Operative temperature

Operative temperature (to) is defined as a uniform temperature of an imaginary black enclosure in which an occupant would exchange the same amount of heat by radiation plus convection as in the actual nonuniform environment. Some references also use the terms 'equivalent temperature" or 'effective temperature' to describe combined effects of convective and radiant heat transfer. In design, operative temperature can be defined as the average of the mean radiant and ambient air temperatures, weighted by their respective heat transfer coefficients. The instrument used for assessing environmental thermal comfort in terms of operative temperature is called a eupatheoscope and was invented by A. F. Dufton in 1929. Mathematically, operative temperature can be shown as;

to=(hrtmr+hcta)hr+hc

where,

hc = convective heat transfer coefficient
hr = linear radiative heat transfer coefficient
ta = air temperature
tmr = mean radiant temperature

Or

to=(tmr+(ta×10v))1+10v

where,

v = air velocity
ta and tmr have the same meaning as above.

It is also acceptable to approximate this relationship for occupants engaged in near sedentary physical activity (with metabolic rates between 1.0 met and 1.3 met), not in direct sunlight, and not exposed to air velocities greater than 0.10 m/s (20 fpm).

to=(ta+tmr)2

where ta and tmr have the same meaning as above.

Measurement

Operative temperature can be determined by combining measurements of air temperature and mean radiant temperature (MRT). Air temperature can be measured by using conventional temperature sensors, which should be shielded from surrounding radiation to avoid measurement errors. MRT is more difficult to determine because it depends on the radiant exchange between an occupant and the surrounding surfaces.

A common method for estimating MRT uses a globe thermometer, consisting of a temperature sensor enclosed within a hollow, matte-black sphere. The instrument measures globe temperature, which is influenced by both radiation and convection. MRT can then be estimated by using globe temperature, air temperature, air velocity, globe diameter, and surface emissivity.

The accuracy of globe thermometer measurements is influenced by instrument characteristics and environmental conditions. Conventional globe thermometers can require approximately 20–30 minutes to respond to changes in the thermal environment, making them less suitable for rapidly changing conditions. Smaller globes respond faster but can introduce additional measurement uncertainties. Conventional corrections for convective heat transfer can systematically underestimate MRT under certain conditions.

MRT can also be estimated using simplified assumptions, such as treating it as equal to air temperature. However, different estimation methods and assumptions have been found to produce significant discrepancies compared with reference measurements in an office environment. These findings emphasize the importance of selecting appropriate measurement methods when determining operative temperature, especially in spaces with substantial differences between air and surrounding surface temperatures.

Since MRT is one of the main components used to determine operative temperature, errors in estimating it can also affect the calculated operative temperature. This is particularly important in environments where surrounding surfaces are much warmer or cooler than the air, because air temperature alone may not accurately represent the thermal conditions experienced by occupants.

Application

Operative temperature is used in heat transfer and thermal comfort analysis in transportation and buildings. Most psychrometric charts used in HVAC design only show the dry bulb temperature on the x-axis(abscissa), however, it is the operative temperature which is specified on the x-axis of the psychrometric chart illustrated in ANSI/ASHRAE Standard 55 – Thermal Environmental Conditions for Human occupancy.

See also

References

  1. 1 2 International Standard Organization (1998). "ISO 7726:1998 Ergonomics of the thermal environment -- Instruments for measuring physical quantities". {{cite journal}}: Cite journal requires |journal= (help)
  2. ↑ International Standard Organization (2005). "ISO 7730:2005 Ergonomics of the thermal environment -- Analytical determination and interpretation of thermal comfort using calculation of the PMV and PPD indices and local thermal comfort criteria". {{cite journal}}: Cite journal requires |journal= (help)
  3. ↑ ASHRAE Standard 55 (2013). "Thermal Environmental Conditions for Human Occupancy". {{cite journal}}: Cite journal requires |journal= (help)CS1 maint: numeric names: authors list (link)
  4. ↑ ASHRAE Terminology, ASHRAE Handbook CD, 1999-2002
  5. ↑ Nilsson, H.O., Comfort Climate Evaluation with Thermal Manikin Methods and Computer Simulation Models, National Institute for Working Life, 2004, pg. 37
  6. ↑ Thermal Comfort, ASHRAE Handbook, Fundamentals, Ch. 9, pg.3, 2009
  7. ↑ Glossary of Meteorology, American Meteorological Society, < "AMS Glossary". Archived from the original on 2011-05-14. Retrieved 2010-09-18.>, accessed Sept 2010
  8. ↑ International Standard Organization (1998). "ISO 7726:1998 Ergonomics of the thermal environment -- Instruments for measuring physical quantities". {{cite journal}}: Cite journal requires |journal= (help)
  9. ↑ ANSI/ASHRAE Standard 55-2010, Thermal Environmental Conditions for Human Occupancy
  10. 1 2 3 d’Ambrosio Alfano, Francesca Romana; Dell’Isola, Marco; Palella, Boris Igor; Riccio, Giuseppe; Russi, Aldo (2013). "On the measurement of the mean radiant temperature and its influence on the indoor thermal environment assessment". Building and Environment. 63: 79–88. doi:10.1016/j.buildenv.2013.01.026.
  11. 1 2 Özbey, Mehmet Furkan; Turhan, Cihan (2022). "A comprehensive comparison and accuracy of different methods to obtain mean radiant temperature in indoor environment". Thermal Science and Engineering Progress. 31: 101295. doi:10.1016/j.tsep.2022.101295. ISSN 2451-9049.{{cite journal}}: CS1 maint: article number as page number (link)
  12. ↑ Teitelbaum, Eric; Alsaad, Hayder; Aviv, Dorit; Kim, Alexander; Voelker, Conrad; Meggers, Forrest; Pantelic, Jovan (2022). "Addressing a systematic error correcting for free and mixed convection when measuring mean radiant temperature with globe thermometers". Scientific Reports. 12 (1). Nature Publishing Group: 6473. doi:10.1038/s41598-022-10172-5. ISSN 2045-2322. PMC 9019106. PMID 35440747.
  13. ↑ Dufton, A. F. The Equivalent Temperature of a room and its Measurement, Building Research Technical Paper No. 13. London, 1932