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Experimental and numerical investigation on the performance of amorphous silicon photovoltaics window in East China Wei He * , Y.X. Zhang, Wei Sun, J.X. Hou, Q.Y. Jiang, Jie Ji Dept. of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei 230026, China article info Article history: Received 29 April 2010 Received in revised form 20 July 2010 Accepted 30 July 2010 Keywords: Photovoltaic double-glazing window Thermal and electrical performance Predicted mean vote East China abstract Experiments in a comparable hot-box have been carried out for the study of the thermal performance and power generation of a double-glazing window system integrated with amorphous silicon (a-Si) photovoltaic (PV) cells in Hefei, east region of China. Compared to PV single-glazing window, the indoor heat gain of PV double-glazing window is reduced to 46.5% based on experiment data. The electric efciencies are both about 3.65% with packing factor 0.8 of PV single-glazing window and PV double- glazing window. The numerical simulation with computational uid dynamics (CFD) method has been performed for the prediction of air ow and thermal performance of PV double-glass window. The temperature distribution and thermal performance predicted by the CFD model are in good agreement with the experimental data. Compared between the experimental and numerical results, temperature differences of PV modules are only 1.7% and 1.1% for PV double-glazing and PV single-glazing window, respectively. Because of the much lower inner surface temperature of PV double-glazing window compared with that of PV single-glazing window, the predicted mean vote (PMV) of the ofce work stage area with PV double-glazing window is well improved. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction The application of Photovoltaic technology in buildings has attracted worldwide attention for energy savings and environ- mental side-effect reductions. Y. Etzion and E. Erell proposed a reversible glazing system that can control transmission of solar radiation into indoor spaces [1]. Brinkworth, B.J. and Cross, B.M. et al. [2] indicated that a ventilated air duct behind a PV panel can decrease temperature of PV cell. CFD package was used to simulate the air ow behind the PV panel and good results were obtained. T.T chow [3] investigated the performance of a PV ventilated window applied to ofce building of Hong Kong by numerical simulations. With the transmittance of PV window in the range of 0.45e0.55, the electricity consumption was found reduced by 55% compared to the single-glazed window without lighting control. Various numerical investigations of PV ventilated windows with different structures had been carried out to evaluate the thermal loads, daylight contribution and electricity production by Remi C, Geun Y.N [4,5], and so on. Gan and Riffat [6] showed that CFD was a useful tool to optimize ventilation systems for comfortable indoor environment and effective cooling of PV. By studying the factors affecting the local and average heat transfer coefcients along the vertical surfaces of a see-through glazing system with PV cells, Jun Han [7] did some research on the convective ow strength and heat transfer variation in the ventilation duct. However, there was little report about the performance and PMV analyses of PV window in mainland China. In this paper, the experiment with a comparable hot-box has been carried out in Hefei (N31.8 , E117.3 , east region of China), to study the thermal performance and electrical generation of a double-glazing window system integrated with amorphous silicon cells. Hefei city locates in subtropical climate region, and the annual horizontal solar radia- tion is about 5000 MJ/m 2 . The numerical investigation of the performance of PV window system has also been carried out by computational uid dynamics (CFD) method. 2. Comparable hot-box and experiments 2.1. Comparable hot-box and a-Si PV windows The PV single-glazing window, as shown in Fig. 1b, is just a window which consists of single amorphous silicon (a-Si) PV glazing. And the PV double-glazing window system, as shown in Figs. 1a and 4, consists of an amorphous silicon (a-Si) PV panel and a clear backing glazing. There are ventilated openings at the top and bottom of the semi-transparent a-Si PV glazing, and the PV glazing * Corresponding author. Tel.: þ86 0551 3601641. E-mail address: [email protected] (W. He). Contents lists available at ScienceDirect Building and Environment journal homepage: www.elsevier.com/locate/buildenv 0360-1323/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2010.07.030 Building and Environment 46 (2011) 363e369

Experimental and numerical investigation on the performance of amorphous silicon photovoltaics window in East China

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lable at ScienceDirect

Building and Environment 46 (2011) 363e369

Contents lists avai

Building and Environment

journal homepage: www.elsevier .com/locate/bui ldenv

Experimental and numerical investigation on the performance of amorphoussilicon photovoltaics window in East China

Wei He*, Y.X. Zhang, Wei Sun, J.X. Hou, Q.Y. Jiang, Jie JiDept. of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei 230026, China

a r t i c l e i n f o

Article history:Received 29 April 2010Received in revised form20 July 2010Accepted 30 July 2010

Keywords:Photovoltaic double-glazing windowThermal and electrical performancePredicted mean voteEast China

* Corresponding author. Tel.: þ86 0551 3601641.E-mail address: [email protected] (W. He).

