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Heat Transfer Characteristics of Radiant Heating and Cooling Systems for Improved Design

Shinoda Jun 早稲田大学

2021.08.04

概要

Radiant heating and cooling systems are now commonly used as a comfortable and energy efficient alternative to conventional all-air systems. As opposed to all-air systems which provide heating and cooling by convection, radiant systems utilize a temperature-controlled surface (active surface), providing heating and cooling by the combination of thermal radiation and convection. Due to the difference in the heat transfer mechanism, there are cases in which common design approaches and assumptions that were primarily made for all-air systems are not applicable for radiant systems. Furthermore, in cooling cases, the surface temperature must be kept higher than the dew point temperature to prevent condensation, which limits the cooling provided by the active surface. Hence, in hot and humid regions, the accurate calculation of heat transfer is critical. This thesis thus reevaluated the heat transfer calculation process of radiant systems and quantified the extent of divergence caused by different calculation inputs.

This thesis is composed of seven chapters, and the major findings are explained as follows.

Chapter 1 gives the research background and objectives, followed with a summary of relevant research.

Chapter 2 introduces the concept of surface heat transfer coefficients for the calculation of heat transfer from an active surface and presents an extensive literature review conducted to collect the diverse heat transfer coefficients available in literature. Recommended values/expressions and measurement results in standards, guidelines and published articles were comprehensively studied. These values and expressions were used to predict the measured data reported in other articles, to examine their accuracy. Larger deviations and prediction errors were found in the total and convective heat transfer values than in radiant heat transfer, which had a range of errors within ± 20% throughout the literature. The major sources of error were shown to be the calculation procedure for each heat transfer mechanism, the choice of reference temperature and its measurement height and position, and room dimensions. It is suggested that heat transfer should be chosen by matching the calculation/measurement conditions in which they were obtained to the purpose and conditions in which they will be applied.

Chapter 3 presents the results of an experiment conducted to compare the temperature measuring performance of market-available room temperature sensors. Results from the literature review in the previous chapter suggested that the choice of room reference temperature was crucial for the calculation of heat transfer. Therefore, measured temperatures of the selected sensors were compared against reference air and globe temperature sensors in a climate chamber with a two-person office setup. The influence of sensor position and cooling load was studied for both all-air and radiant cooling conditions. Sensors placed at the same position had a measurement difference of up to 1.8 K, and assumptions about the type of temperature a sensor measures had the largest impact on the deviation from the reference temperatures. As opposed to common assumptions, conventional wall-mounted temperature sensors measured closer to globe temperature than air temperature and could be a possible indicator for the operative temperature. When the load settings were high, measurements in radiant system cases had smaller deviations from the reference sensors compared with all-air systems, due to the chilled surface compensating for the radiation from the loads.

Chapter 4 presents the results of cooling capacity measurements of suspended radiant ceiling panels. The cooling capacity of a radiant panel is usually measured in a certified test chamber and is provided by manufacturers for engineers to use for their calculations. However, current measurement standards calculate the cooling capacity of a panel based on the heat carried by the circulating water, which does not distinguish the heat extracted from the room and plenum sides. Experiments were conducted in a test chamber certified by the Japanese standard for cooling capacity measurement, with the temperature difference between the room and plenum as the main parameter. The panels were evaluated based on the cooling capacity and the ratio of heat extracted from the room side. The results revealed that an increase in the plenum temperature resulted in an increase in the cooling capacity but a decrease in the ratio of heat extracted from the room side. Within the tested temperature range, which was a room temperature of 26°C and a plenum temperature ±2 °C of the room temperature, the heat extracted from the room-side was 77 – 92% when the panels were insulated and decreased to 46 – 71% when they were not insulated. An empirical approach and equation for estimating the heat transfer at both sides of the panel were proposed, which could enable a more accurate design and sizing of the radiant panel system.

Chapter 5 gives the results of a field measurement conducted in an office building to characterize the dynamic thermal behavior of radiant ceiling panels in relation to the plenum and room temperatures. A newly constructed office building with the same radiant ceiling panels tested in chapter 4 was selected for measurement. The measured heat flux to the room side was compared against values predicted using the methodology proposed in the previous chapter. Measurements were conducted for one week in August 2020, and the plenum temperature was ± 2 °C of the room temperature, which matches the conditions tested to obtain the empirical equation. The average ratio of heat extracted from the room-side was 68% in the measurements and 66% in the predicted values. The validity of the methodology developed to predict the room-side ratio was therefore confirmed in non-steady- state conditions.

