### 06.09.2017 - Operative Temperature / Mean Radian Temperature

Figure.Thermometer

# Operative temperature (air temperature + mean radiant temperature + air velocity)

Operative temperature is indictaion of thermal comfort comes from air temperature, mean radiant temperature and air speed. It is helpful to define or predict thermal comfort for occupants of a building. Basically,  thermal comfort is related with  environmental elements, which are air temperature, air velocity, relative humidity and the consolidation of conditions, also individual properties such as clothing, metabolic heat, acclimatisation, state of health. In many spaces, with low air velocity and where air temperature and mean radiant temperaturemay be similar, air temperature alone can be a reasonable indicator of thermal comfort. However, in spaces where surfaces may be heated or cooled, where there is significant thermal mass, or where solar radiation is present, air and radiant temperatures may be very different and so it is necessary to take account of radiant temperatures in assessing thermal comfort...

Calculation:
Operative temperature = (tr + (ta x √10v)) / (1+√10v)
Where  ta = air temperature / tr = mean radiant temperature / v = air speed (m/s)

Or

Operative temperature = (( hr x tr) + (hc x ta )) / ( hr + hc )
Where  hc = convective heat transfer coefficient /  hr = radiative heat transfer coefficient

Or

Operative temperature = (ta + tr)/2
Where the air speed is less than 0.1m/s, (as is typical in buildings) radiative and convective heat transfers may be similar, and so the equation can be simplified to:

Mean radiant temperature (MRT) is a measure of the average temperature of the surfaces that surround a particular point, with which it will exchange thermal radiation. If the point is exposed to the outside, this may include the sky temperature and solar radiation

Calculation:
Mean radiant temperature could be calculated by globe thermometer. This is a hollow copper sphere painted matt black (to give it a high emissivity) with a temperature sensor at its centre. From the temperature recorded, along with air velocity and air temperature. (needed to account for convective heat exchange)
MRT = globe temperature + 2.42 x air velocity in m/s (globe temperature  air temperature)

Or

The mean radiant temperature (MRT) is a means of expressing the influence of surface temperatures on occupant comfort. It can be calculated many ways. In its simplest and least accurate form it is a homogenous steady state area weighted average of the uncontrolled or unconditioned surface temperatures (AUST) written as
Tmr = T1A1  + T2A2  + …+ TNA / ( A1  + A2  + …+ AN  )
where,
Tmr = mean radiant temperature, °R
TN = surface temperature of surface N, °R (calculated or measured)
AN = area of surface