Thermal comfort in naturally ventilated buildings in ...

Thermal comfort in naturally ventilated buildings in Maceio, Brazil Harimi Djamila

Citation: AIP Conference Proceedings 1903, 080009 (2017); View online: https://doi.org/10.1063/1.5011597 View Table of Contents: http://aip.scitation.org/toc/apc/1903/1 Published by the American Institute of Physics

Thermal Comfort in Naturally Ventilated Buildings in Maceio, Brazil Harimi Djamila Faculty of Engineering, Universiti Malaysia Sabah, Jalan UMS, 88400 Kota Kinabalu, Sabah, Malaysia [email protected] Abstract. This article presents the results from thermal comfort survey carried out in classrooms over two different seasons in Maceio, Brazil. The secondary data were collected from thermal comfort field study conducted in naturally ventilated classrooms. Objective and subjective parameters were explored to evaluate thermal comfort conditions. The potential effect of air movement on subjects’ vote under neutrality was evaluated. Overall, the indoor climate of the surveyed location was classified warm and humid. Conflicting results were depicted when analyzing the effect of air movements on subjects’ vote. The mean air temperature for subjects feeling hot was found to be lower than those feeling warm. A reasonable approach to tackle these two unpredictable results was suggested. Correlation matrix between selected thermal comfort variables was developed. Globe temperature recorded the highest correlation with subjects’ response on ASHRAE seven-point scale. The correlation was significant at the 0.01 level. On the other hand, the correlation between air movement and subjects’ response on ASHRAE seven-point scale was weak but significant. Further field studies on the current topic were recommended.

INTRODUCTION Thermal comfort is commonly addressed in many observational studies due to energy crisis, global warming, heat island effect, and for other reasons. The topic has received much attention in the past due to the spread of airconditioning in many offices. It has become an important research area for the establishment of national and international standards. Several indexes were formulated in the past to better predict the comfort temperature range. To that end, many indexes were found to be geographically delimited. These indexes were only revealing of the region in which they were initially developed [1]. Nerveless, many of the parameters affecting subjects’ thermal comfort are not well understood, so let along addressing thermal comfort indexes. Thermal comfort parameters represent the foundation in which comfort temperature is predicted. In the past, there has been some disagreement with regard to whether air movement is a desired factor affecting human thermal comfort or not. Fanger and Christensen study showed that air movement was perceived as draught by occupants in ventilated spaces [2]. However, only fewer studies addressed the validity of the draught Fanger model [3]. Notwithstanding the generalization consequences, Fanger draught model is recognized by ISO 77300 for predicting people thermal requirements in air-conditioned spaces. That is to say, air movement may not be necessary a desirable factor for people subjected to air-conditioning. However, in naturally ventilated buildings the situation might be different. Such the case when people are subjected to hot or warm humid climate. The situation is most probably the opposite in cold climates. Candido et al. [4] investigated the air movement and thermal comfort in Maceio, Brazil. The climate of the location was categorized as hot humid. The surveyed spaces were naturally ventilated buildings with ceiling fans. The air movement acceptability limits was addressed. Recently, Harimi [5] developed a new approach from a meta-analysis for the prediction of comfort temperature by using ASHRAE RP 884 database. The developed approach was found to be crucial in minimizing some of the statistical issues encountered in thermal comfort studies. Therefore, the objective of this study is to readdress the effect of thermal comfort parameters on subjects vote with the emphasis on air movement by using secondary data.

Proceedings of the 3rd International Conference on Construction and Building Engineering (ICONBUILD) 2017 AIP Conf. Proc. 1903, 080009-1–080009-9; https://doi.org/10.1063/1.5011597 Published by AIP Publishing. 978-0-7354-1591-1/$30.00

080009-1

METHODOLOGY The present study used secondary data from the investigation conducted by Candido et al. [4]. The data was made available by Candido via Researchgate. The field study was carried out at Federal University of Alagoas during August–September and February–March [4]. This represents cool and hot season respectively [4]. Fig.1 shows Maceio Maceio, State of Alagoas, Brazil. The thermal comfort field survey was conducted in naturally ventilated classrooms and studios for drawing activities having celling fans shared collectively. The initial valid number of the collected data by the original investigators was 2075. However, in this study the number was reduced to 1885. This is because the original investigator Candido did not provide the entire data in ResearchGate. Additionally, a few cases were deleted by the present investigator after data screening. The finalized selected methodology for data analysis was made by referring mainly to two publications [5, 6]. Both publications addressed some of the statistical issues in thermal comfort studies. Few strategies were also suggested to tackle such issues.

