Radiation Exchange with Specular Surfaces

All the preceding discussions have considered radiation exchange between diffuse surfaces. In fact, the radiation shape factors defined by Eq. (8-21) hold only for diffuse radiation because the radiation was assumed to have no preferred direction in the derivation of this relation. In this section we extend the analysis to take into account some simple geometries containing surfaces that may have a specular type of reflection. No real surface is completely diffuse or completely specular. We shall assume, however, that all the surfaces to be considered emit radiation diffusely but that they may reflect radiation partly in a specular manner and partly in a diffuse manner. We therefore take the reflectivity to be the sum of a specular component and a diffuse component  

The net heat lost by a surface is the difference between the energy emitted and absorbed  

It is still assumed that KirchhofTs identity applies so that 

We define the diffuse radiosity Jn as the total diffuse energy leaving the surface per unit area and per unit time, or 

Equation (8-77) expresses the diffuse radiation leaving 1 which arrives at 2 and which may contribute to a diffuse radiosity of surface 2. The factor 1 - ps represents the fraction absorbed plus the fraction reflected diffusely. The inclusion of this factor is most important because we are considering only diffuse direct exchange, and thus must leave out the specular-reflection contribution 

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