0Xj ¼ 7.48E�01

P5j¼0Yj ¼ 7.48E�01

P5j¼0Zj ¼ 7.48E�01

P5j¼0Qj ¼ 6.94E�01

bTotal,

ð1�P5j¼0�QjÞ 2.44Eþ00 2.44Eþ00 2.44Eþ00

a Criteria given in Eq. (24).b Criteria given in Eq. (25).

K.T. Zingre et al. / Renewable Energy 75 (2015) 210e223218

3. Results

3.1. Verification and validation of the CRHT model

The CRHT model verification was carried out against analyticalmethod (the conduction transfer function (CTF)) and validationagainst real-scale experiments, similar to the approach suggestedin ASHRAE standard 140 [20].

The CTF method defines the conduction heat flux as a linearfunction of the current and past surface temperatures and past heatfluxes using four set of CTF coefficients [20,40]. The CTF coefficients(which include the interior, exterior, cross and flux terms) repre-sent the material's thermal response as determined by its materialproperties (and independent of weather data). The state-spacemethod [40] was used for the estimation of CTF coefficients forthe cool roof of the test building using ASHRAE toolkit [56]. The CTFcoefficients (as shown in Table 3) were estimated considering fivelayers of the cool roof of the test building i.e., an outdoor air filmlayer, a cool coating layer (0.50-mm-thick), a concrete layer (100-mm-thick), a plaster layer (10-mm-thick) and an indoor air filmlayer. In order to ascertain the correctness of the CTF coefficients, aconventional verification check was performed using the criterion[28] given by Eqs. (24) and (25). It can be observed (from Table 3)that the totals of exterior coefficients, cross coefficients and interiorcoefficients are equal. At the same time, the ratios given by Eq. (25)are also satisfied by the CTF coefficients (see Table 3) and are equalto U-value of the cool roof of the test building i.e., 2.44 W/m2-K,hence both the criterion (as given by Eqs. (24) and (25)) are satisfiedby the CTF coefficients. The verified CTF coefficients were thenutilized in conjunction with the measured weather data, heattransfer coefficients and temperature data on a sunny day (asshown in Fig. 4(a)e(c)). The thermophysical properties of the roofmaterials of the test building are given in Table 2. These propertieswere taken from the literature [7,41,56] or data provided by themanufacturers.

Xpj¼0

Xj ¼Xpj¼0

Yj ¼Xpj¼0

Zj (24)

Ppj¼0 Xj

1�Ppj¼0 �Qj

¼Pp

j¼0 Yj

1�Ppj¼0 �Qj

¼Pp

j¼0 Zj

1�Ppj¼0 �Qj

¼ U (25)

Fig. 4(a) shows the measured hourly-averaged solar irradiation,outdoor air temperature and the solar-air temperatures for bothcool and original roofs on the day of the experiment (a sunny day).On that day, the peak hourly-averaged solar irradiation (940W/m2)occurred at 13:00 h, sunrise occurred at 07:00 h and sunset

occurred at 19:00 h. The measured solar reflectance and thermalemittance of both roofs are shown in Table 1.

CRHT model predictions of ceiling temperature using Eq. (19),roof temperature using Eq. (20) and conduction heat flux using Eq.(21) were compared with the CTF estimation results for original andcool concrete roofs. As one of the inputs for the CRHTmodel, the 24-h solar-air temperature profiles were obtained from Fourier seriessimulation (as shown in Fig. 4(a)) with two harmonics (N ¼ 2). Thecorrection factor for infrared radiation (ε$I

IR

ho) in Eq. (2a) takes into

account the infrared radiation exchanged by a building surface withthe sky and surrounding objects. It is assumed that horizontal flatroof surfaces emit infrared radiation only to the sky, ASHRAE rec-ommends the correction factor be given value of 3.9 �C [41,44,45].Thus, solar-air temperature is cooler by 3.9 �C for horizontal flatsurfaces due to the emitted infrared radiation to the cooler sky.Therefore, the correction factor for infrared radiation in Eq. (2a) wasassumed to be 3.9 �C for flat roofs. The hourly-averaged values of hoand hi for both concrete roofs were obtained from Fig. 4(b) and (c),respectively. Thermophysical properties of the materials that wererequired for the CRHT model are shown in Table 2.

Fig. 5 shows the comparisons between CRHT predictions andCTF estimation for hourly-averaged roof and ceiling surface

(a)

(b)

Fig. 6. (a). Comparison of CRHT predictions with measurements of hourly-averaged roof temperature, ceiling temperature and conduction heat flux through original Vs. coolconcrete roofs. Error bars show 1 standard deviation of the 1-min measurements in each hour. (b). Comparison of CRHT predictions with measurements of hourly-averaged indoortemperature and ceiling heat flux through original Vs. cool concrete roofs and metal roofs. Error bars (in concrete) show 1 standard deviation of the 1-min measurements in eachhour.