FIGURE 1. Maceio, State of Alagoas, Brazil

RESULTS AND DISCUSSION After data collection and an initial screening of the data, preliminary data analysis was made to gain familiarity with the data. The present results and discussion section is divided into eight subsections. Those are namely climate of the location, classification of the indoor air temperature, classification of the indoor relative humidity, classification of the indoor air movement, descriptive statistics of thermal comfort parameters, effect of air movement on subjects’ thermal comfort, and finally correlation matrix between selected thermal comfort variables.

Climate of the Location Many thermal comfort investigators used the Koppen’s classification to describe the climate of the location. For the present study, Candido et al., [4] classified Maceio under tropical climate type (Am). Am refers to Equatorial monsoon [7]. Commonly, the Koppen’s method is developed based on two parameters; air temperature and precipitation. Those are the mostly available climatic parameters in the world. This may explain the popularity of this method in identifying the climate type of any location in a world map. However, little is acknowledged that Koppen’s method was developed to classify the climate according to vegetation [5]. In fact, The Koppen’s method showed some limitations on the observed vegetation distribution. Furthermore, plants are more sensitive to climate variation than humans. The following statement is quoted from Dambul and Jones [8]

080009-2

“It is important to realize that climatic classification is not an objective process, which could rigidly produce a single definitive solution… The subjectivity does not mean that a climate classification provides no benefit. As long as the classification process is coherent with pre-identified aims and purposes, it will be a useful exercise.” Recently, Harimi and Tay [9, 10] showed that the Koppen’s method is not useful in describing and predicting the climate of a location for thermal comfort considerations. Their analysis was made from a case study in Melbourne. In a separate study, the authors also discussed the limitations of two different Koppen’s classification methods. They showed from a case study that those two methods [7, 11] will not necessary lead to similar climate types [10]. Consequently, Harimi [5] developed a new procedure for describing the indoor climate for human thermal comfort so that the comparison among studies will be meaningful. Thus, Harimi method was used to describe the indoor climate in the present study. For an initial analysis of the location for thermal comfort consideration, the Climate Consultant software was used. The required climatic data were extracted from inmet 829940 WMO station number. The latitude and longitude of the location are 9.67”, 35.74” west of Greenwich and the elevation is 64 m. Overall. It was found that the location was mostly subjected to the air temperature variation from 23 to 26 0C. The monthly average variation of the wind speed was from 2 to 3 m/s. It is necessary to highlight that the selected meteorological station may not represent the exact location where the survey was carried out. The climatic data was used for an initial understanding of the overall climate of the location. However, it should be discussed with caution. The psychometric adaptive comfort chart was then generated via the Climate Consultant software. This is illustrated in Fig. 2. The software predicted that 54% of the time, the Maceio, Brazil population will be thermally comfortable and 46% uncomfortable. The recommended strategy for enhancing people thermal requirements is ventilation.

FIGURE 2. Psychometric chart adaptive comfort

Classification of the Indoor Air Temperature This section is concerned with the recorded indoor air temperature during the survey. The indoor temperature classification developed by Harimi was applied [5]. The purpose of the classification is to describe the indoor climate. The results are listed in Table 1. Most of the records (about 75%) were within the range 25 to 30 0C. There were about 11% records within 20 to 250C. The remaining percentage varied from 30 to 350C. Overall, the dominant indoor temperature during field study was categorized as warm.

080009-3

Range

400C

TABLE 1 Classification of the indoor air temperature Description Notation Nbr. of Records

Extremely Cold Very Cold Cold Cool Temperate Warm Hot Very Hot Extremely Hot

EC VC CD CL TE WM HT VHT EHT

Records %

0 0 0 0 210 1424 251 0 0

0 0 0 0 11.1 75.5 13.3 0 0

Classification of the Indoor Relative Humidity Relative humidity is one of the climatic parameters that might affect human thermal comfort. This may occur for instance in the absence of solar radiation and when the air is hot, steady and humid. This situation might prevent the human body from transpiration. Consequently, the person might perceive the indoor thermal environment uncomfortable as opposed when the air is dry. The obtained results from the present study are listed in Table 2. The indoor environment was categorized humid representing 65% of the data; the remaining percentage of 45%, the indoor climate was categorized as neither dry nor humid. Therefore, the dominant indoor climate when considering air temperature and relative humidity was categorized as warm and humid. This location seems to be less humid compared to many locations in the humid tropics such the case of Kota Kinabalu [6]. This observation is made by referring to the collected indoor relative humidity only. TABLE 2 Classification of the indoor relative humidity Description Notation Nbr. of Records

