The treatment of radiative transport through combustion gases is rendered extremely difficult by the strong spectral variation of the absorption coefficients of molecular gases In the full spectrum correlated-k distribution (FSCK) approach, a transformation is invoked, whereby the radiative transfer equation (RTE) is transformed from wavenumber to non-dimensional Planck-weighted wavenumber space after reordering of the spectrum. The reordering results in a relatively smooth spectrum, allowing accurate spectral integration with very few quadrature points. The numerical procedures, required to use the FSCK model for full-scale combustion applications, have been outlined in this article. The FSCK model was first coupled with the Discrete Ordinates Method (DOM) for solution of the transformed RTE. The accuracy of the model was then examined for a variety of cases ranging from homogeneous one-dimensional media to inhomogeneous multi-dimensional media with simultaneous variations in both temperature and concentrations. Comparison with Line-by-line calculations shows that the FSCK model is exact for homogeneous media, and that its accuracy in inhomogeneous media is limited by the accuracy of the scaling approximation, Several approaches for effective seating of the absorption coefficient are examined. The model is finally used for radiation calculations in a full-scale combustor, with full coupling to fluid flow, heat transfer and multi-species chemistry. The computational savings resulting from use of the FSCK model is found to be more than four orders of magnitude when compared with line-by-line calculations.