Table 4Impact of cool coating on concrete roofs at different locations.

Researchgroup

Location(Climate zone)

Roofmaterial

Incrementin solarreflectance(Dr)

Reduction inpeak rooftemperature(�C)

K.T. Zingre et al. / Renewable Energy 75 (2015) 210e223 219

temperatures as well as conduction heat flux through the originaland cool concrete roofs. It can be observed that the CRHT predictedprofiles of roof and ceiling surface temperatures and conductionheat flux almost follow the same trends as those estimated by theCTF method (for the respective parameter) and the values areconsiderably close to each other. The maximum difference betweenthe CRHT prediction and the CTF estimation for all the three pa-rameters (roof surface temperature, ceiling surface temperatureand conduction heat flux) are within 6%.

CRHT model predictions of ceiling temperature using Eq. (19),roof temperature using Eq. (20), conduction heat flux using Eq. (21)and indoor air temperature using Eq. (18) were also compared withexperiments for further validation. Fig. 6(a) shows the comparisonsbetween CRHT predictions and experimental measurements ofhourly-averaged ceiling and roof surface temperatures as well asconduction heatflux through the concrete roofs. The error bars show1 standard deviation of the 1-min measurements in each hour. Themeasured heat flux through the roofs was estimated from themeasured roof and ceiling surface temperatures. Estimating fromtheinstrumentation error of the surface temperature sensors, the errorof the ‘measured’ heat flux was ±3.3 W/m2. The CRHT model cangenerally capture the ceiling and the roof temperature profiles withreasonable accuracy. The difference between CRHT prediction andmeasuredhourly-averagedceiling temperature is±1.1 �Cand for rooftemperature is ±1.5 �C. The higher discrepancy between CRHT pre-diction and measurement found in roof temperature, compared toceiling temperature, may be because the actual ho varied moresignificantly with the transient outdoor conditions than hi.

This study Singapore(Wet tropical)

Concrete 0.44 14.1

Kolokotsaet al. [10]

Crete(Mediterranean)

Concrete 0.69 20

Milleret al. [11]

Atlanta(humid subtropical)

Concrete 0.52 14

Kolokotroniet al. [12]

London(Marine west coast)

Concrete 0.50 7.7

3.2. Impact of cool coating on indoor air temperature, surfacetemperatures and heat gain

Fig. 6(a) also depicts the impact of cool coating on roof tem-perature, ceiling temperature and conduction heat flux (due to thetemperature difference between roof and ceiling) through the

concrete roof. The cool coating, which increases the solar reflec-tance of concrete roof from 0.30 (original) to 0.74, keeps the coolroof and cool ceiling temperatures lower than the original coun-terpart almost for the whole day. During day time, the peak coolroof temperature is lower by up to 14.1 �C and the cool ceilingtemperature is lower by up to 8.3 �C than the original counterpart.While during night time, the cool roof temperature is about 2.6 �Clower and the cool ceiling temperature is about 4.3 �C lower thanthe original counterpart. The impact of cool coating is higher forcool ceiling than cool roof during night time. This is because (insecond half of the day i.e., period after peak solar irradiationoccurred at 13:00 h) the original roof cools down faster than thecool roof (due to the higher temperature difference between theoriginal roof and surrounding). However, the original ceiling coolsdown comparatively slower than the original roof (due to thermalmass) and remain at higher temperature than cool ceiling due tolarge heat stored in (original roof's) thermal mass during day time.This results in, during night time, higher temperature difference isobserved between the original ceiling and the cool ceiling, ascompared to that between the original roof and the cool roof. Thereduction in cool roof temperature (during day time) leads to lower

K.T. Zingre et al. / Renewable Energy 75 (2015) 210e223220

heat gain into the building through the cool roof as compared to theoriginal roof. Cool roof has a peak heat gain reduction of 0.12 kW/m2 (or 53%) compared to the original roof during day time. Duringnight time the heat flow direction reverses, i.e., heat flows upwardfrom ceiling to roof and losses to the surroundings. Even though thecool coating gives a higher thermal emittance to the cool roof (asshown in Table 1), the original roof still shows a higher heat lossrate compared to the cool roof. This is because the original ceilingtemperature remains higher than that of the cool ceiling duringnight time due to the larger amount of heat stored in the thermalmass from daytime heat gain, resulting in a larger temperaturedifference between the roof and the surroundings, giving rise to thehigher heat emission rate found in the original roof compared tothe cool roof. Integrating the heat flux profile with respect to timefor the day using Eq. (26),

