Mean radiant temperature

Last updated June 21, 2024

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. Mean radiant temperature has been both qualitatively defined and quantitatively evaluated for both indoor and outdoor environments.^[1]^[2]^[3]

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 simply 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.^{[ citation needed ]}

MRT also has a strong influence on thermophysiological comfort indexes such as physiological equivalent temperature (PET) or predicted mean vote (PMV).^[5]

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, represented by the mean radiant temperature. The MRT is controlled by enclosure performances.^{[ citation needed ]}

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.^[6] Maintaining a balance between the operative temperature and the mean radiant temperature can create a more comfortable space.^[7] This is done with effective design of the building, interior and with the use of high temperature radiant cooling and low temperature radiant heating.^[8]

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. For example, measurements taken across Chapel Hill, North Carolina to examine urban heat island exposure ranged from 93 to 108 °F (34 to 42 °C).^[9]

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.^[1]^[2]

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.^[4] 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:^[4]^[10]

$MRT^{4}=T_{1}^{4}F_{p-1}+T_{2}^{4}F_{p-2}+...+T_{n}^{4}F_{p-n}$

where:

MRT

is Mean Radiant Temperature;

T_{n}

is the temperature of surface "n", in Kelvins;

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:^[4]^[10]

$MRT=T_{1}F_{p-1}+T_{2}F_{p-2}+...+T_{n}F_{p-n}$

This linear formula tends to give a lower value of MRT, but in many cases the difference is small.^[4]

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

The MRT can be estimated 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 15 centimetres (6 in), 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. ^[4] This thermometer actually measures the globe temperature (GT), 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.^[4] According to ISO 7726 Standard, the equation that is used most frequently (forced convection) is the following:

$MRT=\left[\left(GT+273.15\right)^{4}+{\frac {1.1\cdot 10^{8}\cdot v_{a}^{0.6}}{\varepsilon \cdot D^{0.4}}}(GT-T_{a})\right]^{1/4}-273.15$

When air velocity is less than 1m/s (natural convection), the equation is the following:

$MRT=\left[\left(GT+273.15\right)^{4}+{\frac {0.25\cdot 10^{8}}{\varepsilon }}\left({\frac {|GT-T_{a}|}{D}}\right)^{1/4}(GT-T_{a})\right]^{1/4}-273.15$

where:

MRT

is the mean radiant temperature (°C);

GT

is the globe temperature (°C);

v_{a}

is the air velocity at the level of the globe (m/s);

\varepsilon

is the emissivity of the globe (no dimension);

D

is the diameter of the globe (m);

T_{a}

is air temperature (°C);

And for the standard globe (D = 0.150 m, $\varepsilon$ = 0.95):

$MRT=\left[\left(GT+273.15\right)^{4}+2.5\cdot 10^{8}\cdot v_{a}^{0.6}(GT-T_{a})\right]^{1/4}-273.15$

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.^[10]

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.^[4]

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The Stefan–Boltzmann law, also known as Stefan's law, describes the intensity of the thermal radiation emitted by matter in terms of that matter's temperature. It is named for Josef Stefan, who empirically derived the relationship, and Ludwig Boltzmann who derived the law theoretically.

<span class="mw-page-title-main">Heat transfer</span> Transport of thermal energy in physical systems

Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. Engineers also consider the transfer of mass of differing chemical species, either cold or hot, to achieve heat transfer. While these mechanisms have distinct characteristics, they often occur simultaneously in the same system.

Thermal radiation is electromagnetic radiation emitted by the thermal motion of particles in matter. Thermal radiation transmits as an electromagnetic wave through both matter and vacuum. When matter absorbs thermal radiation its temperature will tend to rise. All matter with a temperature greater than absolute zero emits thermal radiation. The emission of energy arises from a combination of electronic, molecular, and lattice oscillations in a material. Kinetic energy is converted to electromagnetism due to charge-acceleration or dipole oscillation. At room temperature, most of the emission is in the infrared (IR) spectrum. Thermal radiation is one of the fundamental mechanisms of heat transfer, along with conduction and convection.

