On computing radiative heat flux distributions using the F(N) method

An approach which avoids the computational problem encountered in the evaluation of heat fluxes internal to the medium from the primary results associated with the singular eigenfunction expansion, in solving one-dimensional planar media radiative transport problems using the F(N) method, is presented. Separate formulations for eigenvalues in the continuum range between -1 and 1, nu, above and below 0, result in an expression which avoids the numerical singularities in the limit as nu approaches 0. The method is demonstrated with F(9) computations performed using Simpson's rule with 200 uniformly equal intervals between 0 and 1, and computed boundary fluxes are found to agree with alternate expressions involving the F(N) coefficients.