0360-1323/$ e see front matter � 2010 Elsevier Ltd.doi:10.1016/j.buildenv.2010.07.030

a b s t r a c t

Experiments in a comparable hot-box have been carried out for the study of the thermal performanceand power generation of a double-glazing window system integrated with amorphous silicon (a-Si)photovoltaic (PV) cells in Hefei, east region of China. Compared to PV single-glazing window, the indoorheat gain of PV double-glazing window is reduced to 46.5% based on experiment data. The electricefficiencies are both about 3.65% with packing factor 0.8 of PV single-glazing window and PV double-glazing window. The numerical simulation with computational fluid dynamics (CFD) method has beenperformed for the prediction of air flow and thermal performance of PV double-glass window. Thetemperature distribution and thermal performance predicted by the CFD model are in good agreementwith the experimental data. Compared between the experimental and numerical results, temperaturedifferences of PV modules are only 1.7% and 1.1% for PV double-glazing and PV single-glazing window,respectively. Because of the much lower inner surface temperature of PV double-glazing windowcompared with that of PV single-glazing window, the predicted mean vote (PMV) of the office work stagearea with PV double-glazing window is well improved.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

The application of Photovoltaic technology in buildings hasattracted worldwide attention for energy savings and environ-mental side-effect reductions. Y. Etzion and E. Erell proposeda reversible glazing system that can control transmission of solarradiation into indoor spaces [1]. Brinkworth, B.J. and Cross, B.M.et al. [2] indicated that a ventilated air duct behind a PV panel candecrease temperature of PV cell. CFD package was used to simulatethe air flow behind the PV panel and good results were obtained. T.Tchow [3] investigated the performance of a PV ventilated windowapplied to office building of Hong Kong by numerical simulations.With the transmittance of PVwindow in the range of 0.45e0.55, theelectricity consumption was found reduced by 55% compared to thesingle-glazed window without lighting control. Various numericalinvestigations of PV ventilated windows with different structureshad been carried out to evaluate the thermal loads, daylightcontribution and electricity production by Remi C, Geun Y.N [4,5],and so on. Gan and Riffat [6] showed that CFD was a useful tool tooptimize ventilation systems for comfortable indoor environmentand effective cooling of PV. By studying the factors affecting the local

All rights reserved.

and average heat transfer coefficients along the vertical surfaces ofa see-through glazing system with PV cells, Jun Han [7] did someresearch on the convective flow strength and heat transfer variationin the ventilation duct.

However, there was little report about the performance andPMV analyses of PV window in mainland China. In this paper, theexperiment with a comparable hot-box has been carried out inHefei (N31.8�, E117.3�, east region of China), to study the thermalperformance and electrical generation of a double-glazing windowsystem integratedwith amorphous silicon cells. Hefei city locates insubtropical climate region, and the annual horizontal solar radia-tion is about 5000 MJ/m2. The numerical investigation of theperformance of PV window system has also been carried out bycomputational fluid dynamics (CFD) method.

2. Comparable hot-box and experiments

2.1. Comparable hot-box and a-Si PV windows

The PV single-glazing window, as shown in Fig. 1b, is justa window which consists of single amorphous silicon (a-Si) PVglazing. And the PV double-glazing window system, as shown inFigs. 1a and 4, consists of an amorphous silicon (a-Si) PV panel anda clear backing glazing. There are ventilated openings at the top andbottom of the semi-transparent a-Si PV glazing, and the PV glazing

Fig. 1. Schematic structure diagram of the office rooms integrated with a PV double-glass window system. (a) PV double-glazing window, (b) PV single-glazing window.

