The grey Lambert radiator

In radiative exchange calculations, it is preferable to use the model, described in the previous section, of a grey, diffuse radiating body as a simple approximation for the radiative behaviour of real bodies. As Lambert s cosine law is valid for this model, we denote these bodies as grey Lambert radiators. The energy radiated from them is distributed like that from a black body over the directions in 

T) is the Planck function according to (5.50). The emissivity e(T) is the only material function of a grey Lambert radiator all four emissivities are equal and the same as the four absorptivities  

Example 5.4 A material has a directional spectral emissivity that only depends on the polar angle / s x A,P,ip,T) = s (P). This directional dependence is given by 

The external skin of a satellite is made of this material and is exposed to solar radiation with a flux density qso = 1500 W/m2. What temperature does the surface of the satellite assume, when it is hit perpendicularly by the solar radiation What temperature develops when the surface forms an angle of 7r/6 = 30° with the direction of the solar radiation A heat flow between the surface and the inside of the satellite can be neglected the temperature of space may be assumed to be Tw = 0 K. 

Under the assumptions given, the emissive power M(T) = crTA of the satellite surface has to be equal to the energy flux jabs that it absorbs from the incident solar radiation  

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The relationships between emissivity, absorptivity and reflectivity. The grey Lambert radiator... 

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