Discrete ordinates solution of axisymmetric radiative transfer within a condensed semitransparent medium having specularly reflecting boundaries

The axisymmetric transport of radiant energy within a condensed medium of cylindrical geometry is analyzed under the specular boundary condition. The numerical procedure employed to solve the radiative transfer equation utilizes the discrete ordinales method. The approach is validated by comparing the predicted results with the integral solution of one-dimensional radiative transfer within a semitransparent plate. An exponential-type interpolation scheme suggested models the spatial change in the radiative intensity better than the central or the upwind difference schemes for the tested ranges of the discretization parameters. A parametric study revealed that the assumption of one-dimensional radiative transfer can be successfully applied to the core portion of the cylindrical medium, which is more than five optical paths away from all of the transmitting interfaces, if the temperature distribution within the entire medium is one-dimensional.