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### Mean Radiant Temperature Formula and Calculator

Mean Radiant Temperature Formula and Calculator

This is the uniform temperature of an imaginary black enclosure in which an occupant would exchange the same amount of radiant heat as in the actual nonuniform enclosure. Mean radiant temperature can be calculated from measured surface temperatures and the corresponding angle factors between the person and surfaces. It can also be determined from the plane radiant temperature in six opposite directions, weighted according to the projected area factors for a person.

Because of its simplicity, the instrument most commonly used to determine the mean radiant temperature is a black globe thermometer (Bedford and Warmer 1935; Vernon 1932). This thermometer consists of a hollow sphere usually 6 in. in diameter, coated in flat black paint with a thermocouple or thermometer bulb at its center. The temperature assumed by the globe at equilibrium results from a balance between heat gained and lost by radiation and convection.

Mean radiant temperatures are calculated from:

Equation 1
tr = [ ( tg + 459.67 )4 + ( 4.74 x 107 · Va0.6 ) / ( ε · D0.4 ) ( tg - ta ) ]1/4 - 459.67

Where:

tg = globe temperature, °F
Va = air velocity, fpm
ta = air temperature, °F
D = globe diameter, ft
ε = emissivity (0.95 for black globe)
459.67 = conversion farenheit to absolute temperature

According to Equation (1), air temperature and velocity around the globe must also be determined. The globe thermometer is spherical, but mean radiant temperature is defined in relation to the human body. For sedentary people, the globe represents a good approximation. For people who are standing, the globe, in a radiant nonuniform environment, overestimates the radiation from floor or ceiling; an ellipsoidal sensor gives a closer approximation. A black globe also overestimates the influence of short-wave radiation (e.g., sunshine). A flat gray color better represents the radiant characteristic of normal clothing (Olesen et al. 1989). The hollow sphere is usually made of copper, which results in an undesirably high time constant. This can be overcome by using lighter materials (e.g., a thin plastic bubble).

Related:

References:

• Matzarakis, Andreas. Estimation and Calculation of the Mean Radiant Temperature within Urban Structures .
• Fanger, P.O. (1970). Thermal Comfort: Analysis and Applications in Environmental Engineering