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In heat transfer, Kirchhoff's law of thermal radiation refers to wavelength-specific radiative emission and absorption by a material body in thermodynamic equilibrium, including radiative exchange equilibrium. It is a special case of Onsager reciprocal relations as a consequence of the time reversibility of microscopic dynamics, also known as microscopic reversibility.

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The wet-bulb globe temperature (WBGT) is a measure of environmental heat as it affects humans. Unlike a simple temperature measurement, WBGT accounts for all four major environmental heat factors: air temperature, humidity, radiant heat, and air movement. It is used by industrial hygienists, athletes, sporting events and the military to determine appropriate exposure levels to high temperatures.

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Operative temperature 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;

In radiometry, radiant exitance or radiant emittance is the radiant flux emitted by a surface per unit area, whereas spectral exitance or spectral emittance is the radiant exitance of a surface per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. This is the emitted component of radiosity. The SI unit of radiant exitance is the watt per square metre, while that of spectral exitance in frequency is the watt per square metre per hertz (W·m⁻²·Hz⁻¹) and that of spectral exitance in wavelength is the watt per square metre per metre (W·m⁻³)—commonly the watt per square metre per nanometre. The CGS unit erg per square centimeter per second is often used in astronomy. Radiant exitance is often called "intensity" in branches of physics other than radiometry, but in radiometry this usage leads to confusion with radiant intensity.

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The Gebhart factors are used in radiative heat transfer, it is a means to describe the ratio of radiation absorbed by any other surface versus the total emitted radiation from given surface. As such, it becomes the radiation exchange factor between a number of surfaces. The Gebhart factors calculation method is supported in several radiation heat transfer tools, such as TMG and TRNSYS.

The "radiation effect" results from radiation heat exchange between human bodies and surrounding surfaces, such as walls and ceilings. It may lead to phenomena such as houses feeling cooler in the winter and warmer in the summer at the same temperature. For example, in a room in which air temperature is maintained at 22 °C at all times, but in which the inner surfaces of the house is estimated to be an average temperature of 10 °C in the winter or 25 °C in the summer, heat transfer from the surfaces to the individual will occur, resulting in a difference in the perceived temperature.

Radiant heating and cooling is a category of HVAC technologies that exchange heat by both convection and radiation with the environments they are designed to heat or cool. There are many subcategories of radiant heating and cooling, including: "radiant ceiling panels", "embedded surface systems", "thermally active building systems", and infrared heaters. According to some definitions, a technology is only included in this category if radiation comprises more than 50% of its heat exchange with the environment; therefore technologies such as radiators and chilled beams are usually not considered radiant heating or cooling. Within this category, it is practical to distinguish between high temperature radiant heating, and radiant heating or cooling with more moderate source temperatures. This article mainly addresses radiant heating and cooling with moderate source temperatures, used to heat or cool indoor environments. Moderate temperature radiant heating and cooling is usually composed of relatively large surfaces that are internally heated or cooled using hydronic or electrical sources. For high temperature indoor or outdoor radiant heating, see: Infrared heater. For snow melt applications see: Snowmelt system.

In physics and engineering, the radiative heat transfer from one surface to another is the equal to the difference of incoming and outgoing radiation from the first surface. In general, the heat transfer between surfaces is governed by temperature, surface emissivity properties and the geometry of the surfaces. The relation for heat transfer can be written as an integral equation with boundary conditions based upon surface conditions. Kernel functions can be useful in approximating and solving this integral equation.