Chapter 6 presents results of a parametric simulation of a two-zone office building model with radiant ceiling panels. Measurements from chapter 4 were used to develop a numerical model of a suspended radiant ceiling panel capable of calculating the heat transfer at both the room and plenum sides. The developed model was validated against measurements and yielded errors within ±10%. A parametric simulation was then conducted for a total of 735 cases, and the observed parameters were the room control reference temperature type, building construction, radiant percentage of the internal loads, and the convective heat transfer coefficient at both sides of the panels. The objective was to holistically compare individual parameters which were each suggested to influence the heat transfer calculation in literature and in previous chapters of this thesis. Simulations were conducted for a weather data of Tokyo, Japan from May to October with 1-hour intervals. Due to the fast responding nature of metal radiant panels, all cases were able to achieve a room operative temperature of 24.5 ± 1°C, therefore the operating hours of the radiant panel system were compared as a representation for energy use. The setting of the radiant percentage of the internal load had the largest impact on the panel operating hours, ranging from 414 – 1,269 hours (29 – 89% of occupied hours). The operation hours increased as the radiant percentage of the loads increased. The convective heat transfer coefficient of the room-side surface caused a deviation of up to 255 hours of operation. As a variant condition, a comparison was made between non-insulated panels installed in a typical floor of a multi-story building and insulated panels installed at the topmost floor. Results showed that insulated panels were able to provide equivalent levels of room operative temperature with comparable operation time as the non-insulated panels, despite having larger loads in the plenum. It was concluded that the insulated panels were more effective than the commonly adopted use of non-insulated panels to utilize the plenum as heat storage.

Chapter 7 summarizes the main findings of each chapter.

This thesis presents a detailed overview of the heat transfer taking place at the active surface of radiant systems, supported by a sequence of literature review, experiments, field measurement and simulations. The findings can provide guidance for a more accurate calculation at the design phase and energy use analysis of radiant systems. It will thus be possible to provide thermal comfort with less energy, which will make radiant systems a viable heating and cooling option for buildings, contributing to the global trend towards decarbonization.

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参考文献

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Chapter 2

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[2] A.-J.N. Khalifa, Natural convective heat transfer coefficient – a review: I. Isolated vertical and horizontal surfaces, Energy Conversion and Management. 42 (2001) 491–504.

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Chapter 3

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[2] Overview of Existing and Future Residential Use Cases for Connected Thermostats, U.S. Department of Energy, 2016.

[3] A. Keshtkar, S. Arzanpour, F. Keshtkar, P. Ahmadi, Smart residential load reduction via fuzzy logic, wireless sensors, and smart grid incentives, Energy and Buildings. 104 (2015) 165–180.

[4] W. Tushar, N. Wijerathne, W.-T. Li, C. Yuen, H.V. Poor, T.K. Saha, K.L. Wood, Internet of Things for Green Building Management: Disruptive Innovations Through Low-Cost Sensor Technology and Artificial Intelligence, IEEE Signal Processing Magazine. 35 (2018) 100–110.

[5] T. Ueno, A. Meier, A method to generate heating and cooling schedules based on data from connected thermostats, Energy and Buildings. 228 (2020) 110423.

[6] M. Kintner-Meyer, M.R. Brambley, Are Wireless Sensors and Controls Ready for the Building Automation Industry? Selected Case Studies and Technology Development Activities, in: World Energy Engineering Congress (WEEC) 2006 Proceedings, 2006.

[7] C. Lin, C.C. Federspiel, D.M. Auslander, Multi-Sensor Single-Actuator Control of HVAC Systems, in: Proceedings of the Second International Conference for Enhanced Building Operations, Richardson, Texas, 2002.

[8] D. Wang, E. Arens, T. Webster, M. Shi, How the number and placement of sensors controlling room air distribution systems affect energy use and comfort, in: Proceedings of the Second International Conference for Enhanced Building Operations, 2002.

[9] K. Menzel, D. Pesch, B. O’Flynn, M. Keane, C. O’Mathuna, Towards a wireless sensor platform for energy efficient building operation, Tsinghua Science and Technology. 13 (2008) 381–386.

