Nodal synthetic kernel (N-SKN) method for solving radiative heat transfer problems in one- and two-dimensional participating medium with isotropic scattering

Abstract

In this study, a nodal method based on the synthetic kernel (SKN) approximation is developed for solving the radiative transfer equation (RTE) in one- and two-dimensional cartesian geometries. The RTE for a two-dimensional node is transformed to one-dimensional RTE, based on face-averaged radiation intensity. At the node interfaces, double P1 expansion is employed to the surface angular intensities with the isotropic transverse leakage assumption. The one-dimensional radiative integral transfer equation (RITE) is obtained in terms of the node-face-averaged incoming/outgoing incident energy and partial heat fluxes. The synthetic kernel approximation is employed to the transfer kernels and nodal-face contributions. The resulting SKN equations are solved analytically. One-dimensional interface-coupling nodal SK1 and SK2 equations (incoming/outgoing incident energy and net partial heat flux) are derived for the small nodal-mesh limit. These equations have simple algebraic and recursive forms which impose burden on neither the memory nor the computational time. The method was applied to one- and two-dimensional benchmark problems including hot/cold medium with transparent/emitting walls. The 2D results are free of ray effect and the results, for geometries of a few mean-free-paths or more, are in excellent agreement with the exact solutions.