References

1 2 Guo, Hongshan; Aviv, Dorit; Loyola, Mauricio; Teitelbaum, Eric; Houchois, Nicholas; Meggers, Forrest (1 January 2020). "On the understanding of the mean radiant temperature within both the indoor and outdoor environment, a critical review". Renewable and Sustainable Energy Reviews. 117: 109207. doi: 10.1016/j.rser.2019.06.014 . ISSN 1364-0321. S2CID 208834605 . Retrieved 6 December 2022.
1 2 Bean, Robert (2010). "Mean Radiant Temperature (MRT) - Part I". Healthy Heating. Retrieved 6 December 2022.
↑ Di Napoli, Claudia; Hogan, Robin J.; Pappenberger, Florian (1 July 2020). "Mean radiant temperature from global-scale numerical weather prediction models". International Journal of Biometeorology. 64 (7): 1233–1245. doi: 10.1007/s00484-020-01900-5 . ISSN 1432-1254. PMC 7295834 . PMID 32274575.
1 2 3 4 5 6 7 8 "ISO 7726. Ergonomics of the thermal environment - Instruments for measuring physical quantities" . Geneva, Switzerland: International Organization for Standardization. November 1998. Current as of 2021.
↑ Fanger, P.O. (1970). Thermal Comfort: Analysis and Applications in Environmental Engineering. New York: McGraw Hill.
↑ Reynolds, Mike (8 February 2020). "Designing Homes for Human Comfort". ecoHOME.
↑ Matzarakis, Andreas. Estimation and Calculation of the Mean Radiant Temperature within Urban Structures.
↑ Mclntyre and Griffiths, D.A. and I.D. (1972). Subject Response to Radiant and Convective Environments.
↑ Waldrop, M. Mitchell (19 October 2022). "What can cities do to survive extreme heat?". Knowable Magazine. doi: 10.1146/knowable-101922-2 . Retrieved 6 December 2022.
1 2 3 2009 ASHRAE Handbook Fundamentals, ASHRAE, Inc., Atlanta, GA.

External links

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[Guo-1] 1 2 Guo, Hongshan; Aviv, Dorit; Loyola, Mauricio; Teitelbaum, Eric; Houchois, Nicholas; Meggers, Forrest (1 January 2020). "On the understanding of the mean radiant temperature within both the indoor and outdoor environment, a critical review". Renewable and Sustainable Energy Reviews. 117: 109207. doi: 10.1016/j.rser.2019.06.014 . ISSN 1364-0321. S2CID 208834605 . Retrieved 6 December 2022.

[Bean-2] 1 2 Bean, Robert (2010). "Mean Radiant Temperature (MRT) - Part I". Healthy Heating. Retrieved 6 December 2022.

[Di_Napoli-3] Di Napoli, Claudia; Hogan, Robin J.; Pappenberger, Florian (1 July 2020). "Mean radiant temperature from global-scale numerical weather prediction models". International Journal of Biometeorology. 64 (7): 1233–1245. doi: 10.1007/s00484-020-01900-5 . ISSN 1432-1254. PMC 7295834 . PMID 32274575.

[ISO_7726-4] 1 2 3 4 5 6 7 8 "ISO 7726. Ergonomics of the thermal environment - Instruments for measuring physical quantities" . Geneva, Switzerland: International Organization for Standardization. November 1998. Current as of 2021.

[5] Fanger, P.O. (1970). Thermal Comfort: Analysis and Applications in Environmental Engineering. New York: McGraw Hill.

[6] Reynolds, Mike (8 February 2020). "Designing Homes for Human Comfort". ecoHOME.

[7] Matzarakis, Andreas. Estimation and Calculation of the Mean Radiant Temperature within Urban Structures.

[8] Mclntyre and Griffiths, D.A. and I.D. (1972). Subject Response to Radiant and Convective Environments.

[Waldrop-9] Waldrop, M. Mitchell (19 October 2022). "What can cities do to survive extreme heat?". Knowable Magazine. doi: 10.1146/knowable-101922-2 . Retrieved 6 December 2022.

[2009_ASHRAE_Handbook-10] 1 2 3 2009 ASHRAE Handbook Fundamentals, ASHRAE, Inc., Atlanta, GA.

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