Qgain ¼Z

daily

qdt; (26)

where q is thedownward conductionheatflux through roof, the dailyheat gain through the two roofs are estimated. The original roof has1.22kWh/m2ofdailyheatgain,while the cool roofhasonly0.56kWh/m2. The cool coating leads to a reduction of 0.66 kWh/m2 (or 54%)daily heat gain through the roof. Fig. 6(b) shows the ceiling heat flux(using Eq. (3)) and indoor air temperatures (using Eq. (18)) for theoriginal and cool concrete roofs. It can be observed that the coolcoating keeps the indoorair temperature lower than that beneath theoriginal roof almost throughout the day. The cool coating providesmaximum indoor air temperature reduction of 2.4 �C at 16:00 h, dueto the reduction in the ceiling heat flux gain of 2.35W/m2. In order tocomprehend the performance of cool coating at different locations,the results of this study are compared with that of the previousstudies for concrete roofs (as shown in Table 4). It is evident that theimpact of cool coating for concrete roofs in tropical climate seems tobe more prominent compared to other locations.

Other than concrete roofs, about 30% of the buildings inSingapore have metal roof with no insulation such as industrial(work-shops) buildings [57]. The roof temperature, ceiling

Fig. 7. CRHT prediction results for hourly-averaged roof temperature, ceiling temper-ature and conduction heat flux through original Vs. cool galvanized steel (metal) roofs.

temperature and conduction heat flux through an 8-mm-thickgalvanized steel (metal) roof are also predicted using the CRHTmodel with the same environmental conditions and cool coating asthose used in Figs. 5 and 6(a). The prediction results are shown inFig. 7. The cool coating, which increases the solar reflectance of themetal roof from 0.60 (original) to 0.74, keeps the cool roof and coolceiling temperature lower than the original counterpart almost forthe whole day. During day time, the peak cool roof and cool ceilingtemperatures are lower byup to5.4 �C than the original counterpart.Cool coating reduces the peak heat gain during day time by 0.10 kW/m2 (or 23%). Similar to the concrete roof, the heat flow directionreverses during night time, i.e., heat flows upward from ceiling toroof and losses to the surroundings. Even though the cool coatinggives a much higher thermal emittance to the surface (0.90 for coolroof and 0.30 for original roof), the original metal roof still shows aslightly higher heatflow rate compared to the cool roof during nighttime. This is because the addition of cool coating increases the R-value (including overall indoor and outdoor heat transfer co-efficients) of themetal roof from0.162m2-K/W to 0.183m2-K/W i.e.,about 12% increment. In terms of conduction resistance (which isused to estimate the conduction heatflux through bothmetal roofs),the cool coating adds about 11 times higher conduction resistancethan the metal roof's original conduction resistance (see Table 2).The increased conduction resistance due to the cool coating hindersthe upward heat flow through the cool metal roof. The heat storageeffect due to thermal mass as seen in the concrete roof plays anegligible role in the metal roof due to the fact that both the metalroof (8-mm-thick) and the cool coating (0.50-mm-thick) have verysmall thermal mass compared with the 100-mm-thick concrete(plus 10-mm-thick plaster) roof. Integrating the heat flux profilewith respect to time for the day using Eq. (26), the daily heat gainsthrough the two metal roofs are estimated. The original metal roofhas 2.15 kWh/m2 of daily heat gain, while the cool roof has only1.41 kWh/m2. The cool coating leads to a daily heat gain reduction of0.74 kWh/m2 on the metal roof. Fig. 6(b) shows the ceiling heat flux(using Eq. (3)) and indoor air temperatures (using Eq. (18)) for theoriginal and cool metal roofs. The cool coating provides maximumindoor air temperature reduction of 3.7 �C at 13:00 h, due to thereduction in the ceiling heat flux gain of 3.65 W/m2.

4. Discussion on the effect of wind speed on cool roof'sperformance

In addition to solar reflectance and R-value of the original roof,the heat gain reduction brought by cool coatings is largely affected

Fig. 8. Impact of wind speed (V) or ho on reduction in daily heat gain brought by coolcoatings.

K.T. Zingre et al. / Renewable Energy 75 (2015) 210e223 221

by ho, which combines the effects of outdoor convective heattransfer coefficient, ho,conv and outdoor radiative heat transfer co-efficient, ho,r as shown in Eq. (22). The correlation for ho,conv (Eq.(22a)) suggests that the wind speed that the roof is subjected tocould also have an impact on the heat gain reduction.