W. He et al. / Building and Environment 46 (2011) 363e369364

provides shading and electricity for the room. In summer, with thesemi-transparent a-Si PV glazing facing outward, the PV glazingabsorbs solar radiation and reduces the penetration of solar radi-ation into the office room. Part of solar energy absorbed is con-verted into electrical energy, the other is converted into thermalenergy and heats the air in the ventilation gap behind the PV panel.No mechanical ventilated system is provided for the windowsystem. The upward air flow is driven by thermal buoyancy, anda temperature gradient is along the height of the air gap. Thiswindow system also has one advantage that the scenery outsidecan be seen from the inside while it could not be seen from theoutside, as showed in Fig. 3.

The plan view of the test rig with the window systems is shownin Fig. 2. The dimensions of both rooms are 2.80 m (height)�3.00 m (width)� 3.00 m (length). The thickness of room walls is0.10 m. One of the offices has a double-glazing window integratedsemi-transparent a-Si PV cells, and the other has a PV single-glazing window. The two PV windows are both fixed on the southwall. The air-conditioning system inside the comparable hot-boxkeeps temperature of the corridor and the test office rooms ata constant as 25� 0.5 �C. Fig. 3 is the photo of the test rig of hot-boxintegrated a-Si PV window systems.

The two PV windows both have a width of 1.2 m and a heightof 1.15 m. The thickness of semi-transparent a-Si PV panel andclear glazing is 7 mm and 6 mm, respectively. The air gap in thePV double-glazing window is of 20 mm. The ventilated openings

Fig. 2. Schematic planform of

have a width of 120 mm and a height of 6 mm. As seen in Fig. 3,the PV panel is comprised of three PV modules with size of1110mm� 333 mm, which are manufactured by one company ofChina. The packing factor of PV cells on the semi-transparent PVmodules is of 0.8. The characteristics of the PV module are shownin Table 1. Because of packing factor of 0.8, the electrical effi-ciency is 3.65% and is lower than that of standard productionof 5.5%.

2.2. Experiments

The two office rooms were tested at the same time under goodweather conditions. Eleven thermocouples were fixed on theglazing surfaces of two PV windows to analyze the temperaturedistribution and the variation of heat transfer. Two thermocouplesare arranged at the openings of PV double-glazing window tomeasure the inlet and outlet temperature. There were a pyran-ometer and a thermocouple outdoor used to measure irradiancenormal to the plane of the PV cell and outdoor ambient tempera-ture, respectively. The room temperatures of two office roomsweremonitored by two thermocouples. All the thermocouples wereconnected to Data Acquisition/Switch Unit 34901A to record thedata. All the experiments were performed from 9:00 am to17:00 pmwhich conformed to the office hours in China in summer.

PV efficiency (hpv) is an important index to evaluate theperformance of PV cells, as

environmental hot-box.

Fig. 3. Double-glazing window system integrated with semi-transparent amorphous silicon (a-Si) PV modules.

W. He et al. / Building and Environment 46 (2011) 363e369 365

hpv ¼ U$IG$Ac

(1)

Where U is voltage of PV modules, voltage; I is current of PVmodules, ampere; G is vertical irradiance to the south, W/m2; Ac isarea of PV modules, m2.

The PV window system plays an important role in modifyingsolar radiation and heat transmission to the inside of the building.Meanwhile, the total heat gain fromwindow system (Q

,) has a great

impact on the indoor thermal comfort and cooling load. In summer,the cooling load also increases and the indoor thermal comfortdecreases, as a result of the increasing heat gain from windowsystem.

Q,¼ G$A$sþ �

hr;gw þ hc;gi�AðT � TaÞ (2)

Where A is area of window system, m2; s is effective transmittanceof window system; T and Ta are interior surface temperature ofwindow system and indoor air temperature of office roomrespectively, �C; hc,gi is convective heat transfer coefficient betweenglazing and indoor air, W/m2K; hr,gw is radiative heat transfercoefficient between glazing and interior wall, W/m2K.

The temperature difference between window and interior wallsleads to asymmetrical thermal radiation and variety thermalcomfort level. The index termed predictedmean vote (PMV) is usedto evaluate the indoor thermal comfort level, and it is expressedby [8]:

PMV ¼�0:303e�0:036M þ0:028

�nðM�WÞ�3:05�10�3

½5733�6:99ðM�WÞ�pa��0:42½ðM�WÞ�58:15��1:7�10�5Mð5867�paÞ�0:0014Mð34� taÞ�3:96

�10�8fclhðtclþ273Þ4��

trþ273�4i� fclhcðtcl� taÞ

oð3Þ

Table 1Characteristics of a PV module.

