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A novel method for full-scale measurement of the external convective heat transfer coefficient for building horizontal roof
Energy and Buildings 41 (2009) 840–847
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Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
A novel method for full-scale measurement of the external convective heat transfer coefficient for building horizontal roof Jiantao Shao, Jing Liu *, Jianing Zhao, Wenwu Zhang, Dexing Sun, Zhipeng Fu School of Municipal & Environmental Engineering, Harbin Institute of Technology, Nangang District, Harbin 150090, PR China
A R T I C L E I N F O
A B S T R A C T
Article history: Received 20 August 2008 Received in revised form 6 February 2009 Accepted 2 March 2009
The external convective heat transfer coefficient (CHTC) of building horizontal roof is an indispensable parameter for accurately calculating heat transfer through the roof and simulating airflow around the building. A novel method, namely naphthalene sublimation method, was developed for measuring external CHTC and was compared with heat balance method in this study. The comparative field measurements were carried out on the roof of a nine-story building using both methods simultaneously. The measured CHTCs on the roof of building show an approximate linear relation with representative wind velocities. The magnitude of results using the two methods was very close to each other, though the slope of the linear function using the naphthalene sublimation method was a little larger than that using the heat balance method. The difference can be considered as the slow response of heat flux meter used in heat balance method. In addition, the variance of temperature on test specimen’s surfaces was not found to have significant effect on measurement results. ß 2009 Elsevier B.V. All rights reserved.
Keywords: External convective heat transfer coefficient Field measurement Naphthalene sublimation method Heat balance method
1. Introduction A large part of energy consumption of buildings is caused by heat transfer from the external surfaces. This heat transfer consists of two parts: convection and radiation [1]. Convection heat loss is a function of various parameters while radiation heat loss is a function of surface temperature and emissivity. This makes it difficult to get an accurate estimation. In building engineering field, the convective heat transfer coefficient (CHTC) of the external surface of building was once evaluated as a constant number in calculating building envelope load. But an uncertainty of 15% in building surface CHTC can result in uncertainty of 15–20% in heat flux through the envelope [2]. The estimated thermal loads can vary from 20% to 40%, depending on the choice of external CHTC in literature [3]. Additionally, some certain simulation results of heat balance within the urban canyon (in mid-latitudes and summer time) have shown that about 60% of the net radiative heat was balanced by advection of air and 30% of it was stored in the building materials during the midday [4]. Thus the knowledge of convective heat transfer at the external surfaces also allows an accurate estimation of urban heat balance in meteorology field.
* Corresponding author at: School of Municipal & Environmental Engineering, Harbin Institute of Technology, Box 2651, 202 Haihe Road, Nangang District, Harbin 150090, PR China. Tel.: +86 451 8628 2123; fax: +86 451 8628 2123. E-mail address: [email protected] (J. Liu). 0378-7788/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2009.03.005
A large number of researches targeting relationship between wind velocities and CHTCs were conducted in different research fields. One of the earliest experimental studies of external CHTC was that of Jurges, which is still widely quoted by many references [5]. However, the correlations concerning CHTC in various studies seem to be ambiguous. For example, in heat transfer engineering field, a lot of simplified dimensional equations with dimensionless numbers such as Nusselt number, and Reynolds number, were given under various convective heat transfer situations. But there are two limitations in their applications to real buildings. Firstly, most of these correlations are developed based on small-scale experiments such as wind tunnel under relatively simple conditions [6,7]. However, the representative length and velocity in dimensionless numbers cannot be determined easily in real urban situations, due to the complex shape of buildings and complex airflow patterns. Secondly, the external CHTC of building is dependent on many factors such as building surface roughness, wind velocity and wind turbulence, which are difficult to be estimated theoretically. Therefore, in-depth field full-scale measurements are more reliable and needs to be carried out in future. In building engineering field, a number of studies have been carried out to obtain better estimates of the CHTC for building external surfaces in recent years. For example, Clear et al. measured the CHTCs on the horizontal roofs of two commercial buildings, and established correlations of CHTC as functions of surface–air temperature difference, wind velocities, wind direction, roof size and roof roughness [8]. Hagishima and Tanimoto established the correlations of CHTCs with wind velocities through a field measure-
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Nomenclature
English symbols a thermal diffusion coefficient of air (m2/s) Dnaph mass diffusion coefficient of naphthalene in air (m2/s) h CHTC on the external surface of building (W/m2 K) convective mass transfer coefficient (m/s) hm l representative length of the roof (m) n empirical constant atmospheric pressure (Pa) Patm naphthalene saturated vapor pressure on the PV.S surface (Pa) net radiation (W/m2) QR QC sensible convective heat (W/m2) latent convective heat (W/m2) QL conductive heat through the building envelope (W/ QG m2) R gas constant for naphthalene 64.89 (J/(mol K)) external surface temperature of building (K) Ts air temperature near the surface (K) Tair naphthalene surface temperature (K) TW V representative wind velocity (m/s) Dimensionless groups Nu Nusselt number (=hl/l) dimensionless Pr Prandtl number (=n/a) dimensionless Re Reynolds number (=Vl/n) dimensionless Sh Sherwood number (=hml/Dnaph) dimensionless Sc Schmidt number (=n/Dnaph) dimensionless Greek symbols l thermal conductive coefficient (W/(m K)) r density of the air (kg/m3) rV.S naphthalene saturated vapor density on the surface (kg/m3) rV.1 naphthalene vapor density in free stream air (kg/ m3) n kinematical viscosity (m2/s) dm mass loss (kg) dt time interval (s)
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such as solar radiation, long-wave radiation, air temperature, wind speed, roof surface temperature, and conductive thermal flux through the roof need to be measured simultaneously by various measurement instruments. Large error always occurs during the experiment even with high accurate instruments due to the accumulation of small errors. In addition, heat balance method cannot be used easily on building surfaces with complex shapes. On the other hand, in many wind tunnel experiments, heat and mass transfer analogy method was used. For example, Narita carried out heat and mass transfer analogy experiments using wet filter paper in wind tunnel to calculate mass transfer coefficients distributions in urban canyons [16]. Barlow et al. reported this method using naphthalene sublimation instead of water evaporation to calculate convective heat flux in urban canyons [17]. Comparatively, in the heat and mass transfer analogy method, the conductive heat flux and radiative heat flux do not need to be considered, therefore the measurement do not require the complex insulation or conductive heat flux and radiative heat flux. It makes the measurement use less instruments and eliminates the corresponding errors. Additionally, this method is particularly useful in complex geometries. Thus in many research fields, the heat and mass transfer analogy method is considered to be a most developed high-accuracy method [18]. However, up to date, this method is often be used in the scale model experiments under constant airflow and temperature. Few researches have been found under actual outdoor transient conditions. Narita et al. measured the mass transfer rate of a window in the real urban environment using the above-mentioned water evaporation method [19]. They put a piece of wet filter paper on the window and then obtained the CHTCs based on the measured water evaporation rate. The disadvantages of this method are: (1) parts of wet filter paper sometimes became dry during the measurement, so the wet surface area could not be estimated accurately; (2) the accuracy of this method was significantly dependant on the humidity level of the free stream, especially dry condition. Based on the literature survey, the main objectives of this study are: (1) To develop a naphthalene sublimation method which can measure CHTC under real outside conditions on a full-scale building surface, in order to overcome the shortcomings of heat balance method and heat and mass transfer analogy method used in scale model experiments. (2) To carry out full-scale CHTC measurements using naphthalene sublimation method on the horizontal roof of a real building, and validate by a simultaneous measurement using heat balance method. 2. Field measurements using naphthalene sublimation method
ment. In their study, the effect of wind turbulence on CHTCs was estimated simply. The distribution of CHTCs on building roof was also given [9]. Loveday and Taki conducted a full-scale measurement for external CHTCs on a vertical surface of a building with 28 m height, and compared with the values in other literatures and handbooks [10]. Furthermore, a number of similar full-scale measurements of CHTCs were respectively conducted by Ito et al. [11], Sharple [12], Yazdanian and Kelm [13], Zhang et al. [14]. The basic conclusion to be drawn from the above-mentioned review is that significant discrepancies and inconsistencies are found among the measurements even with the same measurement method [15]. Most of the above-mentioned full-scale measurements were conducted using the heat balance method. In this method, convective heat transfer from the building surface to air can be calculated by subtracting conductive heat through the wall from the net radiate heat received by the surface. The detailed description of this method is shown in Appendix A. In this method, a large number of parameters associated to heat transfer,
In heat transfer engineering field, naphthalene sublimation technique is one of the most well developed heat and mass transfer analogy method to measure CHTC with high accuracy [18]. There are two general methods to measure the mass transfer rate: weighing to obtain time-average coefficients and local measurement using a tip gauge. Local measurement can provide detailed information about the spatial distribution of CHTC. However because the real roof of a building is always too large to measure all local CHTCs on it, in this study time-averaged CHTCs were measured by weighing test specimens at multi-points on the building roof. Using the weighing method, a time-averaged convective mass transfer coefficient can be calculated by weighing the test specimens at the beginning and the end of a time interval, which is shown in Eq. (7) in Appendix B. Then the averaged convective mass transfer coefficient can be converted to the averaged CHTC by the heat/mass transfer analogy in Eq. (10) in Appendix B. The test specimen used in measurement was cast with carefulness, as shown in Fig. 1. In this study, the test specimen had the
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Fig. 2. Photograph of the measured building. Fig. 1. Naphthalene test specimen used in field measurements.
