Lambert radiator

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

The body has a diffuse radiating surface (Lambert radiator) then eA = eA(A, T) is valid. 

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... 

Fig. 5.31 Hemispherical spectral emissive power Mx(, T) = e(T) MXs(, T) of a grey Lambert radiator at a certain temperature...

Here, MXs(X,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 ... 

The model of a grey Lambert radiator, with a(T) = e(T) can therefore not be applied to the absorption of solar radiation. Rather, it is to be expected that the absorptivities deviate vastly from the tabulated emissivities. These absorptivities as for the absorption of predominantly short-wave solar radiation, generally... 

Radiative exchange between grey Lambert radiators... 

If the bodies participating in radiative exchange cannot be assumed to be black bodies, then the reflected radiation flows also have to be considered. In hollow enclosures, multiple reflection combined with partial absorption of the incident radiation takes place. A general solution for radiative exchange problems without simplifying assumptions is only possible in exceptional cases. If the boundary walls of the hollow enclosure are divided into isothermal zones, like in 5.5.2, then a relatively simple solution is obtained, if these zones behave like grey Lambert radiators. Each zone is characterised purely by its hemispherical total emissivity si — whilst at = is valid for its absorptivity, and for the reflectivity... 

For a grey Lambert radiator the absorptivity a for every incident radiation is the same as the emissivity i(Ti), so that (5.157) is once again yielded. 

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. 

A Lambert radiator emits radiation at a certain temperature only in the wavelength interval (Ai, A2), where its spectral intensity... 

What proportion AM of the emissive power M of a Lambert radiator falls in the portion of the hemisphere for which the polar angle is / < 30° ... 

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