A modification of the cumulative wavenumber method to compute the radiative heat flux in non-uniform media

This paper presents a modification of the cumulative wavenumber (CW) method to determine the radiative heat flux in non-uniform participating gases. Previous works in the literature have shown that the CW method renders accurate estimates of the radiative volumetric heat source in the medium. However, as will be shown in this work, the radiative heat flux can present considerable deviation of the correct solution, which results from the radiative energy balance not being satisfied by the CW method. A modification of the method is devised in this work to satisfy the radiative energy balance while keeping the same value of the radiative volumetric heat source. The proposed methodology is applied together with the discrete ordinates method to solve the radiation heat transfer in a one-dimensional slab containing a non-isothermal layer of carbon dioxide. The results are compared to the benchmark line-by-line (LBL) integration, and show that the modified CW method can satisfy the radiative energy balance, improving the estimation of the radiative heat flux in the medium.