sublimating surface of 10.4 cm 10.4 cm. In order to reduce edge mass loss, the test specimens were sealed at the rear and sides. 2.1. Site of the full-scale measurement The field measurements were carried out on a horizontal roof of a nine-storey building in Harbin during daytime periods in July 2007. The building is shown in Fig. 2. The height of the building is 46 m. No more large and tall buildings existed in its immediate vicinity. The plan and the dimensions of the measuring site are shown in Fig. 3. There is a parapet made of iron with 1.25 m height around the edge of roof, and some extrusive concrete square columns are arrayed in matrix, also as shown in Fig. 3. The height of the gutter was 0.4 m. The targeting surface was somewhat rough which was covered with squire tiles. There were also some wind cowls with 0.6 m height arranged on the roof, which can be seen in Fig. 4. The positions of measured CHTC were arranged centrally on the surface, as shown in Fig. 3. 2.2. Measured parameters and instrumentations The measured parameters and instrumentations using the naphthalene sublimation method are listed in Table 1.
By literature investigation, the height of representative velocities were dissimilar significantly, from 0.13 m [9], 0.6 m [9] to 3 m [8] and even 11 m [10]. It is difficult to estimate the thickness of the boundary layer on the roof, because airflow around the building is extremely complicated and erratic. The top of the building consists of separation cavities, reattached flow and vortices [20,21]. In this study, the 3D ultrasonic anemometer used to measure wind velocity and direction (shown in Fig. 4) was mounted on a mast 1.6 m above the roof. The effect of the height of representative wind velocity will be conducted in further study. The measuring point of representative wind velocity was mounted at the position which was close to the measuring point of CHTC, shown in Fig. 3. The data of wind velocities and wind directions were collected at 0.1 s intervals. The semiconductor resistance thermometer used to measure free air temperature was also mounted at the position at 1.6 m height, using a shelter to avoid solar radiation. The naphthalene surface temperatures were measured using the semiconductor resistance thermometers. In order to have the similar absorptivity and emissivity with the naphthalene test specimen surface, the upper surfaces of thermometers were painted by naphthalene, and tied toughly to the centre of naphthalene surfaces, as shown in Fig. 1. The data of air and naphthalene surface temperatures were collected at 30 s intervals.
Fig. 3. The plan of the measuring site.
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Table 1 The measured parameters and corresponding instrumentations used in the naphthalene sublimation method. Parameter
Instrumentation
Accuracy
Wind velocity
3D ultrasonic anemometer
1% rms 0.05 m/s (0–30 m/s) 3% rms (30–40 m/s)
Wind direction
3D ultrasonic anemometer
28 (1–30 m/s) 58 (30–40 m/s)
Air temperature Surface temperature of the test specimen Sublimated naphthalene rate
The semiconductor resistance thermometer The semiconductor resistance thermometer Electronic balance
0.2 8C 0.2 8C 1 mg
Fundamentally, the measuring interval of naphthalene mass flux should not be too large in order to eliminate the uncertainty of wind and temperature turbulence. However, the time interval also should not be too small with the consideration of the accuracy of electronic balance. After preliminary tests, the intervals for measuring mass difference of naphthalene were determined optimally at 5 min. When weighing the naphthalene test speci-
mens, the test specimens were closed carefully to avoid extraneous sublimation losses, and the electronic mass balance used a windbreak set to protect the wind disturbance. At the end of the measurements, all the data were calculated to 5 min averaged values, corresponding to the time of the weighing measurement. The calculation of time-averaged CHTCs by the means of naphthalene sublimation method was shown in Appendix B. The uncertainty analysis of the naphthalene sublimation method was shown in Appendix C2. 3. Validation measurements using heat balance method
Fig. 4. 3D ultrasonic anemometer used in the field measurements.
In order to validate the naphthalene sublimation method developed in this paper, a field measurement using heat balance method was carried out simultaneously on the same experimental site. The latent convective heat of evaporation can be neglected, due to the impervious roof and the successive sunny days. The measuring points of the two methods were quite close, also as shown in Fig. 3. The data of representative wind velocities, wind directions and air temperatures measured in naphthalene sublimation method was also used here. For the experimental set-up of heat balance method in this study, a single test panel was made, which was similar in essence with that described by previous publications [1,9,10], as shown in Fig. 5. The dimensions of the test panel were 1.5 m 1 m. The test panel consisted a glass wooden board, a heat flux meter and a semiconductor resistance thermometer. The heat flux meter was used to measure the conductive heat flux through the wooden board. The thermal electrical resistance was used to measure the surface temperature of the test panel. In order to keep the same emissivity and reflectivity, the outside surface of the wooden board, the outside surface of the heat flux meters and the thermal electrical resistance were all painted in the same color. Additionally, a net radiometer was mounted above the test panel to measure the net radiation received by the test panel.
Fig. 5. The schematic of heat balance method.
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Table 2 The measured parameters and corresponding instrumentations used in the heat balance method. Parameter
Instrumentation
Accuracy
Wind velocity
3D ultrasonic anemometer
1% rms 0.05 m/s (0–30 m/s) 3% rms (30–40 m/s)
Wind direction
3D ultrasonic anemometer
28 (1–30 m/s) 58 (30–40 m/s)
Air temperature Surface temperature of the test panel surface Conductive heat flux through the test panel surface Net radiation received by test panel
The semiconductor resistance thermometer The semiconductor resistance thermometer Heat flux meter Net radiate meter
0.2 8C 0.2 8C 5% 5%
The measured parameters and instrumentations used by the heat balance method were summarized in Table 2. All measured data were collected and averaged in the time interval of 5 min, corresponding to that using naphthalene sublimation method. The calculation of time-averaged CHTCs by the means of heat balance method is shown in Appendix A. The uncertainty analysis of the heat balance method is shown in Appendix C1. 4. Results and discussions Hagishima and Tanimoto found that using the heat balance method, when the temperature difference between test panel and free air were less than 15 8C, lesser convective heat flux would aggravate the accuracy of measurement [9]. In order to avoid this problem, the measured data obtained from these two methods were selected only when temperature differences between test panel and free air were higher than 15 8C. Finally, a total of 110 pairs of values were used for comparison. The relationship between CHTCs and time-averaged wind velocities at the height of 1.6 m V obtained by both the naphthalene sublimation method and heat balance method is shown in Fig. 6. For the case of naphthalene sublimation method, plots can be fitted by the linear regression h = 6.91V + 3.9, with a high correlation coefficient of 0.94. The similar relationship is also reported in other literatures [9,10]. The CHTC values varied from 7.6 to 36.4 W/m2 K on the building roof, when representative wind speed ranged from 0.72 to 4.93 m/s during the measurement period. On the other hand, for the heat balance method, a similar positive linear relationship was also established as h = 6.36V + 4.66. The plots are a little more scattered and the
Fig. 6. Comparison between the results using naphthalene sublimation method and heat balance method.
