The concept of mean radiant temperature (MRT) is used to quantify the exchange of radiant heat between a human and their surrounding environment, with a view to understanding the influence of surface temperatures on personal comfort and heat stress. Mean radiant temperature has been both qualitatively defined and quantitatively evaluated for both indoor and outdoor environments. MRT 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 useful concept as the net exchange of radiant energy between two objects is approximately proportional to the product of their temperature difference multiplied by their emissivity (ability to emit and absorb heat). The MRT is the area weighted mean temperature of all the objects surrounding the body. This is meaningful as long as the temperature differences of the objects are small compared to their absolute temperatures, allowing linearization of the Stefan-Boltzmann Law in the relevant temperature range. MRT also has a strong influence on thermophysiological comfort indexes such as the predicted mean vote (PMV). What we experience and feel relating to thermal comfort in a built environment is related to the influence of, among other variables, both the air temperature and the temperature of surfaces in that space, represented by the mean radiant temperature. The MRT is affected by enclosure performances. The operative temperature, which is a more functional measure of thermal comfort in a building, is calculated from air temperature, mean radiant temperature and air speed. In mechanically conditioned office buildings, mean radiant temperature is often close to air temperature and, under typical office conditions, air temperature is usually a sufficient estimate of mean radiant temperature for thermal comfort estimation and control. In outdoor settings, mean radiant temperature is affected by air temperature but also by the radiation of absorbed heat from the materials used in sidewalks, streets, and buildings. It can be mitigated by tree cover and green space, which act as sources of shade and promote evaporative cooling. The experienced mean radiant temperature outdoors can vary widely depending on local conditions.
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:
M R T 4 = T 1 4 F p − 1 + T 2 4 F p − 2 + . . . + T n 4 F p − n {\displaystyle MRT^{4}=T_{1}^{4}F_{p-1}+T_{2}^{4}F_{p-2}+...+T_{n}^{4}F_{p-n}}
where:
M R T {\displaystyle MRT} is Mean Radiant Temperature;
T n {\displaystyle T_{n}} is the temperature of surface "n", in Kelvins;
F p − n {\displaystyle F_{p-n}} 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:
M R T = T 1 F p − 1 + T 2 F p − 2 + . . . + T n F p − n {\displaystyle MRT=T_{1}F_{p-1}+T_{2}F_{p-2}+...+T_{n}F_{p-n}}
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. There is currently no way to effectively collect this data. For this reason, an easier way to determine the MRT is by measuring it with a particular thermometer.
Measurement
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