Grey radiator

In many cases a simple assumption is made about the radiator it is treated as a grey radiator. This is only an approximation but it simplifies matters greatly. The absorptivity of a grey radiator does not depend on the type of incident radiation, and it always agrees with the emissivity, such that a = e. 

The difference between the fourth power of the temperature of the emitter and that of the body which receives the radiation, is characteristic of radiative exchange. This temperature dependence is found in numerous radiative heat transfer problems involving grey radiators. 

Example 1.2 A poorly insulated horizontal pipe (outer diameter d = 0.100m), with a surface temperature = 44 °C, runs through a large room of quiescent air at = 18 °C. The heat loss per length L of the pipe, Q/L has to be determined. The pipe is taken to behave as a grey radiator with emissivity s = 0.87. The walls of the room are treated as black surroundings which are at temperature = a = 18 °C. 

The directional spectral emissivity is independent of the wavelength A sA = s x(f3,cp,T). A body with this property is called a grey body or a grey radiator. 

Fig. 5.32 Approximately constant spectral emissivity for A > Ai as well as the pattern of the hemispherical spectral emissive power M and the spectral irradiance E, such that a grey radiator can be assumed...

Here, (5.75) has been used because a grey radiator (s x independent of A) is present. The temperature T of the satellite surface will then be... 

Surfaces with low emissivities often exhibit approximately mirrorlike or specular reflection rather than diffuse reflection. We want to investigate how the assumption of mirrorlike reflection affects the heat transfer. The assumptions regarding the emission of diffuse and grey radiation remain unaltered. Grey Lambert radiators with mirrorlike reflection are therefore assumed. 

Gases only absorb and emit radiation in narrow wavelength regions, so-called bands. Their spectral emissivities show a complex dependency on the wavelength, in complete contrast to solid bodies. This means that gases cannot be idealised as grey radiators without a loss of accuracy. 

A further problem in the calculation of radiative exchange is the consideration of the fact that gases only absorb and emit within certain wavelength intervals or bands. Here, sometimes the highly simplified assumption will be made that the gas behaves like a grey radiator. A better model of real radiation behaviour is band approximation. This is extensively discussed in [5.37], p. 549-567 and 607-609. 

A very long cylinder is struck by radiation that comes from a single direction, perpendicular to its axis (parallel directed radiation). The surface of the cylinder behaves like a grey radiator with the directional total emissivity = 0.85 cos/ . Calculate the reflected fraction of the incident radiative power. 

Two very thin, radiation protection shields, A and B, are positioned parallel to and between two very large, parallel plates at temperatures Ti = 750 K and T2 = 290 K. All surfaces are grey radiators with the same emissivity s = 0.82. 

This is the common ore of antimony, and is generally a dark grey radiated fusible ciystaHine mass, Sp. G. 4 62. When formed by the action of sulphuretted hydrogen on salts of antimony, it is precipitated as a hydrate, of a brownish orange colour,... 

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