The reduction in daily heat gain through the concrete and metalroofs brought by cool coatings under different wind speeds (2, 6 or10 m/s) is predicted by the CRHT model and the results are pre-sented in Fig. 8. Constant wind speed throughout the day (2, 6 or10 m/s), and thus constant ho, was used in this investigation. Thesurface temperatures of themetal roof required in the calculation ofho are taken from Ref. [52]. It shows that the reduction in daily heatgain brought by the addition of cool coating drops as wind speedincreases, meaning that cool coating provides more heat gainreduction at lower wind speed. It is because as wind speed in-creases (higher ho) the roof surface gets cooler due to the increasedconvective heat transfer. This reduces the amount of heat gainreduction by the cool coating since part of that has already beenachieved by the higher wind speed. Similar observations are foundin both concrete and metal roof.

The drop in daily heat gain reduction by cool coating as windspeed increases becomes less significant for lower solar reflectance.It is because the heat gain by solar radiation becomes more sig-nificant at lower solar reflectance and the impact of increasingwind speed (increase ho) on heat gain becomes relatively less sig-nificant than that at high solar reflectance. This can also be seen inFig. 8 which shows the prediction results of reduction in daily heatgain for solar reflectance of 0.74 and solar reflectance of 0.90 forboth roofs. It suggests that the increased wind speed affects onlythe ho which has the same effects on both roof materials.

5. Conclusions

In this study, a novel and general cool roof heat transfer (CRHT)model, capable of incorporating transient outdoor and indoorboundary conditions, is developed using the spectral approxima-tion method. The CRHT model overcomes the limitations of theconduction transfer function (CTF) and response factor (RF)methods and largely simplifies the cool roof heat transfer calcula-tion as compared to the FD/FE methods. The CRHT model providesan easy means for building designers to evaluate the impact of coolcoating on roof temperature, ceiling temperature, indoor air tem-perature and heat flux through all opaque solid building surfaces(walls and roofs with no air-gap).

The proposed CRHT model was verified against the analytical(CTF) method and was further validated against experiments per-formed in two identically configured, side-by-side, naturally-ventilated apartments with 100-mm-thick concrete (plus 10-mm-thick plaster) flat roofs in Singapore. CRHT model predictionsgenerally follow the same trend as the CTF predictions, with amaximum error of 6%. CRHT model predictions of roof heat flux,hourly-averaged ceiling temperature and roof temperature arewithin ±3.3W/m2, ±1.1 �C and ±1.5 �C, respectively, as compared toexperimental measurements.

The impact of cool coating on building heat transfer in thetropical climate of Singapore is investigated using the CRHT modeland the apartment building used in model validation. On a sunnyday, a cool coating (having a solar reflectance of 0.74) reduces thepeak roof temperature by up to 14.1 �C and the peak heat gain by upto 0.12 kW/m2 (or 53%) through the concrete roof. The peak indoorair temperature is reduced by up to 2.4 �C in the apartment. FurtherCRHT modeling is conducted on the same apartment building butfitted with an 8-mm-thick galvanized steel (metal) roof. Modelpredictions show that the same cool coating reduces the peak rooftemperature by up to 5.4 �C and the peak heat gain by up to

0.10 kW/m2 (or 23%) on a sunny day. This leads to a reduction ofpeak indoor air temperature by up to 3.7 �C in the apartment.

Cool coating provides more significant heat gain reduction asthe roof is subjected to lower wind speed. As wind speed increases,roof cooling by convective heat transfer increases, reducing theamount of heat gain reduction through the radiation meansbrought by the cool coating. This effect diminishes if less reflectivecool coating is used.

The conclusions provided in this study are based on the resultsobtained on a sunny day in Singapore. These results may vary atdifferent weather conditions.

Acknowledgments

This study is jointly supported by MND-A*Star Green BuildingJoint Grant through grant no. 1121760021 and the Housing andDevelopment Board (HDB) of Singapore through grant no.M4060819. The technical and logistical support by Energy ResearchInstitute at NTU (ERI@N) is greatly appreciated.