[10] A. Mylonas, O.B. Kazanci, R.K. Andersen, B.W. Olesen, Capabilities and limitations of wireless CO2, temperature and relative humidity sensors, Building and Environment. 154 (2019) 362–374.

[11] X. Liu, B. Akinci, J.H. Garret, Ö. Akin, Requirements for a computerized approach to plan sensor placement in the HVAC systems, in: 2010.

[12] B. Dong, V. Prakash, F. Feng, Z. O’Neill, A review of smart building sensing system for better indoor environment control, Energy and Buildings. 199 (2019) 29–46.

[13] T.L. Madsen, T.P. Schmidt, U. Helk, How Important is the Location of the Room Thermostat?, in: ASHRAE Transactions, 1990: pp. 847–852.

[14] M. Alhashme, N. Ashgriz, A virtual thermostat for local temperature control, Energy and Buildings. 126 (2016) 323–339.

[15] G. Huang, P. Zhou, L. Zhang, Optimal Location of Wireless Temperature Sensor Nodes in Large-scale Rooms, in: 13th International Conference on Indoor Air Quality and Climate, Hong Kong, 2014.

[16] M. Arnesano, G.M. Revel, F. Seri, A tool for the optimal sensor placement to optimize temperature monitoring in large sports spaces, Automation in Construction. 68 (2016) 223–234.

[17] Y. Yu, C. Megri, A Novel Method for Thermostat Set Point Prediction for Energy Savings and/or Better Human Thermal Comfort - A Zonal Modelling Approach, International Journal of Ventilation. 13 (2014) 299– 318.

[18] W. Tian, X. Han, W. Zuo, Q. Wang, Y. Fu, M. Jin, An optimization platform based on coupled indoor environment and HVAC simulation and its application in optimal thermostat placement, Energy and Buildings. 199 (2019) 342–351.

[19] G.D. Kontes, G.I. Giannakis, P. Horn, S. Steiger, D.V. Rovas, Using Thermostats for Indoor Climate Control in Office Buildings: The Effect on Thermal Comfort, Energies. 10 (2017) 1368.

[20] H. Wang, B.W. Olesen, O.B. Kazanci, Using thermostats for indoor climate control in offices: The effect on thermal comfort and heating/cooling energy use, Energy and Buildings. 188–189 (2019) 71–83.

[21] B.W. Olesen, H. Wang, O.B. Kazanci, D. Coakley, The effect of room temperature control by air- or operative temperature on thermal comfort and energy use, in: Proceedings of Building Simulation 2019: 16th Conference of IBPSA, 2019.

[22] Jones J., Wellman G., Kim Y., Singh H., Krafthefer B., Performance Comparison for Thermal Comfort Sensors, Journal of Architectural Engineering. 4 (1998) 99–106.

[23] M. Dawe, P. Raftery, J. Woolley, S. Schiavon, F. Bauman, Comparison of mean radiant and air temperatures in mechanically-conditioned commercial buildings from over 200,000 field and laboratory measurements, Energy and Buildings. 206 (2020) 109582.

[24] A. Simone, J. Babiak, M. Bullo, G. Langkilde, B.W. Olesen, Operative temperature control of radiant surface heating and cooling systems, in: Proceedings of Clima 2007 Wellbeing Indoors, 2007.

[25] O.M. Borier, O.B. Kazanci, B.W. Olesen, D. Khovalyg, Which sensor type at which location should offices with south orientated window choose to improve comfort and reduce energy consumption?, J. Phys.: Conf. Ser. 1343 (2019) 012147.

[26] EN ISO 7726: Ergonomics of the thermal environment – Instruments for measuring physical quantities, European Committee for Standardization, Brussels, 2001.

[27] J. Kolarik, B.W. Olesen, Influence of measurement uncertainty on classification of thermal environment in buildings according to European Standard EN 15251, in: Proceedings of 7PHN Sustainable Cities and Buildings, 2015.

[28] J. Toftum, G. Langkilde, P.O. Fanger, New indoor environment chambers and field experiment offices for research on human comfort, health and productivity, Energy and Buildings. 36 (2004) 899–903.

[29] ANSI/ASHRAE Standard 55-2017: Thermal Environmental Conditions for Human Occupancy, ASHRAE, 2017.

