The Exact Solution to a Simple Nongray Radiative Transfer Problem

The problem of energy transfer through a nongray absorbing and emitting medium capable of generating heat is studied. The medium is bounded by two nongray surfaces which are opaque and diffuse. Radiative transfer theory is used to formulate the problem rigorously. The energy equation is transformed into two singular Fredholm integral equations for two universal functions. The universal functions are identical with those derived in the gray situation. The temperature distribution and radiative flux are presented graphically for the case of radiative equilibrium. The analysis is restricted to an absorption coefficient Kv of the Milne-Eddington type, i.e. Kv = α(v)β(T), and to the case when the ratio of heat generation rate per unit of volume S(T) to β(T) is a constant. Numerical results presented in the paper are limited to those of black walls and S = 0