Nomenclature

ach air change per hour {m3/hr}C specific heat capacity of roof material {J/kg-K}Cair specific heat capacity of air {J/kg-K}CTF conduction transfer functionCRHT cool roof heat transfer modelDh hydraulic diameter {m}F intermediate variables

F_

R;sky view factor of roof surface to the sky

F_

C;floor view factor of ceiling surface to the floor surfacehi;conv indoor convective heat transfer coefficient {W/m2-K}hi;r indoor radiative heat transfer coefficient {W/m2-K}hi overall indoor heat transfer coefficient {W/m2-K}ðhiÞcool overall indoor heat transfer coefficient for cool roof {W/

m2-K}ðhiÞorg overall indoor heat transfer coefficient for original roof

{W/m2-K}ho overall outdoor heat transfer coefficient {W/m2-K}ðho;rÞcool outdoor radiative heat transfer coefficient for cool roof

{W/m2-K}ðho;rÞorg outdoor radiative heat transfer coefficient for original roof

{W/m2-K}ðhoÞcool overall outdoor heat transfer coefficient for cool roof {W/

m2-K}ðhoÞorg overall outdoor heat transfer coefficient for original roof

{W/m2K}ho;conv outdoor convective heat transfer coefficient {W/m2-K}ho;r outdoor radiative heat transfer coefficient {W/m2-K}Iabs absorbed radiation {W/m2}Iin incident radiation {W/m2}Iout outgoing radiation {W/m2}IIR infrared radiation {W/m2}j CTF term index in Eqs. (24) and (25)k thermal conductivity of roof material {W/m-K}kcoating thermal conductivity of cool coating {W/m-K}lcoating thickness of cool coating {m}Li indoor distance from ceiling where adiabatic condition

can be assumed {m}L thickness of roof {m}LW long wavesm integern order of harmonic in Fourier seriesq heat flux {W/m2}

K.T. Zingre et al. / Renewable Energy 75 (2015) 210e223222

qcool conduction heat flux through cool roof {W/m2}qorg conduction heat flux through original roof {W/m2}ðqCÞcool heat flux through the ceiling of cool roof {W/m2}ðqCÞorg heat flux through the ceiling of original roof {W/m2}Qgain daily heat gain (integrated-hourly downward conduction

heat flux) {kWh/m2}RH relative humidity {%}SW short wavest time {hour}TC ceiling temperature {K}TC temperature of ceiling at time t ¼ 0 {K}ðTCÞcool cool ceiling temperature {K}ðTCÞorg original ceiling temperature {K}Tfloor temperature of floor {K}T floor temperature of floor at time t ¼ 0 {K}Ti indoor air temperature {K}Ti indoor air temperature of at time t ¼ 0 {K}ðTiÞcool cool indoor air temperature {K}ðTiÞorg original indoor air temperature {K}To outdoor air temperature {K}To outdoor air temperature of at time t ¼ 0 {K}TR roof temperature {K}ðTRÞcool cool roof temperature {K}ðTRÞorg original roof temperature {K}Tsky sky temperature {K}Tesol�air solar-air temperature obtained from experiment {K}Tssol�air simulated solar-air temperature {K}ðTe

sol�airÞcool solar-air temperature of cool roof obtained fromexperiment {K}

ðTssol�airÞcool simulated solar-air temperature of cool roof {K}

ðTesol�airÞorg solar-air temperature of original roof obtained from

experiment {K}ðTs

sol�airÞorg simulated solar-air temperature of original roof {K}Tsol�air;M mean solar-air temperature {K}Twall temperature of inside surface of wall {K}Twall temperature of inside surface of wall at time t ¼ 0 {K}U U-value of roof {W/m2-K}Ucool U-value of cool roof {W/m2-K}Uorg U-value of original roof {W/m2-K}V wind speed {m/s}VOLi volume of indoor environment {m3}W width of roof in Eq. (23c), {m}X exterior coefficient in Eqs. (24) and (25)Y cross coefficient in Eqs. (24) and (25)y space coordinateZ interior coefficient in Eqs. (24) and (25)

Greek symbolsa solar absorptance (0<a<1) for opaque surface a ¼ 1� r

a* thermal diffusivity {m2/sec}b decrement factor (0 � b � 1)ε thermal emittance (0< ε<1)εi thermal emittance of indoor facing surfaces (ceiling, walls

and floor)FðyÞ basis functionf time lag between harmonic of roof and ceiling surface

temperaturesqðtÞ time dependent coefficient4 tilt angle of the roof surfaceQ flux in Eqs. (24) and (25)r solar reflectance (0< r<1)r* mass density {kg/m3}s StefaneBoltzmann constant, 5.67 � 10�8 {W/m2-K4}

εIIR=ho correction factor for infrared radiation {K}, defined in Eqs.(2) and (2a)

n; x;m intermediate variablesw angular velocity {radian/hour}

Subscriptsabs absorbedair indoor airC ceilingconv convectivecool cool roofh hydraulici indoorin incident radiationM meanm integern order of harmonic in Fourier seriesN no. of harmonics in Fourier serieso outdoororg originalout outgoing radiationr radiativeR roofsol-air solar-air

Superscriptse experimentalIR infrared radiations simulated

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