The Limiting Case of a Transparent Medium

The Limiting Case of a Transparent Medium For the special case of a transparent medium, K = 0, many practical engineering applications can be modeled with the zone method. These include combustion-fired muffle furnaces and electrical resistance furnaces. 

When K — 0, sg — Oand SG— 0. Equations (5-118) through (5-119) then reduce to three simple matrix relations  

The radiant surface flux vector Q, as computed from Eq. (5-122a), always satisfies the (scalar) conservation condition Im Q = 0 or  

LVi X Qi = 0, which is a statement of the overall radiant energy i= 1 The matrix conservation relations also simplify to balance. 

And the M x M arrays for all the direct and total view factors can be readily computed from 

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