The Zone Method and Directed Exchange Areas

The Zone Method and Directed Exchange Areas Spectral dependence of real gas spectral properties is now introduced into the zone method via the WSGG spectral model. It is still assumed, however, that all surface zones are gray isotropic emitters and absorbers. 

Having formulated the directed exchange areas, the governing matrix equations for the radiative flux equations at each surface zone and the radiant source term are then given as follows  

It may be proved that the Q and S vectors computed from Eqs. (5-162) and (5-163) always exactly satisfy the overall (scalar) radiant energy balance Im Q = lJ)-S. In words, the total radiant gas emission for all gas zones in the enclosure must always exactly equal the total radiant energy received at all surface zones which comprise the enclosure. In Eqs. (5-162) and (5-163), the following definitions are employed for the four forward-directed exchange areas 

Subject to the restrictions of no scatter and diffuse surface emission and reflection, the above equations are the most general matrix statement possible for the zone method. When P = 1, the directed exchange areas all reduce to the total exchange areas for a single gray gas. If, in addition, K = 0, the much simpler case of radiative transfer in a transparent medium results. If, in addition, all surface zones are black, the direct, total, and directed exchange areas are all identical. 

Allowance for Flux Zones As in the case of a transparent medium, we now distinguish between source and flux surface zones. Let M = MS + Mf represent the total number of surface zones where Ms is the number of source-sink zones and My is the number of flux zones. The flux zones are the last to be numbered. To accomplish this, partition the 

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