[30] P. Mustakallio, Z. Bolashikov, K. Kostov, A. Melikov, R. Kosonen, Thermal environment in simulated offices with convective and radiant cooling systems under cooling (summer) mode of operation, Building and Environment. 100 (2016) 82–91.

[31] P. Mustakallio, Z.D. Bolashikov, L. Rezgals, A. Lipczynska, A.K. Melikov, R. Kosonen, Thermal environment in a simulated double office room with convective and radiant cooling systems, Building and Environment. 123 (2017) 88–100.

[32] O.B. Kazanci, D. Khovalyg, T. Iida, Y. Uno, T. Ukiana, B.W. Olesen, Experimental comparison of the thermal indoor environment created by a radiant, and a combined radiant and convective cooling system, in: Proceedings— Roomvent & Ventilation 2018, 2018: pp. 223–228.

[33] J. Babiak, B.W. Olesen, D. Petras, Low Temperature Heating and High Temperature Cooling, REHVA, 2007.

[34] EN 16798-1: Energy performance of buildings - Ventilation for buildings - Part 1: Indoor environmental input parameters for design and assessment of energy performance of buildings addressing indoor air quality, thermal environment, lighting and acoustics, European Committee for Standardization, Brussels, 2019.

[35] TIDA-01596 Smart Thermostat Localized Heat Compensation for Ambient Temperature Sensing Reference Design, Texas Instruments, 2018.

[36] E. Teitelbaum, K.W. Chen, F. Meggers, H. Guo, N. Houchois, J. Pantelic, A. Rysanek, Globe thermometer free convection error potentials, Scientific Reports. 10 (2020) 2652.

[37] A.K. Melikov, D.G. Markov, Validity of CO2 based ventilation design, in: E3S Web of Conferences, 2019: p. 05007.

[38] M.P. Bivolarova, T. Snaselova, D.G. Markov, A.K. Melikov, CO2 Based Ventilation Control – Importance of Sensor Positioning (in press), in: Roomvent 2020, 2020.

Chapter 4

[1] ASHRAE Handbook, Chapter 6 Radiant Heating and Cooling, in: 2016 HVAC Systems and Equipment, SI, 2016.

[2] J. Babiak, B.W. Olesen, D. Petras, Low Temperature Heating and High Temperature Cooling, REHVA, 2007.

[3] M.S. Shin, K.N. Rhee, S.H. Park, M.S. Yeo, K.W. Kim, Enhancement of cooling capacity through open-type installation of cooling radiant ceiling panel systems, Building and Environment. 148 (2019) 417–432.

[4] M. Mosa, M. Labat, S. Lorente, Constructal design of flow channels for radiant cooling panels, International Journal of Thermal Sciences. 145 (2019) 106052.

[5] M. Mosa, M. Labat, S. Lorente, Role of flow architectures on the design of radiant cooling panels, a constructal approach, Applied Thermal Engineering. 150 (2019) 1345–1352.

[6] X. Wu, J. Zhao, B.W. Olesen, L. Fang, F. Wang, A new simplified model to calculate surface temperature and heat transfer of radiant floor heating and cooling systems, Energy and Buildings. 105 (2015) 285–293.

[7] ISO 11855-2, Building environment design - Design, dimensioning, installation and control of embedded radiant heating and cooling systems - Part 2: Determination of the design heating and cooling capacity, International Organization For Standardization, 2012.

[8] J. Shinoda, O.B. Kazanci, S.-I. Tanabe, B.W. Olesen, A review of the surface heat transfer coefficients of radiant heating and cooling systems, Building and Environment. 159 (2019).

[9] T. Cholewa, M. Rosiński, Z. Spik, M.R. Dudzińska, A. Siuta-Olcha, On the heat transfer coefficients between heated/cooled radiant floor and room, Energy and Buildings. 66 (2013) 599–606.

[10] S.-H. Park, D.-W. Kim, G.-S. Joe, S.-R. Ryu, M.-S. Yeo, K.-W. Kim, Establishing Boundary Conditions Considering Influence Factors of the Room Equipped with a Ceiling Radiant Cooling Panel, Energies. 13 (2020) 1684.

[11] J.-W. Jeong, S.A. Mumma, Ceiling radiant cooling panel capacity enhanced by mixed convection in mechanically ventilated spaces, Applied Thermal Engineering. 23 (2003) 2293–2306.

