A method for calculating the radiation power coefficients of black and gray bodies with dimensions commensurable with the radiated wavelengths

A technique is proposed and the calculations of the dependences of the emissivity of an abso-lute black body (BBB) on the size of the diaphragms of the emitting aperture are performed for hypothetical cases when the sizes of the diaphragms are commensurate with the emitted wavelengths, and the diaphragms are made of a dielectric opaque for radiation. The value of the cutoff wavelength  = 1.772A for the square aperture of the diaphragm was determined, where A is the side of the square and  = 1. 571D for the round hole. where D is the hole di-ameter, i.e. it is shown that the body cannot emit wavelengths λ greater than 1.772A in the case of a square hole and 1.571D in the case of a round hole. It is shown that if the “cut off” wavelengths made any significant contribution to the integral radiation of a blackbody with temperature T at standard diaphragm diameters (i.e., at diameters of much larger radiated wavelengths), then the emissivity of this body becomes less than unity and rapidly decreases when the size of the diaphragms is commensurate with . In these cases, such a body ceases to be an absolutely black body and the laws of Planck and Stefan–Boltzmann cannot be used to calculate the power of its radiation, but the technique proposed in this work can be used.

Thermal radiation ofsubwavelengthparticles

A method is proposed for calculating the dependences of the emissivity of subwavelength parti-cles (SP) from various materials in the form of disks, spheres, cubes and cylinders on their sizes (D) and temperature (T), for cases when external electromagnetic radiation practically does not affect their temperature. For all the listed types of particles, the cutoff wavelengths λcutoffdepending on the size of the SP and the particle shape coefficients ξare determined. With a decrease in the particle size, from the radiation spectrum, which was originally described by Planck's law, wavelengths exceeding λcutoffare gradually excluded. This leads to a decrease in the integral radiation, a decrease in the emissivity and a shift of the radiation spectrum to the blue region. A simple scheme is also proposed for determining ε -the emission coefficients of the midrange according to the calculated graph ε (U), where: U = (ξ × D × T) / B; B is the con-stant of the Wien displacement formula.

Correcting the Error in Measuring Radiation Received by a Person: Introducing Cylindrical Radiometers

Most human energy budget models consider a person to be approximately cylindrical in shape when estimating or measuring the amount of radiation that they receive in a given environment. Yet, the most commonly used instrument for measuring the amount of radiation received by a person is the globe thermometer. The spherical shape of this instrument was designed to be used indoors where radiation is received approximately equally from all directions. But in outdoor environments, radiation can be strongly directional, making the sphere an inappropriate shape. The international standard for measuring radiation received by a person, the Integral Radiation Measurement (IRM) method, yields a measure of the Mean Radiant Temperature (Tmrt). This method uses radiometers oriented in the four cardinal directions, plus up and down. However, this setup essentially estimates the amount of energy received by a square peg, not a cylinder. This paper identifies the errors introduced by both the sphere and the peg, and introduces a set of two new instrument that can be used to directly measure the amount of radiation received by a vertical cylinder in outdoor environments. The Cylindrical Pyranometer measures the amount of solar radiation received by a vertical cylinder, and the Cylindrical Pyrgeometer measures the amount of terrestrial radiation received. While the globe thermometer is still valid for use in indoor environments, these two new instruments should become the standard for measuring radiation received by people in outdoor environments.