correlation coefficient became 0.90. The reason for the difference between the two methods will be discussed in detail below. 4.1. The effect of varying surface temperatures using naphthalene sublimation method In order to investigate the effect of varying surface temperature on corresponding saturated vapor pressure on the naphthalene specimen surface, the relationship between CHTCs and V at 1.6 m height was classified by the standard deviation of measured naphthalene surface temperature at 5 min interval. As shown in Fig. 7, CHTCs is insensitive to the different standard deviations of surface temperature, whether less than 1 8C, between 1 and 2 8C, or higher than 2 8C. The conclusion to be drawn is that, an adequate estimate of CHTC will be given under either a lower or higher variance of naphthalene surface temperatures. 4.2. Comparison between results using the two methods From Fig. 6, it can be observed that the linear relationships established using the two different methods are a little dissimilar. The slope of linear equation for the case of naphthalene sublimation method is a little sharper than that for the heat balance method. It can be seen that there is a good agreement between the CHTCs obtained by the two different methods at lower wind velocities, especially when wind velocities ranges from 1 to 2 m/s. However, at high wind velocities, the CHTCs obtained from the naphthalene sublimation method become higher than those from the heat balance method, especially when wind velocities are higher than 2.5 m/s.
Fig. 7. Relationship between CHTCs and standard deviations of temperatures D on the naphthalene surfaces.
J. Shao et al. / Energy and Buildings 41 (2009) 840–847
Fig. 8. The variation over time of CHTCs vs. wind velocities using both the naphthalene sublimation method and heat balance method.
In order to explain this finding, the time variation of the CHTCs vs. wind velocities using the two methods during one certain day is shown in Fig. 8. It is obvious that the measured CHTCs from the heat balance method often did not follow the rapid variation of wind velocities. The reason for this discrepancy cannot be given exactly at present, but can be speculated to the sensitivity of the heat flux meter. The natural wind pattern through the roof is complicated and erratic, which requires sophisticated equipment if accurate results are to be achieved. In this paper, the responding time of the heat flux meter was 30 s, but the outside wind turbulence was always strong and wind velocity might fluctuate rapidly from 0.34 to 5.26 m/s within 30 s according to the measured records. It means that the conductive heat transfer in Eq. (3) might not be estimated precisely under such rapidly varying conditions. In fact, Zhang et al. pointed out the similar slowresponding characteristic in measuring CHTCs on the building external surfaces using the heat balance method [14]. 4.3. Comparison with other studies The comparison between the results of CHTCs vs. V from this study and those from other studies is shown in Fig. 9. The results by present study give good agreement with the results by Cole and Strurrock [22]. The two simple algorithm models developed in EnergyPlus software reflect the difference of surface roughness, which can destroy the viscous inner layer in boundary layer of heat transfer [23]. The CHTC predicted from this study shows an intermediate level between the predicted values from the two models. However, poor agreement is observed between present study and the other four studies. The difference of correlations
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among studies can not be explained exactly, because the influencing factors of CHTCs have no detailed description in a large number of literatures, but differences in the surrounding situation of the individual test building, geometries of the buildings, surface roughness, wind turbulence and wind direction are the most likely reasons. In addition, comparing the two correlations by Aya Hagishima and Tanimoto, it is obvious that measurement conditions such as the height of representative wind speed play an important role in the magnitude of CHTCs [9]. Clear et al. and Emmel et al. considered the wind direction, and have given different results at different wind directions [3,8]. Here, we only give the correlations that gave highest values in their study. Therefore in order to validate the naphthalene sublimation method conceivably, the simultaneous measurement using heat balance method for the same test building under the same measurement conditions in this study is absolutely necessary. 5. Conclusions This study focuses on the development of test set-up of naphthalene sublimation method for measuring CHTCs on the building horizontal roof under outdoor conditions. The findings are summarized as follows. (1) A commonly used correlation of CHTCs vs. V was obtained using naphthalene sublimation method. The correlation was compared with the conventional heat balance method for validation, and the results show good agreement using the two different methods. The differences at higher wind speeds are likely to be the slow response of heat flux meter used in the heat balance method. (2) Variation of naphthalene surface temperature does not have a significant effect on measured CHTCs when using naphthalene sublimation method. (3) The correlation of CHTCs vs. wind speed obtained in this study were compared with other studies. The discrepancy between the studies may be caused by many factors, such as differing building geometries, surface roughness, height of representative wind velocities, wind directions. Therefore for the purpose of validation, the simultaneous measurement using heat balance method for the same test building and under the same measurement conditions in this study is indispensable. Further measurements are recommended to be carried out under differing building geometries and measurement conditions. Acknowledgments This study was supported by the National Natural Science Foundation of China (Grant number 40505025) and National key Technologies R&D Program in the 11th Five-Year Plan of China (Grant number 2006BAJ01A02-4). The authors would like to thank Prof. Aya Hagishima and Prof. Jun Tanimoto for their helpful advice on this study.
Appendix A. Heat balance method In the heat balance method, the heat balance of the external surface of the building is given by [24]: QR ¼ QC þ QL þ QG
Fig. 9. CHTCs vs. wind velocities: comparison between this study and other studies.
(1)
where QR is the net radiation, QC is the sensible convective heat transfer, QL is the latent heat transfer, which can be neglected for the case of impervious artificial surface like building envelope in
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sunny experimental days. QG is the conductive heat through the envelope. QC can be expressed using h as Q C ¼ hðT s T air Þ
(2)
where h is CHTC on the external building surface, Ts is the temperature on the external surfaces of building, Tair is the air temperature near the surface. In sunny experimental day situation, h can be given as h¼
QR QG T s T air
Nu ¼ cRem Pr n
(4)
Assuming heat and mass transfer analogy, mass transfer results can also be expressed in the same form: Sh ¼ cRe Sc
n
(5)
where Nusselt number is defined as Nu = hl/l, Sherwood number is defined as Sh = hml/Dnaph, Reynolds number is defined as Re = ul/n, Prandtl number is defined as Pr = n/a, and Schmidt number is defined as Sc = n/Dnaph. The parameters in the definitions of the above dimensionless numbers, h, hm, l, Dnaph, n, a, u and l are heat transfer coefficient, mass transfer coefficient, thermal conductive coefficient, mass diffusion coefficient, kinematical viscosity, thermal diffusion coefficient, representative wind velocity and representative length of the roof, respectively. The Dnaph in Schmidt number can be defined as Dnaph ¼ 0:0681
Combining Eqs. (4)–(9), the CHTC on the outside surface of buildings can be given as
(3)
Appendix B. Naphthalene sublimation method In naphthalene sublimation method described in this paper, mass transfer results of naphthalene sublimation process can also be applied to heat transfer process as well, because of the similarity of the governing equation between the two processes. Basic principle of the analogy can be found in many heat and mass transfer books. In the research field of heat and mass transfer, fluid flow and convective heat transfer are often expressed in terms of the empirical corrections between the dimensionless Nusselt, Reynolds and Prandtl numbers [18]:
m
where the exponent n is a constant determined from the empirical results and has been found in the range of 1/3 to 0.4 depending on the flow conditions. In this paper, n is assumed as 0.4 for turbulent condition of flow around building. The detailed discussions for n are presented by Eckert and Goldstein [26], and Goldstein and Cho [18].
