Cavity radiators: an ecumenical theory.

Multiple reflection considerations give cavity emissivity as an infinite series of nested integrals. The Liou-ville-Neumann series solution to the Fredholm integral equation of the second kind gives the same series for integral equation formulation of the cavity problem when the walls are gray, Lambertian, and isothermal. A compact solution, derived from the series, stimulates interesting comparisons among the multiple reflection analyses of Gouffé, De Vos, Treuenfels, Kelly, and Bartell and Wolfe and the integral equation theories of Sparrow, Albers, and Eckert; Sparrow and Jonsson; Syndor; Bedford and Ma; and Chandos and Chandos.