An Analytical Solution For a Planar Nongray Medium in Radiative Equilibrium

The problem of energy transfer through a nongray absorbing and emitting medium, bounded by two black surfaces, in radiative equilibrium is investigated. A nearly exact analytical solution for the temperature distribution within the nongray medium is found by an asymptotic matching technique. The nongray characteristics of the medium are accounted for by using the exponential wide-band model. The analytical solution is valid for all optical thickness and has an error of less than 0.5 percent as compared to the existing numerical solution.