1:93 T air 101; 325 P atm 298:13
(6)
where Tair is the air temperature, Patm is the pressure of the air.
h ¼ 5:01la1:6 R
C.1. Uncertainly analysis of the heat balance method The uncertainty of the convective heat flux (appeared in Appendix A) QC = QR QG is evaluated from the following expression [27]:
DQ C QC
" ¼
where dm is the mass difference of naphthalene test specimen at dt time interval, rV.S is the saturated vapor density on test specimens surface, rV.1 is the vapor density of naphthalene in free stream air. rV.S can be determined from the ideal gas law, and rV.1 can be assumed to be 0.
rV:S ¼
PV:S RT W
#1=2 DQ R 2 DQ G 2 QR QG þ QR QG QR QR QG QG
(11)
According to the accuracies of instruments in Table 2, the lowest values of heat fluxes, the maximum ratio between radiate heat flux and convective heat flux QR/(QR QG) and ratio between conductive heat flux and convective heat flux QG/(QR QG) during the field measurement, the uncertainty of convective heat flux is about 9.55%. Similarly, the uncertainty of temperature difference (Ts Tair) can be evaluated from the following expression:
DðT s T air Þ T s T air
" ¼
2 #1=2 DT s 2 Ts T air DT air þ T s T air T s T s T air T air
(12)
According to the extreme values of temperature in Eq. (12) during the field measurement and the accuracy of the semiconductor resistance thermometers, the uncertainty of the temperature difference is about 1.5%. Finally, the uncertainty of the convective heat transfer coefficient h can be evaluated from the following expression:
Dh (7)
(10)
Appendix C. Uncertainly analysis
The hm in Sherwood number is defined by [18]:
dm=dt hm ¼ rV:S rV:1
0:6 1:158 T W dm P atm T air P V:S dt 101; 325 298:13
h
¼
" 2 #1=2 DðQ R Q G Þ 2 þ DðT s T a Þ Q Q T T s a R G
(13)
As the uncertainty of the two terms in brackets are estimated, the overall uncertainty of the convective heat transfer coefficient is about 9.7%. C.2. Uncertainly analysis of the naphthalene sublimation method
(8)
where TW is the surface temperature of test specimen. PV.S is the saturated vapor pressure on the naphthalene test specimen surface. It is often expressed as the function of TW. The correlation proposed by Ambrose is widely used [25]. Then comparing Eqs. (4) and (5), the following form is obtained: n Nu Pr ¼ (9) Sh Sc
Considering the expression of h given by Eq. (10), the uncertainty of the convective heat transfer coefficient is evaluated from: " 2 2 DT W 2 Dh þ Ddm þ 1:158DT air ¼ h TW dm T air #1=2 DP V:S 2 Ddt 2 þ þ PV:S dt
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The correlation used in this measurement for calculating the saturated vapor pressure on the naphthalene test specimen surface PV.S gave an uncertainty of 3.77% [23]. According to the accuracies of instruments, the minimum values of the measured variables in Eq. (14) during field measurement, the overall uncertainty of the convective heat transfer coefficient is about 4.5%. It can be concluded that the naphthalene sublimation method has smaller uncertainty than the heat balance method in this study, due to the additional conduction and radiation errors in the conductive heat flux meter and radiative heat flux meter. References [1] Y. Liu, D.J. Harris, Full-scale measurements of convective heat transfer coefficient on external surface of a low-rise building in sheltered conditions, Building and Environment 42 (2007) 2718–2736. [2] N.E. Wijeysundera, S.K. Chou, S.E.G. Jayamaha, Heat flow through walls under transient rain conditions, Journal of Insulation and Building Envelopes 17 (1993) 118–141. [3] M.G. Emmel, M.O. Abadie, N. Mendes, New external convective heat transfer coefficient correlations for isolated low-rise buildings, Energy and Buildings 39 (2007) 335–342. [4] M. Nunez, T.R. Oke, The energy balance of an urban canyon, Journal of Applied Meteorology 16 (1977) 11–19. [5] H. Kondo, Y. Genchi, Y. Kikegawa, et al., Development of a multi-layer urban canopy model for the analysis of energy consumption in a big city: structure of the urban canopy model and it’s performance, Boundary-Layer Meteorology 116 (2005) 395–421. [6] H.A. Johnson, M.W. Rubesin, Aerodynamic heating and convective heat transfersummary of literature survey, Transactions of the ASME 71 (5) (1949) 447–456. [7] W.H. Mc Adams, Heat Transfer, 3rd edition, McGraw-Hill, New York, 1954. [8] R.D. Clear, L. Gartland, F.C. Winkelmann, An empirical correlation for outside convective air-film coefficient for horizontal roofs, Energy and Buildings 35 (2003) 796–811. [9] A. Higishima, J. Tanimoto, Field measurements for estimating the convective heat transfer coefficient at building surface, Buildings and Environment 38 (2003) 873–881.
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[10] D.L. Loveday, A.H. Taki, Convective heat transfer coefficients at a plane surface on a full scale building facade, International Journal of Heat and Mass Transfer 39 (1996) 1729–1742. [11] N. Ito, K. Kimura, J. Oka, Full-scale measurements of convective energy losses from exterior building surface, ASHRAE Transactions 78 (1972) 184–191. [12] S. Sharple, Full-scale measurements of convective energy losses from exterior building surface, Building and Environment 19 (1984) 31–39. [13] M. Yazdanian, J.H. Kelm, Measurement of the exterior convective film coefficient for windows in low-rise building, ASHRAE Transactions 100 (1994) 1087–1096. [14] L. Zhang, N. Zhang, F. Zhao, et al., A genetic-algorithm-based experimental technique for determining heat transfer coefficient of exterior wall surface, Applied Thermal Engineering 24 (2004) 339–349. [15] J.A. Palyvos, A survey of wind convection coefficient correlations for building envelope energy systems’ modeling, Applied Thermal Engineering 28 (2008) 801– 808. [16] K. Narita, Experimental study of transfer velocity on urban surface with water evaporation method, Boundary-Layer Meteorology 122 (2007) 293–320. [17] J.F. Barlow, I.N. Harman, S.E. Belcher, Scalar flux from urban street canyon. Part I. Laboratory simulation, Boundary-Layer Meteorology 113 (2004) 369–385. [18] R.J. Goldstein, H.H. Cho, A review of mass transfer measurement using naphthalene sublimation, Experimental Thermal and Fluid Science 10 (1995) 416–434. [19] K. Narita, Y. Nunomura, A. Ogasa, Real scale measurement of convective mass transfer coefficient at window in nature wind, Journal of Architectural and Planning Environmental Engineering 491 (1997) 49–56. [20] S. Murakami, Current status and future trends in computational wind engineering, Journal of Wind Engineering and Industrial Aerodynamics 67–68 (1997) 3– 34. [21] S. Murakami, Overview of turbulence models application in CWE-1997, Journal of Wind Engineering and Industrial Aerodynamics 67–68 (1998) 1–24. [22] R.J. Cole, N.S. Sturrock, The convective heat exchange at the external surface of buildings, Building and Environment 12 (1977) 207–214. [23] http://apps1.eere.energy.gov/buildings/energyplus/pdfs/engineeringreference. pdf. [24] A. Hagishima, J. Tanimoto, K. Narita, Intercomparisons of experimental convective heat transfer coefficients and mass transfer coefficient of urban surfaces, Boundary-Layer Meteorology 117 (2005) 551–576. [25] D. Ambrose, I.J. Lawrenson, C.H.S. Sparke, The vapor pressure of naphthalene, Journal of Chemical Thermodynamics 7 (1975) 1173–1176. [26] E.R.G. Eckert, R.J. Goldstein, Measurements In Heat Transfer, 2nd edition, McGraw-Hill Inc., New York, 1976. [27] J.P. Holman, Experimental Method for Engineers, 2nd edition, McGraw-Hill, New York, 1978.