Open circuit voltage 41.98 V PV packing factor 0.8Short circuit current 0.553 A Power rating 10.8 WPower efficiency 3.65% in standard condition Temperature coefficient �0.1%

Where M is rate of metabolic heat production, W; W is rate ofmechanical work accomplished, W; ta is indoor temperature, �C; pais water vapor pressure of indoor air, Pa; tcl is surface temperatureof clothing, �C; fcl is clothing area factor; tr is weighted surfaceradiant temperature, �C; hc is convective heat transfer coefficientbetween body and indoor air, W/m2; The expressions of tcl, hc, fcl, trare given in Appendix.

3. Numerical simulation

3.1. Simulation program

The computational fluid dynamics (CFD) was employed to studythe performance of PV windows. A general-purpose commercialCFD software FLUENT was applied to calculate the air flow andtemperature distribution of the office rooms. The pre-processorsoftware GAMBIT was adopted in the simulate work. The physical,vertical irradiance and temperature date obtained from theexperiment of PV window system were used as input parametersinto the simulation.

3.2. CFD modelling

The FLUENT package was used in modelling the ventilation bysolving the conservation equations for mass, momentum andenergy with the finite volume method.

Previous studies have suggested that the renormalization group(RNG) k-epsilon turbulence model [9] performs better than otherturbulence model in the prediction of indoor air flow [10]. There-fore, the RNG k-epsilon turbulence model was adopted to simulatethe effect of turbulence of air flow as air flow in PV double-glazingwindow system.

In order to simulate the effect of buoyancy, the Boussinesqmodel, in which the fluid density was taken as a function oftemperature, was used. The discrete transfer radiation model [11]was used to evaluate the radiative heat transfer of the office inte-rior surfaces, which were assumed to be gray. To simplify thesimulation of PVwindows, it was assumed that fresh air flowed intooffice room from an inlet opening in the ceiling and out of officeroom via an outlet opening in the north wall. The inlet opening of0.2 m width was located at the center of the ceilings, 1.4 m to the

Fig. 5. Second heat gain from the two windows. solid quadrel: Second heat gain fromPV double-glazing window (exp); open quadrel: Second heat gain from PV double-glazing window (num); solid circle: Second heat gain from PV single-glazing window(exp); open circle: Second heat gain from PV single-glazing window (num); crosssymbol line: solar irradiation.

W. He et al. / Building and Environment 46 (2011) 363e369366

north wall, and the extract opening of 0.15 m high was located neartop of the north wall.

All the boundaries of the two office rooms were modeled asadiabatic no-slip wall boundaries, except the ventilation openings.When a-Si PV modules operated, most of the solar irradiationabsorbed by them was converted into heat energy, so the temper-ature of PV modules increased. As a result of the low temperaturecoefficient of a-Si PV module, the energy that solar irradiation wasconverted into heat was almost the same as what it used to be.Therefore, the semi-transparent a-Si PV modules could be assumedas a constant heat source.

Because of the symmetry of the office, a two-dimensional modelwas used to simplify the simulation of the office’s ventilation andthermal performance to reduce computational time. This wouldimply no air flow or heat transfer through the side walls. The airflow inside PV double-glazing window system is affected by heatconduction, convective and radiative heat transfer. The first-orderupwind discretization scheme was used in the simulation model-ling. A nonuniform computational grid was used for the predictionof two-dimensional flow in the office rooms.

Convergence was considered to have been reached when theresiduals of energy equation were less than 1e-6, and the residualsof other equations were by less than 10�3.

4. Performance evaluation

The experiment was conducted in the summer of 2009, andlasted for more than one month. The experimental data ofSeptember 22 was selected as a typical sample to analyze theperformance of PV window systems. Fig. 4 shows the ambienttemperature and incident irradiation on south façade from 9:00 amand 17:00 pm in September 22. They were used in computersimulation as the boundary conditions.

4.1. Heat gain and energy saving

Figs. 5 and 6 show second heat gain and total heat gain from PVdouble-glazing window and PV single-glazing window from9:00 am to 17:00 pm respectively. The total heat gain can be dividedinto second heat gain and direct heat gain from solar irradiation.The second heat gain is the combination of the convective andinfrared radiative heat transfer between glazing and the indoorspace, which is represented by the second right item in Eq. (2). Thedirect heat gain is the solar radiation transmitted from the windowsystem, which is represented by the first right item in Eq. (2).