Range

81

Very Dry Dry Nether Dry nor Humid Humid Very Humid

VD DR NDH HD VH

Records %

0 0 658 1227 0

0 00 34.9 65.1 0.0

Classification of the Indoor Air Movement Air movement is widely recognized parameter affecting human thermal comfort [12, 13. 14, 15, 16]. Air movement has a desirable effect when the human body perceives the indoor thermal environment as warm or hot. Probably, it has the opposite effect under cold environment by causing a perception of draught [17]. In the present study, a new classification was designed to categorize the indoor air movement. The results are listed in Table 3. Overall, 50% of the collected air movement values were not greater than 0.2 m/s. This represents the highest percentage. Range

1.8

TABLE 3. Classification of the indoor air movement (m/s) Description Number of Records Percentage of Records

AV1 AV2 AV3 AV4 AV5 AV6 AV7 AV8 AV9 AV10

939 408 262 101 18 39 45 29 11 33

080009-4

50 22 14 5 1 2 2 2 1 2

The next highest percentage was 22% with the variation of air movement from 0.3 to 0.4 m/s. The third highest percentage of 14% was observed for the air movement from 0.5 to 0.6 m/s. Overall, the dominant air movement was no more than 0.2 m/s. It represents half of the records. It might be of interest to report that air movement of 0.2 m/s does not offset any elevation in operative temperature [18].

Descriptive Statistics of thermal Comfort Parameters Descriptive statistics offers the researcher the option of checking and gaining familiarity with the data. Additionally, it provides further insight about the scope so that comparison among studies will be meaningful. In the demographic survey, the age range of the subjects was from 16 to 30 years. The mean age was close to 21. Nearly 30% of the participants were males and 70% were females. The average surface area of the subjects under investigation was 1.66 m2. This estimation was made according to DuBois [19] method. The estimated was below the international average surface area of 1.8m2[6]. This probably reflects better the average surface area of a typical person in Maceio, Brazil. Detailed descriptive statistics were performed on environmental and personal measurements. The results are listed in Table 4. Overall, the minimum globe temperature was higher than air temperature by about 20C. The situation is reversed for the maximum air temperature reaching 3 0C difference. Despite the obvious difference of the standard deviation values between both parameters, the average records for air and globe temperatures were almost the same. In the present study, it was observed that air temperature was subjected to more variation compared to globe air temperature. For the case of relative humidity and air movement, the average records were 62.7% and 0.4 m/s respectively. TABLE 4. Descriptive statistics of some thermal comfort parameters Parameters Min Max Mean Std. Deviation

Temp. Glob.Temp. RH (%) Air Mvt. (m/s) Clo S.v.A.s.

24.5 26.5 52.0 0.1 0.3 -2.0

32.0 29.0 77.0 4.2 0.8 3.0

27.7 27.9 62.7 0.4 0.4 0.4

2.2 1.1 4.4 0.4 0.1 0.9

S.v.A.s. Subjects vote on ASHRAE scale. The used data for air and globe temperatures were binned at 0.5 bin. Relative humidity data rounded to 0 digits

Clothing insulation is an important parameter in adjusting people thermal requirements specifically in naturally ventilated buildings. The indoor clothing insulation levels also reveal the outdoor weather condition [20]. For the present case study, the average clothing level was 0.4 clo. This indicates that the subjects were wearing light summer cloths. It is reflected by the low clothing insulation level. De Vecchi et al. observed lower clothing insulation levels were worn by people in classrooms compared to offices in a temperate and humid climate in Brazil [21]. They attributed the discrepancy to students ’expectations in their daily activities and to the absence of a corporate dress code. Another interesting point worth discussion is related to the combined effects of body movements and wind on subjects’ thermal comfort. According to Holmer et al., such combinations improve noticeably heat loss from the human body [22]. Little is known on how such combination may affect human thermal perception toward the indoor environment. Therefore it is recommended for future investigation. Finally, the average subjects’ vote on ASHRAE 7-point scale was estimated. The obtained value was 0.4. Interestingly, the estimated standard deviation was at least twice the average subjects’ vote. This most probably occurred because the subjects vote were coded from (-3) when feeling cold to (+3) when feeling hot. Thus, positive and negative values were assigned according to subjects vote on ASHRAE 7-point scale. This procedure is widely used in thermal comfort studies. Humphreys et al. [23] suggested in their notable book on adaptive thermal comfort-foundation and analysis avoiding negative numbers for survey study and in some type of analysis. Their suggestion was not considered in the present investigation. This is because; the analysis and the interpretation of most of the results in this study will not be affected.