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Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
A novel method for full-scale measurement of the external convective heat transfer coefficient for building horizontal roof Jiantao Shao, Jing Liu *, Jianing Zhao, Wenwu Zhang, Dexing Sun, Zhipeng Fu School of Municipal & Environmental Engineering, Harbin Institute of Technology, Nangang District, Harbin 150090, PR China
A R T I C L E I N F O
A B S T R A C T
Article history: Received 20 August 2008 Received in revised form 6 February 2009 Accepted 2 March 2009
The external convective heat transfer coefficient (CHTC) of building horizontal roof is an indispensable parameter for accurately calculating heat transfer through the roof and simulating airflow around the building. A novel method, namely naphthalene sublimation method, was developed for measuring external CHTC and was compared with heat balance method in this study. The comparative field measurements were carried out on the roof of a nine-story building using both methods simultaneously. The measured CHTCs on the roof of building show an approximate linear relation with representative wind velocities. The magnitude of results using the two methods was very close to each other, though the slope of the linear function using the naphthalene sublimation method was a little larger than that using the heat balance method. The difference can be considered as the slow response of heat flux meter used in heat balance method. In addition, the variance of temperature on test specimen’s surfaces was not found to have significant effect on measurement results. ß 2009 Elsevier B.V. All rights reserved.
Keywords: External convective heat transfer coefficient Field measurement Naphthalene sublimation method Heat balance method
1. Introduction A large part of energy consumption of buildings is caused by heat transfer from the external surfaces. This heat transfer consists of two parts: convection and radiation [1]. Convection heat loss is a function of various parameters while radiation heat loss is a function of surface temperature and emissivity. This makes it difficult to get an accurate estimation. In building engineering field, the convective heat transfer coefficient (CHTC) of the external surface of building was once evaluated as a constant number in calculating building envelope load. But an uncertainty of 15% in building surface CHTC can result in uncertainty of 15–20% in heat flux through the envelope [2]. The estimated thermal loads can vary from 20% to 40%, depending on the choice of external CHTC in literature [3]. Additionally, some certain simulation results of heat balance within the urban canyon (in mid-latitudes and summer time) have shown that about 60% of the net radiative heat was balanced by advection of air and 30% of it was stored in the building materials during the midday [4]. Thus the knowledge of convective heat transfer at the external surfaces also allows an accurate estimation of urban heat balance in meteorology field.
* Corresponding author at: School of Municipal & Environmental Engineering, Harbin Institute of Technology, Box 2651, 202 Haihe Road, Nangang District, Harbin 150090, PR China. Tel.: +86 451 8628 2123; fax: +86 451 8628 2123. E-mail address: [email protected] (J. Liu). 0378-7788/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2009.03.005
A large number of researches targeting relationship between wind velocities and CHTCs were conducted in different research fields. One of the earliest experimental studies of external CHTC was that of Jurges, which is still widely quoted by many references [5]. However, the correlations concerning CHTC in various studies seem to be ambiguous. For example, in heat transfer engineering field, a lot of simplified dimensional equations with dimensionless numbers such as Nusselt number, and Reynolds number, were given under various convective heat transfer situations. But there are two limitations in their applications to real buildings. Firstly, most of these correlations are developed based on small-scale experiments such as wind tunnel under relatively simple conditions [6,7]. However, the representative length and velocity in dimensionless numbers cannot be determined easily in real urban situations, due to the complex shape of buildings and complex airflow patterns. Secondly, the external CHTC of building is dependent on many factors such as building surface roughness, wind velocity and wind turbulence, which are difficult to be estimated theoretically. Therefore, in-depth field full-scale measurements are more reliable and needs to be carried out in future. In building engineering field, a number of studies have been carried out to obtain better estimates of the CHTC for building external surfaces in recent years. For example, Clear et al. measured the CHTCs on the horizontal roofs of two commercial buildings, and established correlations of CHTC as functions of surface–air temperature difference, wind velocities, wind direction, roof size and roof roughness [8]. Hagishima and Tanimoto established the correlations of CHTCs with wind velocities through a field measure-
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Nomenclature
English symbols a thermal diffusion coefficient of air (m2/s) Dnaph mass diffusion coefficient of naphthalene in air (m2/s) h CHTC on the external surface of building (W/m2 K) convective mass transfer coefficient (m/s) hm l representative length of the roof (m) n empirical constant atmospheric pressure (Pa) Patm naphthalene saturated vapor pressure on the PV.S surface (Pa) net radiation (W/m2) QR QC sensible convective heat (W/m2) latent convective heat (W/m2) QL conductive heat through the building envelope (W/ QG m2) R gas constant for naphthalene 64.89 (J/(mol K)) external surface temperature of building (K) Ts air temperature near the surface (K) Tair naphthalene surface temperature (K) TW V representative wind velocity (m/s) Dimensionless groups Nu Nusselt number (=hl/l) dimensionless Pr Prandtl number (=n/a) dimensionless Re Reynolds number (=Vl/n) dimensionless Sh Sherwood number (=hml/Dnaph) dimensionless Sc Schmidt number (=n/Dnaph) dimensionless Greek symbols l thermal conductive coefficient (W/(m K)) r density of the air (kg/m3) rV.S naphthalene saturated vapor density on the surface (kg/m3) rV.1 naphthalene vapor density in free stream air (kg/ m3) n kinematical viscosity (m2/s) dm mass loss (kg) dt time interval (s)
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such as solar radiation, long-wave radiation, air temperature, wind speed, roof surface temperature, and conductive thermal flux through the roof need to be measured simultaneously by various measurement instruments. Large error always occurs during the experiment even with high accurate instruments due to the accumulation of small errors. In addition, heat balance method cannot be used easily on building surfaces with complex shapes. On the other hand, in many wind tunnel experiments, heat and mass transfer analogy method was used. For example, Narita carried out heat and mass transfer analogy experiments using wet filter paper in wind tunnel to calculate mass transfer coefficients distributions in urban canyons [16]. Barlow et al. reported this method using naphthalene sublimation instead of water evaporation to calculate convective heat flux in urban canyons [17]. Comparatively, in the heat and mass transfer analogy method, the conductive heat flux and radiative heat flux do not need to be considered, therefore the measurement do not require the complex insulation or conductive heat flux and radiative heat flux. It makes the measurement use less instruments and eliminates the corresponding errors. Additionally, this method is particularly useful in complex geometries. Thus in many research fields, the heat and mass transfer analogy method is considered to be a most developed high-accuracy method [18]. However, up to date, this method is often be used in the scale model experiments under constant airflow and temperature. Few researches have been found under actual outdoor transient conditions. Narita et al. measured the mass transfer rate of a window in the real urban environment using the above-mentioned water evaporation method [19]. They put a piece of wet filter paper on the window and then obtained the CHTCs based on the measured water evaporation rate. The disadvantages of this method are: (1) parts of wet filter paper sometimes became dry during the measurement, so the wet surface area could not be estimated accurately; (2) the accuracy of this method was significantly dependant on the humidity level of the free stream, especially dry condition. Based on the literature survey, the main objectives of this study are: (1) To develop a naphthalene sublimation method which can measure CHTC under real outside conditions on a full-scale building surface, in order to overcome the shortcomings of heat balance method and heat and mass transfer analogy method used in scale model experiments. (2) To carry out full-scale CHTC measurements using naphthalene sublimation method on the horizontal roof of a real building, and validate by a simultaneous measurement using heat balance method. 2. Field measurements using naphthalene sublimation method
ment. In their study, the effect of wind turbulence on CHTCs was estimated simply. The distribution of CHTCs on building roof was also given [9]. Loveday and Taki conducted a full-scale measurement for external CHTCs on a vertical surface of a building with 28 m height, and compared with the values in other literatures and handbooks [10]. Furthermore, a number of similar full-scale measurements of CHTCs were respectively conducted by Ito et al. [11], Sharple [12], Yazdanian and Kelm [13], Zhang et al. [14]. The basic conclusion to be drawn from the above-mentioned review is that significant discrepancies and inconsistencies are found among the measurements even with the same measurement method [15]. Most of the above-mentioned full-scale measurements were conducted using the heat balance method. In this method, convective heat transfer from the building surface to air can be calculated by subtracting conductive heat through the wall from the net radiate heat received by the surface. The detailed description of this method is shown in Appendix A. In this method, a large number of parameters associated to heat transfer,
In heat transfer engineering field, naphthalene sublimation technique is one of the most well developed heat and mass transfer analogy method to measure CHTC with high accuracy [18]. There are two general methods to measure the mass transfer rate: weighing to obtain time-average coefficients and local measurement using a tip gauge. Local measurement can provide detailed information about the spatial distribution of CHTC. However because the real roof of a building is always too large to measure all local CHTCs on it, in this study time-averaged CHTCs were measured by weighing test specimens at multi-points on the building roof. Using the weighing method, a time-averaged convective mass transfer coefficient can be calculated by weighing the test specimens at the beginning and the end of a time interval, which is shown in Eq. (7) in Appendix B. Then the averaged convective mass transfer coefficient can be converted to the averaged CHTC by the heat/mass transfer analogy in Eq. (10) in Appendix B. The test specimen used in measurement was cast with carefulness, as shown in Fig. 1. In this study, the test specimen had the
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Fig. 2. Photograph of the measured building. Fig. 1. Naphthalene test specimen used in field measurements.
