Two-dimensional radiative equilibrium of a gray medium in a plane layer bounded by gray nonisothermal walls

Radiative equilibrium temperature and surface heat flux distributions are calculated for an absorbing-emitting gray medium in an infinite plane layer bounded by gray diffuse walls with arbitrary temperature distributions. Superposition is used to obtain the solution for the differential approximation, which yields good accuracy for the optically thick medium. To also obtain accurate results for optically thin and intermediate regimes, the differential approximation is subsequently improved by a number of geometrical parameters, which are derived from the exact expression for the intensity. As an example, the case of constant temperature at the upper wall and a temperature step at the lower wall without heat generation in the medium is presented. Comparison with other available results shows excellent agreement.