Emissivity of Isothermal Cavities

The emissivity of a unit area of the opening of a cavity ∊c is a function of its geometry as well as of the emissivity of its walls ∊0.If fn is a fraction of incident radiation which is reflected n times before emerging from the cavity, then ρc=∑fnρ0n is the reflectance, and ∊c=1−ρc is the effective emissivity. Under diffuse reflection f1=∫F2dA/∫FdA, where F is the viewfactor from cavity wall to open space. If fn=(1−f1)n−1f1 then ∊c=∊0/[∊0+f1(1−∊0)]. The approximation is good in the domain of low reflectivity. The f1 have been calculated for a variety of cavity shapes.