sublimating surface of 10.4 cm 10.4 cm. In order to reduce edge mass loss, the test specimens were sealed at the rear and sides. 2.1. Site of the full-scale measurement The field measurements were carried out on a horizontal roof of a nine-storey building in Harbin during daytime periods in July 2007. The building is shown in Fig. 2. The height of the building is 46 m. No more large and tall buildings existed in its immediate vicinity. The plan and the dimensions of the measuring site are shown in Fig. 3. There is a parapet made of iron with 1.25 m height around the edge of roof, and some extrusive concrete square columns are arrayed in matrix, also as shown in Fig. 3. The height of the gutter was 0.4 m. The targeting surface was somewhat rough which was covered with squire tiles. There were also some wind cowls with 0.6 m height arranged on the roof, which can be seen in Fig. 4. The positions of measured CHTC were arranged centrally on the surface, as shown in Fig. 3. 2.2. Measured parameters and instrumentations The measured parameters and instrumentations using the naphthalene sublimation method are listed in Table 1.
By literature investigation, the height of representative velocities were dissimilar significantly, from 0.13 m [9], 0.6 m [9] to 3 m [8] and even 11 m [10]. It is difficult to estimate the thickness of the boundary layer on the roof, because airflow around the building is extremely complicated and erratic. The top of the building consists of separation cavities, reattached flow and vortices [20,21]. In this study, the 3D ultrasonic anemometer used to measure wind velocity and direction (shown in Fig. 4) was mounted on a mast 1.6 m above the roof. The effect of the height of representative wind velocity will be conducted in further study. The measuring point of representative wind velocity was mounted at the position which was close to the measuring point of CHTC, shown in Fig. 3. The data of wind velocities and wind directions were collected at 0.1 s intervals. The semiconductor resistance thermometer used to measure free air temperature was also mounted at the position at 1.6 m height, using a shelter to avoid solar radiation. The naphthalene surface temperatures were measured using the semiconductor resistance thermometers. In order to have the similar absorptivity and emissivity with the naphthalene test specimen surface, the upper surfaces of thermometers were painted by naphthalene, and tied toughly to the centre of naphthalene surfaces, as shown in Fig. 1. The data of air and naphthalene surface temperatures were collected at 30 s intervals.
Fig. 3. The plan of the measuring site.
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Table 1 The measured parameters and corresponding instrumentations used in the naphthalene sublimation method. Parameter
Instrumentation
Accuracy
Wind velocity
3D ultrasonic anemometer
1% rms 0.05 m/s (0–30 m/s) 3% rms (30–40 m/s)
Wind direction
3D ultrasonic anemometer
28 (1–30 m/s) 58 (30–40 m/s)
Air temperature Surface temperature of the test specimen Sublimated naphthalene rate
The semiconductor resistance thermometer The semiconductor resistance thermometer Electronic balance
0.2 8C 0.2 8C 1 mg
Fundamentally, the measuring interval of naphthalene mass flux should not be too large in order to eliminate the uncertainty of wind and temperature turbulence. However, the time interval also should not be too small with the consideration of the accuracy of electronic balance. After preliminary tests, the intervals for measuring mass difference of naphthalene were determined optimally at 5 min. When weighing the naphthalene test speci-
mens, the test specimens were closed carefully to avoid extraneous sublimation losses, and the electronic mass balance used a windbreak set to protect the wind disturbance. At the end of the measurements, all the data were calculated to 5 min averaged values, corresponding to the time of the weighing measurement. The calculation of time-averaged CHTCs by the means of naphthalene sublimation method was shown in Appendix B. The uncertainty analysis of the naphthalene sublimation method was shown in Appendix C2. 3. Validation measurements using heat balance method
Fig. 4. 3D ultrasonic anemometer used in the field measurements.
In order to validate the naphthalene sublimation method developed in this paper, a field measurement using heat balance method was carried out simultaneously on the same experimental site. The latent convective heat of evaporation can be neglected, due to the impervious roof and the successive sunny days. The measuring points of the two methods were quite close, also as shown in Fig. 3. The data of representative wind velocities, wind directions and air temperatures measured in naphthalene sublimation method was also used here. For the experimental set-up of heat balance method in this study, a single test panel was made, which was similar in essence with that described by previous publications [1,9,10], as shown in Fig. 5. The dimensions of the test panel were 1.5 m 1 m. The test panel consisted a glass wooden board, a heat flux meter and a semiconductor resistance thermometer. The heat flux meter was used to measure the conductive heat flux through the wooden board. The thermal electrical resistance was used to measure the surface temperature of the test panel. In order to keep the same emissivity and reflectivity, the outside surface of the wooden board, the outside surface of the heat flux meters and the thermal electrical resistance were all painted in the same color. Additionally, a net radiometer was mounted above the test panel to measure the net radiation received by the test panel.
Fig. 5. The schematic of heat balance method.
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Table 2 The measured parameters and corresponding instrumentations used in the heat balance method. Parameter
Instrumentation
Accuracy
Wind velocity
3D ultrasonic anemometer
1% rms 0.05 m/s (0–30 m/s) 3% rms (30–40 m/s)
Wind direction
3D ultrasonic anemometer
28 (1–30 m/s) 58 (30–40 m/s)
Air temperature Surface temperature of the test panel surface Conductive heat flux through the test panel surface Net radiation received by test panel
The semiconductor resistance thermometer The semiconductor resistance thermometer Heat flux meter Net radiate meter
0.2 8C 0.2 8C 5% 5%
The measured parameters and instrumentations used by the heat balance method were summarized in Table 2. All measured data were collected and averaged in the time interval of 5 min, corresponding to that using naphthalene sublimation method. The calculation of time-averaged CHTCs by the means of heat balance method is shown in Appendix A. The uncertainty analysis of the heat balance method is shown in Appendix C1. 4. Results and discussions Hagishima and Tanimoto found that using the heat balance method, when the temperature difference between test panel and free air were less than 15 8C, lesser convective heat flux would aggravate the accuracy of measurement [9]. In order to avoid this problem, the measured data obtained from these two methods were selected only when temperature differences between test panel and free air were higher than 15 8C. Finally, a total of 110 pairs of values were used for comparison. The relationship between CHTCs and time-averaged wind velocities at the height of 1.6 m V obtained by both the naphthalene sublimation method and heat balance method is shown in Fig. 6. For the case of naphthalene sublimation method, plots can be fitted by the linear regression h = 6.91V + 3.9, with a high correlation coefficient of 0.94. The similar relationship is also reported in other literatures [9,10]. The CHTC values varied from 7.6 to 36.4 W/m2 K on the building roof, when representative wind speed ranged from 0.72 to 4.93 m/s during the measurement period. On the other hand, for the heat balance method, a similar positive linear relationship was also established as h = 6.36V + 4.66. The plots are a little more scattered and the
Fig. 6. Comparison between the results using naphthalene sublimation method and heat balance method.