Subjects Thermal Perception toward the Indoor Environment When a person is subjected to the indoor thermal environment, the memory stores the previous experiences and thus the person will respond to similar situations accordingly. This may occur all the time while other possible

080009-5

options are taken into consideration to enhance the person state of mind. Consequently, some adjustments will probably be made when possible or necessary. In many research field studies, investigators only capture a single moment of subjects’ response toward the indoor thermal environment. This was also the present case as well. The analyzed results showed that more than 900 records were categorized under neutrality. It represents the highest percentage when considering subjects vote on the ASHRAE 7-point scale. The next highest percentage was for those voting warm. The detailed results are illustrated in Fig. 3.

FIGURE. 3 Number of votes on ASHRAE Seven-Point Scale. (-2 Cool), (-1 Slightly Cool), (0 Neutral), (1 Slightly Warm), (2 Warm), (3 Hot)

In our present study, the average air temperature was also estimated according to subjects’ vote on ASHRAE 7-point scale and plotted in Fig. 4. The most surprising result to emerge from the data is that the average temperature for those voted (hot) was lower than those voted (warm). The number of subjects voted (hot) was 41. Yet, the single most striking observation was the slightly higher average air movement for those voted warm than those voted hot. Then again, the average clothing insulation values were similar for both groups despite this. One of the challenging aspects when analyzing thermal comfort votes is obtaining inconsistent results. There are several explanations for such situation. A possible situation that may arise is when only small number of votes is recorded at any point on the ASHRAE seven-point scale [5]. In fact, this was not the case for this study. It could also be attributed to the influence of other thermal comfort parameters on subject ‘vote such with the elevation of air movement. Again this was not the case. These rather contradictory results require thorough analysis. A reasonable approach is by reanalyzing the data according to season. This is probably important due to the fact that all those voted (hot) on the ASHRAE seven-point scale were recorded during hot season only. Most advanced statistical methods are also recommended.

080009-6

FIGURE. 4 Average air temperature on ASHRAE 7-Point Scale. (-2 Cool), (-1 Slightly Cool), (0 Neutral), (1 Slightly Warm), (2 Warm), (3 Hot). Air temperature rounded to zero degit

The average thermal comfort parameters were also estimated according to subjects vote on ASHRAE 7-point scale. The results are listed in Table 5. The finding revealed that under neutrality, the average indoor air and globe temperatures were 27.30C and 27.90C respectively. The clothing insulation and metabolic rate values under neutrality were 0.4 clo and 1.2 met respectively. Further investigation on the effect of seasonal variation on subjects vote on ASHRAE 7-point scale is recommended for better interpretation of the results. Indoor Thermal Comfort Parameters

Average Temp. Avg. Globe.Temp. Avg. Air Mvt. Avg. of Sqrt (Air Mvt.) Avg. RH (%) Avg. Clo Avg. Met

TABLE 5 Subjects vote on ASHRAE scale ASHRAE Scale -2.0 -1.0 0.0 1.0

26.1 27.3 0.3 0.5 61.0 0.4 1.2

26.5 27.5 0.3 0.5 63.4 0.4 1.1

27.3 27.9 0.4 0.6 62.9 0.4 1.2

28.6 28.4 0.4 0.6 62.4 0.4 1.2

2.0

3.0

29.6 28.8 0.5 0.6 62.3 0.4 1.2

28.7 28.9 0.4 0.6 63.1 0.4 1.2

Air temperature and globe temperatures rounded to zero digits.

