Algebraic Formulas for a Single Gas Zone

The Limiting Case M = 1 and N = 1 The directed exchange areas for this special case correspond to a single well-mixed gas zone completely surrounded by a single surface zone A2. ffere the reflectivity matrix is a 1 x 1 scalar quantity which follows directly from the 

The results of this development may be further expanded into algebraic form with the aid of Eq. (5-127) to yield the following 

Put N = 1 and M = 2, and let zone 2 represent the refractory surface. Let Q2 = 0 and e2 0, and it then follows that we may define a refractory-aided directed exchange area SyGjjby 

Assuming radiative equilibrium, the emissive power of the refractory may also be calculated from the companion equation 

---