correlation coefficient became 0.90. The reason for the difference between the two methods will be discussed in detail below. 4.1. The effect of varying surface temperatures using naphthalene sublimation method In order to investigate the effect of varying surface temperature on corresponding saturated vapor pressure on the naphthalene specimen surface, the relationship between CHTCs and V at 1.6 m height was classified by the standard deviation of measured naphthalene surface temperature at 5 min interval. As shown in Fig. 7, CHTCs is insensitive to the different standard deviations of surface temperature, whether less than 1 8C, between 1 and 2 8C, or higher than 2 8C. The conclusion to be drawn is that, an adequate estimate of CHTC will be given under either a lower or higher variance of naphthalene surface temperatures. 4.2. Comparison between results using the two methods From Fig. 6, it can be observed that the linear relationships established using the two different methods are a little dissimilar. The slope of linear equation for the case of naphthalene sublimation method is a little sharper than that for the heat balance method. It can be seen that there is a good agreement between the CHTCs obtained by the two different methods at lower wind velocities, especially when wind velocities ranges from 1 to 2 m/s. However, at high wind velocities, the CHTCs obtained from the naphthalene sublimation method become higher than those from the heat balance method, especially when wind velocities are higher than 2.5 m/s.
Fig. 7. Relationship between CHTCs and standard deviations of temperatures D on the naphthalene surfaces.
J. Shao et al. / Energy and Buildings 41 (2009) 840–847
Fig. 8. The variation over time of CHTCs vs. wind velocities using both the naphthalene sublimation method and heat balance method.
In order to explain this finding, the time variation of the CHTCs vs. wind velocities using the two methods during one certain day is shown in Fig. 8. It is obvious that the measured CHTCs from the heat balance method often did not follow the rapid variation of wind velocities. The reason for this discrepancy cannot be given exactly at present, but can be speculated to the sensitivity of the heat flux meter. The natural wind pattern through the roof is complicated and erratic, which requires sophisticated equipment if accurate results are to be achieved. In this paper, the responding time of the heat flux meter was 30 s, but the outside wind turbulence was always strong and wind velocity might fluctuate rapidly from 0.34 to 5.26 m/s within 30 s according to the measured records. It means that the conductive heat transfer in Eq. (3) might not be estimated precisely under such rapidly varying conditions. In fact, Zhang et al. pointed out the similar slowresponding characteristic in measuring CHTCs on the building external surfaces using the heat balance method [14]. 4.3. Comparison with other studies The comparison between the results of CHTCs vs. V from this study and those from other studies is shown in Fig. 9. The results by present study give good agreement with the results by Cole and Strurrock [22]. The two simple algorithm models developed in EnergyPlus software reflect the difference of surface roughness, which can destroy the viscous inner layer in boundary layer of heat transfer [23]. The CHTC predicted from this study shows an intermediate level between the predicted values from the two models. However, poor agreement is observed between present study and the other four studies. The difference of correlations
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among studies can not be explained exactly, because the influencing factors of CHTCs have no detailed description in a large number of literatures, but differences in the surrounding situation of the individual test building, geometries of the buildings, surface roughness, wind turbulence and wind direction are the most likely reasons. In addition, comparing the two correlations by Aya Hagishima and Tanimoto, it is obvious that measurement conditions such as the height of representative wind speed play an important role in the magnitude of CHTCs [9]. Clear et al. and Emmel et al. considered the wind direction, and have given different results at different wind directions [3,8]. Here, we only give the correlations that gave highest values in their study. Therefore in order to validate the naphthalene sublimation method conceivably, the simultaneous measurement using heat balance method for the same test building under the same measurement conditions in this study is absolutely necessary. 5. Conclusions This study focuses on the development of test set-up of naphthalene sublimation method for measuring CHTCs on the building horizontal roof under outdoor conditions. The findings are summarized as follows. (1) A commonly used correlation of CHTCs vs. V was obtained using naphthalene sublimation method. The correlation was compared with the conventional heat balance method for validation, and the results show good agreement using the two different methods. The differences at higher wind speeds are likely to be the slow response of heat flux meter used in the heat balance method. (2) Variation of naphthalene surface temperature does not have a significant effect on measured CHTCs when using naphthalene sublimation method. (3) The correlation of CHTCs vs. wind speed obtained in this study were compared with other studies. The discrepancy between the studies may be caused by many factors, such as differing building geometries, surface roughness, height of representative wind velocities, wind directions. Therefore for the purpose of validation, the simultaneous measurement using heat balance method for the same test building and under the same measurement conditions in this study is indispensable. Further measurements are recommended to be carried out under differing building geometries and measurement conditions. Acknowledgments This study was supported by the National Natural Science Foundation of China (Grant number 40505025) and National key Technologies R&D Program in the 11th Five-Year Plan of China (Grant number 2006BAJ01A02-4). The authors would like to thank Prof. Aya Hagishima and Prof. Jun Tanimoto for their helpful advice on this study.
Appendix A. Heat balance method In the heat balance method, the heat balance of the external surface of the building is given by [24]: QR ¼ QC þ QL þ QG
Fig. 9. CHTCs vs. wind velocities: comparison between this study and other studies.
(1)
where QR is the net radiation, QC is the sensible convective heat transfer, QL is the latent heat transfer, which can be neglected for the case of impervious artificial surface like building envelope in
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sunny experimental days. QG is the conductive heat through the envelope. QC can be expressed using h as Q C ¼ hðT s T air Þ
(2)
where h is CHTC on the external building surface, Ts is the temperature on the external surfaces of building, Tair is the air temperature near the surface. In sunny experimental day situation, h can be given as h¼
QR QG T s T air
Nu ¼ cRem Pr n
(4)
Assuming heat and mass transfer analogy, mass transfer results can also be expressed in the same form: Sh ¼ cRe Sc
n
(5)
where Nusselt number is defined as Nu = hl/l, Sherwood number is defined as Sh = hml/Dnaph, Reynolds number is defined as Re = ul/n, Prandtl number is defined as Pr = n/a, and Schmidt number is defined as Sc = n/Dnaph. The parameters in the definitions of the above dimensionless numbers, h, hm, l, Dnaph, n, a, u and l are heat transfer coefficient, mass transfer coefficient, thermal conductive coefficient, mass diffusion coefficient, kinematical viscosity, thermal diffusion coefficient, representative wind velocity and representative length of the roof, respectively. The Dnaph in Schmidt number can be defined as Dnaph ¼ 0:0681
Combining Eqs. (4)–(9), the CHTC on the outside surface of buildings can be given as
(3)
Appendix B. Naphthalene sublimation method In naphthalene sublimation method described in this paper, mass transfer results of naphthalene sublimation process can also be applied to heat transfer process as well, because of the similarity of the governing equation between the two processes. Basic principle of the analogy can be found in many heat and mass transfer books. In the research field of heat and mass transfer, fluid flow and convective heat transfer are often expressed in terms of the empirical corrections between the dimensionless Nusselt, Reynolds and Prandtl numbers [18]:
m
where the exponent n is a constant determined from the empirical results and has been found in the range of 1/3 to 0.4 depending on the flow conditions. In this paper, n is assumed as 0.4 for turbulent condition of flow around building. The detailed discussions for n are presented by Eckert and Goldstein [26], and Goldstein and Cho [18].