Effect of Air movement on subjects’ Thermal Comfort In order to assess the effect of air movement on subjects’ thermal comfort, the mean values of thermal comfort parameters were analyzed from the collected data. The analysis was made within the selected air movement range from 0.1 m/s to 1.3 m/s. Additionally, the data were analyzed only when there are at least 25 votes at each point ASHRAE scale. This requirement was made to avoid statistical bias in the interpretation of the results. The obtained results are listed in Table 6. A close observation in Table 6 revealed that the highest percentage of neutral votes was recorded when air movement was 1.1 m/s. The estimated average air temperature was 27.6 0C. Surprisingly, the next highest percentage was recorded when air movement was 0.1 m/s. The average air temperature was 26.7 0C. This was beyond our expectation. The surprising results showed obvious difficulty in tackling the effect of air movements on human thermal comfort. Additionally, given that the field study was conducted in classrooms, this added one additional complexity in this investigation. Further consideration of seasonal variation might provide further insight by using more advanced statistical methods.

080009-7

Air Mvt

0.1 0.2 0.3 0.4 0.5 0.6 0.7 1.1 1.3

TABLE 6. Effect of air movement on indoor thermal comfort parameters Number of Votes on ASHRAE Avg. Avg. Avg. Avg. Globe 7-point Scale Amp Temp. Votes RH Met Clo temp. -2 -1 0 1 2 3

0.2 0.4 0.3 0.6 0.7 0.9 0.6 0.1 0.4

0.4 0.5 0.4 0.4 0.6 0.7 0.7 0.4 0.3

64.1 61.5 61.6 62.5 63.0 64.5 63.6 64.3 63.5

1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2

0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4

27.6 28.2 28.1 28.3 28.4 28.6 28.5 28.3 28.0

26.7 28.1 27.7 28.3 28.8 29.1 28.7 27.6 27.2

9 5 3 1 1

62 49 42 17 13 5

1

2 4

266 237 127 56 66 32 35 19 12

115 105 60 40 56 32 22 7 5

37 41 25 23 25 22 10

2 11 10 4 5 5

3

1

Nbr. of Votes

491 448 267 141 165 97 67 29 25

% of % of Neutral Votes Votes

26.0 23.8 14.2 7.5 8.8 5.1 3.6 1.5 1.3

54.2 52.9 47.6 39.7 40.0 33.0 52.2 65.5 48.0

Correlation Matrix between Selected Variables This section is about expressing subjects’ vote on ASHRAE seven-point scale as a function of thermal comfort parameters. The analyzed results are summarized in Table 7. TABLE 7. Correlation matrix between selected variables Temp. RH (%) Glob. Temp. Air Mvt. (m/s)

Clo -0.171** 0.913** 0.160** -0.405** Temp. -0.171** 0.011 -0.046* 0.004 RH (%) ** 0.913 0.011 0.201** -0.379** Glob.Temp. 0.160** -0.046* 0.201** -0.097** Air Mvt. (m/s) ** ** ** Clo -0.405 0.004 -0.379 -0.097 S.v.A.s. 0.416** -0.046* 0.429** 0.095** -0.190** **. Correlation is significant at the 0.01 level (2-tailed). *. Correlation is significant at the 0.05 level (2-tailed). S.v.A.s. Subjects votes on ASHRAE scale The used data for air and globe temperatures were binned at 0.5 bin. Relative humidity data rounded to 0 digit

S.v.A.s.

0.416** -0.046* 0.429** 0.095** -0.190**

Among all the selected variables, the correlation between air and globe temperatures was high and significant at the 0.01 level. This means that one of the two variables is redundant [12]. When considering subjects vote on ASHRAE 7-point scale, the globe temperature recorded the highest value. The next highest percentage was for air temperature. Both correlation values were significant at the 0.01 level. On the other hand, the air movement has a weak correlation with subjects vote on ASHRAE scale but significant. The correlation between this parameter with globe and relative humidity are significant. In thermal comfort studies, the square root of air movement is considered a better alternative in investigating the correlation between thermal comfort parameters [12].It is important to emphasize that the significant of correlation between two parameters does not necessary imply causality [24]. Other statistical methods are required to investigate causality [25]. The correlation matrix only helps in the selection of the most important parameters in predicting for instance neutral temperature. The correlation between clothing insulation and subject vote on ASHRAE 7-point scale was small and significant. The week and insignificant correlation between clothing insulation and occupants’ thermal sensation could be probably attributed to the narrow range of clothing insulation level. For the case of relative humidity, the correlation between relative humidity and air temperature was small but significant. However, the correlation between relative humidity and globe temperature was not significant. To sum up, due to the discrepancy of the initial analysis and to avoid misinterpretation of the results, further analysis was not made. Seasonal variation should be considered in the analysis.