[12] J.-W. Jeong, S.A. Mumma, Practical cooling capacity estimation model for a suspended metal ceiling radiant cooling panel, Building and Environment. 42 (2007) 3176–3185.

[13] Z. Tian, X. Yin, Y. Ding, C. Zhang, Research on the actual cooling performance of ceiling radiant panel, Energy and Buildings. 47 (2012) 636–642.

[14] R. Li, T. Yoshidomi, R. Ooka, B.W. Olesen, Field evaluation of performance of radiant heating/cooling ceiling panel system, Energy and Buildings. 86 (2015) 58–65.

[15] S. Ito, Y. Akashi, J. Lim, N. Miura, A. Kawamura, Performance prediction method for ceiling radiant cooling panel, Journal of Environmental Engineering (Japan). 83 (2018) 737–747.

[16] K. Ojima, S. Ito, J. Lim, Y. Akashi, Designing a ceiling radiant cooling system for different installation conditions, in: IOP Conference Series: Earth and Environmental Science, 2019.

[17] EN 14240, Ventilation for buildings - Chilled ceilings - Testing and rating, European Committee for Standardization, 2004.

[18] ANSI/ASHRAE Standard 138-2009, Method of Testing for Rating Ceiling Panels for Sensible Heating and Cooling, American Society of Heating, Refrigerating and Air-Conditioning Engineers, 2009.

[19] ISO 18566-2, Building environment design - Design, test methods and control of hydronic radiant heating and cooling panel systems - Part 2: Determination of heating and cooling capacity of ceiling mounted radiant panels, International Organization For Standardization, 2017.

[20] ARCH 2017 CHTRS, Cooling and Heating - Testing and Rating Standard (CHTRS) Ver. 1.1, The Association of Radiant Cooling and Heating systems of Japan, 2017.

[21] K. Kimura, U. Inoue, S. Tanabe, K. Fujino, T. Akimoto, A. Ito, S. Sugiura, Simplified Method for Measurement of Radiation Flux from Heating and Cooling Panel, Summaries of Technical Papers of Annual Meeting Architectural Institute of Japan. D, Environmental Engineering. (1987) 829–830.

[22] N. Fonseca Diaz, Modeling of a hydronic ceiling system and its environment as energetic auditing tool, Applied Energy. 88 (2011) 636–649.

[23] Y. Yuan, X. Zhang, X. Zhou, J. Gao, An experiment-oriented simulation method for cooling capacity determination of cooling ceiling radiant panel system, Science and Technology for the Built Environment. 22 (2016) 831–844.

[24] M. Andrés-Chicote, A. Tejero-González, E. Velasco-Gómez, F.J. Rey-Martínez, Experimental study on the cooling capacity of a radiant cooled ceiling system, Energy and Buildings. 54 (2012) 207–214.

[25] F. Causone, S.P. Corgnati, M. Filippi, B.W. Olesen, Experimental evaluation of heat transfer coefficients between radiant ceiling and room, Energy and Buildings. 41 (2009) 622–628.

[26] T. Cholewa, R. Anasiewicz, A. Siuta-Olcha, M.A. Skwarczynski, On the heat transfer coefficients between heated/cooled radiant ceiling and room, Applied Thermal Engineering. 117 (2017) 76–84.

[27] Y. Yuan, X. Zhang, X. Zhou, Simplified correlations for heat transfer coefficient and heat flux density of radiant ceiling panels, Science and Technology for the Built Environment. 23 (2017) 251–263.

[28] ISO 18566-3, Building environment design - Design, test methods and control of hydronic radiant heating and cooling panel systems - Part 3: Design of ceiling mounted radiant panels, International Organization For Standardization, 2017.

[29] T. Yu, P. Heiselberg, B. Lei, C. Zhang, M. Pomianowski, R. Jensen, Experimental study on the dynamic performance of a novel system combining natural ventilation with diffuse ceiling inlet and TABS, Applied Energy. 169 (2016) 218–229.

Chapter 5

[1] R. Li, T. Yoshidomi, R. Ooka, B.W. Olesen, Field evaluation of performance of radiant heating/cooling ceiling panel system, Energy and Buildings. 86 (2015) 58–65.

[2] S. Ito, Y. Akashi, J. Lim, N. Miura, A. Kawamura, Performance prediction method for ceiling radiant cooling panel, Journal of Environmental Engineering (Japan). 83 (2018) 737–747.