1:93 T air 101; 325 P atm 298:13
(6)
where Tair is the air temperature, Patm is the pressure of the air.
h ¼ 5:01la1:6 R
C.1. Uncertainly analysis of the heat balance method The uncertainty of the convective heat flux (appeared in Appendix A) QC = QR QG is evaluated from the following expression [27]:
DQ C QC
" ¼
where dm is the mass difference of naphthalene test specimen at dt time interval, rV.S is the saturated vapor density on test specimens surface, rV.1 is the vapor density of naphthalene in free stream air. rV.S can be determined from the ideal gas law, and rV.1 can be assumed to be 0.
rV:S ¼
PV:S RT W
#1=2 DQ R 2 DQ G 2 QR QG þ QR QG QR QR QG QG
(11)
According to the accuracies of instruments in Table 2, the lowest values of heat fluxes, the maximum ratio between radiate heat flux and convective heat flux QR/(QR QG) and ratio between conductive heat flux and convective heat flux QG/(QR QG) during the field measurement, the uncertainty of convective heat flux is about 9.55%. Similarly, the uncertainty of temperature difference (Ts Tair) can be evaluated from the following expression:
DðT s T air Þ T s T air
" ¼
2 #1=2 DT s 2 Ts T air DT air þ T s T air T s T s T air T air
(12)
According to the extreme values of temperature in Eq. (12) during the field measurement and the accuracy of the semiconductor resistance thermometers, the uncertainty of the temperature difference is about 1.5%. Finally, the uncertainty of the convective heat transfer coefficient h can be evaluated from the following expression:
Dh (7)
(10)
Appendix C. Uncertainly analysis
The hm in Sherwood number is defined by [18]:
dm=dt hm ¼ rV:S rV:1
0:6 1:158 T W dm P atm T air P V:S dt 101; 325 298:13
h
¼
" 2 #1=2 DðQ R Q G Þ 2 þ DðT s T a Þ Q Q T T s a R G
(13)
As the uncertainty of the two terms in brackets are estimated, the overall uncertainty of the convective heat transfer coefficient is about 9.7%. C.2. Uncertainly analysis of the naphthalene sublimation method
(8)
where TW is the surface temperature of test specimen. PV.S is the saturated vapor pressure on the naphthalene test specimen surface. It is often expressed as the function of TW. The correlation proposed by Ambrose is widely used [25]. Then comparing Eqs. (4) and (5), the following form is obtained: n Nu Pr ¼ (9) Sh Sc
Considering the expression of h given by Eq. (10), the uncertainty of the convective heat transfer coefficient is evaluated from: " 2 2 DT W 2 Dh þ Ddm þ 1:158DT air ¼ h TW dm T air #1=2 DP V:S 2 Ddt 2 þ þ PV:S dt
J. Shao et al. / Energy and Buildings 41 (2009) 840–847
The correlation used in this measurement for calculating the saturated vapor pressure on the naphthalene test specimen surface PV.S gave an uncertainty of 3.77% [23]. According to the accuracies of instruments, the minimum values of the measured variables in Eq. (14) during field measurement, the overall uncertainty of the convective heat transfer coefficient is about 4.5%. It can be concluded that the naphthalene sublimation method has smaller uncertainty than the heat balance method in this study, due to the additional conduction and radiation errors in the conductive heat flux meter and radiative heat flux meter. References [1] Y. Liu, D.J. Harris, Full-scale measurements of convective heat transfer coefficient on external surface of a low-rise building in sheltered conditions, Building and Environment 42 (2007) 2718–2736. [2] N.E. Wijeysundera, S.K. Chou, S.E.G. Jayamaha, Heat flow through walls under transient rain conditions, Journal of Insulation and Building Envelopes 17 (1993) 118–141. [3] M.G. Emmel, M.O. Abadie, N. Mendes, New external convective heat transfer coefficient correlations for isolated low-rise buildings, Energy and Buildings 39 (2007) 335–342. [4] M. Nunez, T.R. Oke, The energy balance of an urban canyon, Journal of Applied Meteorology 16 (1977) 11–19. [5] H. Kondo, Y. Genchi, Y. Kikegawa, et al., Development of a multi-layer urban canopy model for the analysis of energy consumption in a big city: structure of the urban canopy model and it’s performance, Boundary-Layer Meteorology 116 (2005) 395–421. [6] H.A. Johnson, M.W. Rubesin, Aerodynamic heating and convective heat transfersummary of literature survey, Transactions of the ASME 71 (5) (1949) 447–456. [7] W.H. Mc Adams, Heat Transfer, 3rd edition, McGraw-Hill, New York, 1954. [8] R.D. Clear, L. Gartland, F.C. Winkelmann, An empirical correlation for outside convective air-film coefficient for horizontal roofs, Energy and Buildings 35 (2003) 796–811. [9] A. Higishima, J. Tanimoto, Field measurements for estimating the convective heat transfer coefficient at building surface, Buildings and Environment 38 (2003) 873–881.
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[10] D.L. Loveday, A.H. Taki, Convective heat transfer coefficients at a plane surface on a full scale building facade, International Journal of Heat and Mass Transfer 39 (1996) 1729–1742. [11] N. Ito, K. Kimura, J. Oka, Full-scale measurements of convective energy losses from exterior building surface, ASHRAE Transactions 78 (1972) 184–191. [12] S. Sharple, Full-scale measurements of convective energy losses from exterior building surface, Building and Environment 19 (1984) 31–39. [13] M. Yazdanian, J.H. Kelm, Measurement of the exterior convective film coefficient for windows in low-rise building, ASHRAE Transactions 100 (1994) 1087–1096. [14] L. Zhang, N. Zhang, F. Zhao, et al., A genetic-algorithm-based experimental technique for determining heat transfer coefficient of exterior wall surface, Applied Thermal Engineering 24 (2004) 339–349. [15] J.A. Palyvos, A survey of wind convection coefficient correlations for building envelope energy systems’ modeling, Applied Thermal Engineering 28 (2008) 801– 808. [16] K. Narita, Experimental study of transfer velocity on urban surface with water evaporation method, Boundary-Layer Meteorology 122 (2007) 293–320. [17] J.F. Barlow, I.N. Harman, S.E. Belcher, Scalar flux from urban street canyon. Part I. Laboratory simulation, Boundary-Layer Meteorology 113 (2004) 369–385. [18] R.J. Goldstein, H.H. Cho, A review of mass transfer measurement using naphthalene sublimation, Experimental Thermal and Fluid Science 10 (1995) 416–434. [19] K. Narita, Y. Nunomura, A. Ogasa, Real scale measurement of convective mass transfer coefficient at window in nature wind, Journal of Architectural and Planning Environmental Engineering 491 (1997) 49–56. [20] S. Murakami, Current status and future trends in computational wind engineering, Journal of Wind Engineering and Industrial Aerodynamics 67–68 (1997) 3– 34. [21] S. Murakami, Overview of turbulence models application in CWE-1997, Journal of Wind Engineering and Industrial Aerodynamics 67–68 (1998) 1–24. [22] R.J. Cole, N.S. Sturrock, The convective heat exchange at the external surface of buildings, Building and Environment 12 (1977) 207–214. [23] http://apps1.eere.energy.gov/buildings/energyplus/pdfs/engineeringreference. pdf. [24] A. Hagishima, J. Tanimoto, K. Narita, Intercomparisons of experimental convective heat transfer coefficients and mass transfer coefficient of urban surfaces, Boundary-Layer Meteorology 117 (2005) 551–576. [25] D. Ambrose, I.J. Lawrenson, C.H.S. Sparke, The vapor pressure of naphthalene, Journal of Chemical Thermodynamics 7 (1975) 1173–1176. [26] E.R.G. Eckert, R.J. Goldstein, Measurements In Heat Transfer, 2nd edition, McGraw-Hill Inc., New York, 1976. [27] J.P. Holman, Experimental Method for Engineers, 2nd edition, McGraw-Hill, New York, 1978.