CONCLUSIONS This study analyzed subjects thermal comfort in Maceio, Brazil. The environmental and personnel thermal comfort parameters were evaluated. The evaluation was made while considering subjects vote on ASHRAE seven-

080009-8

point scale. In this study, the indoor climate was classified as warm-humid. The average temperature for those voted hot was found to be lower than those voted warm. Further, contradicting results were observed when analyzing the effect of air movement on subjects’ thermal comfort. The conflicting and the unexpected results were attributed to seasonal variation. Therefore it was recommended for future work. In this study, correlation matrix between thermal comfort variables was constructed and analyzed. Globe temperature recorded the highest correlation with subjects’ vote on ASHRAE seven-point scale. The correlation was significant at the 0.01 level. On the other hand, the correlation between air movement and subjects’ response on ASHRAE seven-point scale was weak but significant. It seems important and interesting to investigate the similarities and differences of subjects’ thermal requirements in a hot or warm humid location versus a tropical humid location. This is because; there is less seasonal variation in the humid tropics.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.

J.R. Rafael Batista & L.T.G. Fabio & P.d. R, Present climate and future projections of the thermal comfort index for the metropolitan region of São Paulo, Brazil (Climatic Change, Springer, 2016). P.O. Fanger, N.K. Christensen, Ergonomics 29(2), 215-235 (1986). K. E. Charles, Fanger’s Thermal Comfort and Draught Models. IRC Research Report RR-162, Ottawa, Canada (2003). C. Candido, R.J. de Dear, R. Lamberts, L. Bittencourt, Building and Environment 45, 222–229 (2010). Harimi Djamila, Renewable and Sustainable Energy Reviews 74, 569-580, (2017) Harimi Djamila, Chi-Ming Chu, Sivakumar Kumaresan, Building and Environment 62, 133-142 (2013). M. Kottek, J. Grieser, C. Beck, B. Rudolf and F. Rubel, Meteorologische Zeitschrift 15, 259-263 (2006). R. Dambul, P. Jones, Geografia, OnlineTM Malaysia Journal of Society and Space 3, 84 – 105(2007). Harimi Djamila, T. L. Yong, Sustainable Cities and Society 27, 42–48 (2016). Harimi Djamila, T. L. Yong, Advanced Science Letters 23, 1403-1406, (2017). M. C. Peel, B. L. Finlayson, T. A. Mcmahon, Earth Syst. Sci. 11, 1633–1644 (2007). J. Toftum, Indoor Air. 14, 40-45 (2004) W. Srivajana, Thammasat Int. J. Sc. Tech 8(2), 45-54 (2003) L. Daniel, T. Williamson, V. Soebarto and D. Chen, A model for the cooling effect of air movement 2015, edited by R.H. Crawford and A. Stephan (The Architectural Science Association and the University of Melbourne, p. 1077. G. Brager, H. Zhang, and E. Arens, Building Research & Information 43, 274-287 (2015). Rajapaksha, H. Nagai, M. Okumiya, Indoor Air 2002, Proceedings of the 9th International Conference on Indoor Air Quality and Climate , Monterey, CA, 2002, p.1072. P.O. Fanger, A.K. Melikov, H. Hanzawa, J. Ring, Energy and Buildings 12, 121-3 (1988). A. Foruzanmehr, Thermal Comfort in Hot Dry Climates: Traditional Dwellings in Iran (Routledge, 2017). D. DuBois, EF DuBois, Arch Int Med 17, 863-71 (1916). C. Morgan, R. de Dear. Weather, Inter-Research 24, 267–284 (2003). R. DE Vecchi, R. Lamberts, C. Candido, Ambiente Construído, Porto Alegre 17, 69-81, (2017). I. Holmer, D. CE. Gavhed, S. Grahn, H. O Nilsson, Proceedings of the Fifth Int. Conf. on Environmental Ergonomics, edited by W.A. Lotens and G. Havenith (Maasnicht, the Netherlands, 1992), p.67. M. Humphreys, F. Nicol, S. Roaf, Adaptive thermal comfort (Routledge, London and New York, 2016). J. Miles and M. Shevlin, Applying regression & correlation (Sage, Los Angeless, 2001). A. Agresiti and B. Finlay, Statistical methods for the social science (Prentice Hall, New Jersey, 1997).

080009-9