Fig. 4. Ambient temperature and vertical irradiation of south façade.

As is shown in Figs. 5 and 6, the trend of total heat gain isbasically the same as that of second heat gain. The direct heat gainof PV single-glazing window is 20% higher than that of PV double-glazing window. But the direct heat gain from solar irradiationonly occupies a small part of total heat gain. Therefore, secondheat gains from window systems have a decisive impact on totalheat gains.

The predicted mean second and total heat gains are close to themeasured values. In the morning, the predicted mean values area little more than the measured ones, while they are a little lessthan the measured ones in the afternoon. The difference betweenexperiment and numerical simulation could due to the two-dimensional flow simulation to three-dimensional flow in fact.

The average heat gain and temperature of PVmodules from 9:00to 17:00 from experiments and numerical simulation are given inTable 2. The average measured heat gains are all a little larger thanpredicted. The average measured second heat gain from double-

Fig. 6. Total heat gain from the two windows. solid quadrel: total heat gain from PVdouble-glazing window (exp); open quadrel: total heat gain from PV double-glazingwindow (num); solid circle: total heat gain from PV single-glazing window (exp); opencircle: total heat gain from PV single-glazing window (num); cross symbol line: solarirradiation.

Table 2Average indoor heat gain and temperature of PV modules (9:00e17:00 h).

Construction PV double-glazing window PV single-glazing window

Experimental Numerical Difference Experimental Numerical Difference

Second heat gain (W) 51.8 46 12.6% 113.2 112.1 1.0%Total heat gain (W) 78.3 70.2 11.5% 146.3 142.3 2.7%Temperature of PV modules (�C) 36.1 36.7 1.7% 37.1 36.7 1.1%

W. He et al. / Building and Environment 46 (2011) 363e369 367

glazing window is about 51.8 W, and it is 12.6% larger than theaverage predicted value which is 46 W. The average measured totalheat gain fromdouble-glazingwindow is 78.3 W, and is 11.5% largerthan the predicted. For the single-glazing window, the difference ofsecond heat gain between experimental and numerical data is 1.0%and that of total heat gain is 2.8%. According to the experimentaldata, second and total heat gain of PV double-glazing window are45.8% and 53.5% of that of PV single-glazing window, respectively,and the values are 41.0% and 49.3% respectively from simulationresults. It indicates that PV double-glazing window can effectivelyreduce indoor heat gain and air-conditioning load, compared withPV single-glazing window. The better thermal performance of PVdouble-glazing window is due to its ventilated openings at the topand bottom, which improves the thermal resistance of PV windowsignificantly.

As seen from Figs. 5 and 6, the second heat gain and total heatgain were affected by incident solar irradiation and ambienttemperature significantly. There is a time lag of the effect of solarirradiation on second and total heat gains. When the incidentirradiation reaches the peak at about 12:00, second, total heatgains are still in the upswing. On the other hand, the downwardtrend of second and total heat gains is not as sharp as that ofincident solar irradiation in the afternoon, due to the impact ofambient temperature.

4.2. Temperature and PMV

Fig. 7 gives the temperature distributions of different glazing at12:00 from the simulation and experiment. The temperatures of

Fig. 7. Glazing temperature distribution of different glazing at 12:00. solid circle: PVmodels of PV single-glazing window (num); open circle: PV models of PV single-glazing window (exp); solid triangle: PV models of PV double-glazing window (num);open quadrel: PV models of PV double-glazing window (exp); solid square: clear glassof PV double-glazing window (num); open square: clear glass of PV double-glazingwindow (exp).

experiment and simulation are close to each other except that ofthe bottom. At the bottom of clear glazing of PV double-glazingwindow, the difference between experimental and calculatedtemperature is about 3 �C. This could be due to the relative lowRayleigh numbers in the air gap of PV double-glazing window,according to the RNG -epsilon turbulence model.

Fig. 8 shows the variety of glazing temperature from 9:00 to17:00. Experimental data and numerical simulation data of glazingtemperature are basically consistent. The experimental PVtemperature of single-glazing window keeps a little higher thanthat of PV double-glazing, and this could be due to the enhancedheat transfer coefficient in the ventilation construction. Theincreasing of PV cells temperature has a negative influence on theperformance of electrical power. Therefore, PV double-glazingwindow is better for the operation of PV modules.