[3] K. Ojima, S. Ito, J. Lim, Y. Akashi, Designing a ceiling radiant cooling system for different installation conditions, in: IOP Conference Series: Earth and Environmental Science, 2019.

[4] K. Hidari, H. Watanabe, Y. Takahashi, D. Kawahara, M. Kobayashi, Y. Sonoda, T. Kikuchi, K. Wada, Study on the City Hall in SDGs Future City for Zero Energy Building Part 1. Summary of the ZEB project, in: Summaries of Technical Papers of Annual Meeting Architectural Institute of Japan, Architectural Institute of Japan, 2019: pp. 965–966.

Chapter 6

[1] I. Beausoleil-Morrison, The adaptive simulation of convective heat transfer at internal building surfaces, Building and Environment. 37 (2002) 791–806.

[2] K. Goethals, H. Breesch, A. Janssens, Sensitivity analysis of predicted night cooling performance to internal convective heat transfer modelling, Energy and Buildings. 43 (2011) 2429–2441.

[3] K. Goethals, M. Delghust, G. Flamant, M. De Paepe, A. Janssens, Experimental investigation of the impact of room/system design on mixed convection heat transfer, Energy and Buildings. 49 (2012) 542–551.

[4] M.H. Hosni, B.W. Jones, H. Xu, Measurement of Heat Gain and Radiant/Convective Split from Equipment in Buildings, ASHRAE Research Project Report, 1999.

[5] M.H. Hosni, B.W. Jones, J.M. Sipes, Y. Xu, Total Heat Gain and the Split Between Radiant and Convective Heat Gain from Office and Laboratory Equipment in Buildings, in: ASHRAE Transactions, 1998.

[6] M.H. Hosni, B.W. Jones, H. Xu, Experimental Results for Heat Gain and Radiant/Convective Split from Equipment in Buildings, in: ASHRAE Transactions, 1999.

[7] B.W. Jones, M.H. Hosni, J.M. Sipes, Measurement of Radiant Heat Gain from Office Equipment Using a Scanning Radiometer, in: ASHRAE Transactions, 1998.

[8] M.H. Hosni, B.T. Beck, Updated Experimental Results for Heat Gain from Office Equipment in Buildings, in: ASHRAE Transactions, 2011.

[9] J.D. Spitler, Load Calculation Applications Manual (Second Edition), SI, ASHRAE, 2014.

[10] A. Moftakhari, S. Bourne, A. Novoselac, Experimental Verification of Cooling Load Calculations for Spaces with Non-Uniform Temperature Radiant Surfaces, ASHRAE RP 1729, 2019.

[11] TRNSYS 18 Documentation Volume 4 Mathematical Reference, Solar Energy Laboratory, University of Wisconsin-Madison and Thermal Energy System Specialists, LLC, 2018.

[12] B.W. Olesen, K. Sommer, B. Düchting, Control of Slab Heating and Cooling Systems Studied by Dynamic Computer Simulations, in: ASHRAE Transactions, 2002.

[13] B.W. Olesen, F.C. Dossi, Operation and Control of Activated Slab Heating and Cooling Systems, in: Procedings of CIB World Buildings Congress 2004, 2004.

[14] J. Kolarik, J. Toftum, B.W. Olesen, K.L. Jensen, Simulation of energy use, human thermal comfort and office work performance in buildings with moderately drifting operative temperatures, Energy and Buildings. 43 (2011) 2988–2997.

[15] R. Li, T. Yoshidomi, R. Ooka, B.W. Olesen, Case-study of Thermo Active Building Systems in Japanese Climate, Energy Procedia. 78 (2015) 2959–2964.

[16] ANSI/ASHRAE Standard 140-2017: Standard Method of Test for the Evaluation of Building Energy Analysis Computer Programs, ASHRAE, 2017.

[17] ISO 7730, Ergonomics of the thermal environment - Analytical determination and interpretation of thermal comfort, International Organization For Standardization, 2005.

[18] J.-W. Jeong, S.A. Mumma, Ceiling radiant cooling panel capacity enhanced by mixed convection in mechanically ventilated spaces, Applied Thermal Engineering. 23 (2003) 2293–2306.

[19] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization, John Wiley & Sons, 2015.

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