The mean radiant temperature is defined as the uniform temperature of an
imaginary enclosure in which the radiant heat transfer from the human body is
equal to the radiant heat transfer in the actual non-uniform enclosure.
MRT is a concept arising from the fact that the net exchange of radiant energy
between two objects is approximately proportional to their temperature
difference multiplied by their ability to emit and absorb heat. It is simply
the area weighted mean temperature of all the objects surrounding the body.
This is valid as long as the absolute temperatures of objects in question are
large compared to the temperature differences, allowing linearization of
the Stefan-Boltzmann Law in the relevant temperature range.
MRT also has a strong influence on thermophysiological comfort indexes such
as physiological equivalent temperature or predicted mean vote.
What we experience and feel relating to thermal comfort in a building is related
to the influence of both the air temperature and the temperature of
surfaces in that space. The mean radiant temperature is expressed as this surface
temperature and is controlled by enclosure performances. Maintaining a
balance between the operative temperature and the mean radiant
temperature can create a more comfortable space. This is done with
effective design of the building, interior and with the use of high
temperature radiant cooling and low temperature radiant heating.
Calculation There are different ways to estimate the
mean radiant temperature, either applying its definition and using
equations to calculate it, or measuring it with particular thermometers or
sensors. Since the amount of radiant heat lost or
received by human body is the algebraic sum of all radiant fluxes exchanged by
its exposed parts with the surrounding sources, MRT can be calculated from the
measured temperature of surrounding walls and surfaces and their positions
with respect to the person. Therefore, it is necessary to measure those
temperatures and the angle factors between the person and the surrounding
surfaces. Most building materials have a high emittance ε, so all surfaces in the
room can be assumed to be black. Because the sum of the angle factors is unity,
the fourth power of MRT equals the mean value of the surrounding surface
temperatures to the fourth power, weighted by the respective angle
factors. The following equation is used:
where: is Mean Radiant Temperature;
is the temperature of surface "n", in Kelvins;
is the angle factor between a person and surface "n".
If relatively small temperature differences exist between the surfaces
of the enclosure, the equation can be simplified to the following linear form:
This linear formula tends to give a lower value of MRT, but in many cases
the difference is small. In general, angle factors are difficult
to determine, and they normally depend on the position and orientation of the
person.Furthermore, this method becomes complex and time consuming as the number
of surfaces increases and they have elaborate shapes. For this reason, an
easier way to determine the MRT is by measuring it with a particular
thermometer. Measurement
The MRT can be measured using a black-globe thermometer. The black-globe
thermometer consists of a black globe in the center of which is placed a
temperature sensor such as the bulb of a mercury thermometer, a thermocouple or a
resistance probe. The globe can in theory have any diameter but as the
formulae used in the calculation of the mean radiant temperature depend on the
diameter of the globe, a diameter of 0.15 metres, specified for use with
these formulae, is generally recommended. The smaller the diameter of
the globe, the greater the effect of the air temperature and air velocity, thus
causing a reduction in the accuracy of the measurement of the mean radiant
temperature. So that the external surface of the globe absorbs the
radiation from the walls of the enclosure, the surface of the globe
shall be darkened, either by the means of an electro-chemical coating or, more
generally, by means of a layer of matte black paint. This thermometer actually
measures the globe temperature, tending towards thermal balance under the effect
of convection and radiation coming from the different heat sources in the
enclosure. Thanks to this principle, knowing GT allows the mean radiant
temperature MRT to be determined. According to ISO 7726 Standard, the
equation that is used most frequently is the following:
where: is the mean radiant temperature;
is the globe temperature; is the air velocity at the level of the
globe; is the emissivity of the globe;
is the diameter of the globe; is air temperature;
And for the standard globe: The measurement is affected by air
movement because the measured GT depends on both convection and radiation
transfer. By effectively increasing the size of the thermometer bulb, the
convection transfer coefficient is reduced and the effect of radiation is
proportionally increased. Because of local convective air currents GT
typically lies between the air temperature and MRT. The faster the air
moves over the globe thermometer, the closer GT approaches the air
temperature. Moreover, since the MRT is defined with
respect to the human body, the shape of the sensor is also a factor. The
spherical shape of the globe thermometer gives a reasonable approximation of a
seated person; for people who are standing, the globe, in a radiant
nonuniform environment, overestimates the radiation from floor or ceiling, so
an ellipsoid sensor gives a better approximation.
There are several other precautions to be taken when using a black-globe
thermometer, depending on the conditions of the measurement. Furthermore, there
are different measuring methods, such as the two-sphere radiometer and the
constant-air-temperature sensor. See also
Thermal comfort Heating, Ventilation and
Air-Conditioning ASHRAE
Glossary of HVAC References
^ a b c d e f g h "ISO 7726. Ergonomics of the thermal environment - Instrument
for measuring physical quantities". Geneva, Switzerland: International
Organization for Standardization. November 1998.
^ Fanger, P.O.. Thermal Comfort: Analysis and Applications in
Environmental Engineering. New York: McGraw Hill.
^ Matzarakis, Andreas. Estimation and Calculation of the Mean Radiant
Temperature within Urban Structures. ^ Mclntyre and Griffiths, D.A. and I.D..
Subject Response to Radiant and Convective Environments.
^ a b c 2009 ASHRAE Handbook Fundamentals, ASHRAE, Inc., Atlanta, GA.
External links o.human.cornell.edu/DEA3500allnotes.html
Free online thermal comfort and mean radiant temperature calculation tool
developed by CBE at UC Berkeley