The position at 0.75 m from floor level, 1 m from window and1.5 m from nearby sidewall is chosen as the reference one normallywhere the office work stage zone is. And indoor relative humidity isassumed to be 40%, M is 58.15 W/m2, Icl is 0.6, Fg and Fwall are both0.5. Then the daily variation of PMV of the office work stage zonewith PV single-glazing window and PV double-glazing windowbased on experimental data are showed in Fig. 9.

The PMV of the office work stage zone with PV single-glazingwindow varies between 1.4 and 2.6, and this index means that thethermal sensation of person is warm or even hot. As the innersurface temperature of clear glass is much lower than that of PVsingle-glazing, the PMV of the office work stage area with PVdouble-glazing window varies between 0.9 and 1.7, i.e. the thermalsensation of person is mostly kept in the band between neutral andslightly warm.

Fig. 8. Glazing temperature of different glazing. solid circle: PV models of PV single-glazing window (num); open circle: PV models of PV single-glazing window (exp);solid triangle: PV models of PV double-glazing window (num); open quadrel: PVmodels of PV double-glazing window (exp); solid square: clear glass of PV double-glazing window (num); open square: clear glass of PV double-glazing window (exp).

Fig. 9. PMV. solid circle: PV single-glazing window; solid square: PV double-glazingwindow.

Fig. 10. Pv Power and efficiency in the testing period. solid square: power of PVdouble-glazing window; solid circle: efficiency of PV double-glazing window; opensquare: power of PV single-glazing window; open circle: efficiency of PV single-glazingwindow.

W. He et al. / Building and Environment 46 (2011) 363e369368

4.3. PV power output and efficiency

The electrical power output and efficiency of PV cells areimportant parameters to evaluate the performance of PV modules.Compared to mono-silicon cells, the efficiency of semi-transparenta-Si models with packing factor 0.8 is just 3.65% under standardconditions, but the semi-transparent a-Si models has better visionlandscape and lower temperature coefficient. These were reporteda few years ago [12,13]. Fig. 10 shows the PV power output andefficiency in the testing period. It is found that the variation of PVpowerfully traces the variation of solar radiation. The PV temper-atures of the two window systems in the testing period are veryclose to each other and the electrical efficiencies of the twowindows both keep at about 2.5%, although the PV temperaturevaries greatly in the testing period.

5. Conclusions

Experimental and numerical analysis of two kinds of PVwindows in East China, which are PV double-glazing window andPV single-glazing window integrated with a-Si PV panel, have been

reported in this paper. Results show that the PV double-glazingwindow can reduce indoor heat gain and cooling load significantlyby setting up an air gap behind PV modules, and because of themuch lower inner surface temperature of PV double-glazingwindow compared with that of PV single-glazing window, the PMVof the office work stage zone is improved obviously compared withPV single-glazing window. So the PV double-glazing window hasthe large potential application in office building with the costdecreasing and efficiency increasing. The work also demonstratesthat the CFD package Fluent can be used in simulate and optimizingthe performance of PV window system with acceptable error, soCFD package Fluent can be used to help HVAC engineers to predictthe cooling load before design of a building with PV window.

Acknowledgment

The work described in this paper was supported by the grantsfrom the National Key Technology R&D Program in the 11th Fiveyear Plan of china (Project No. 2006BAA04B04) and the NationalNature Science Fund of China (Project No. 50876098).

Appendix

tr ¼ TgFg þ TwallFwall

tcl ¼ ðhclts þ fclðhr þ hcÞtaÞ=ðhcl þ fclðhr þ hcÞÞ

hr ¼ 4:6�1þ 0:01tr

hc ¼ 2:38ðtcl � taÞ0:25

hcl ¼ 1:0=0:155Icl

fcl ¼ 1:05þ 0:1Icl

Where hr is radiative heat transfer coefficient between body andinterior walls, W/m2; hcl is heat transfer coefficient between theskin surface and clothing, W/m2; Icl is thermal resistance of theclothing; Tg is temperature of the inner surface of the glazing, �C;Twall is temperature of the interior wall, �C; Fg is view factorbetween reference point and the glazing; Fwall is view factorbetween reference point and the interior wall, tcl is surfacetemperature of clothing, �C; fcl is clothing area factor.

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