Conduction and radiation in a rectangular isotropic scattering medium with black surfaces by the RTNAM

The ray tracing-node analyzing method (RTNAM) has been successfully developed to solve 1-D coupled heat transfer in isotropic and anisotropic scattering media in the past, and in this paper it is further extended to solving the 2-D coupled heat transfer in a rectangular isotropic scattering medium. Using the control-volume method, the partial transient energy equation is discretized in implicit scheme. The effect of radiation on heat transfer is considered as a radiative source term (RST) in the discretized energy equation, and in combination with spectral band model, the RST is calculated using the radiative transfer coefficients (RTCs), which are deduced by the ray tracing method. The Patankar's linearization method is used to linearize the RST and the opaque boundary condition, and the linearized equations are solved by the ADI method. Before solving the RTCs for isotropic scattering media, the RTCs without considering scattering must be solved at first. And then, the RTCs without considering scattering are normalized according to their integrality relationships. In addition, the correctness of the results obtained by the RTNAM is validated, and effects of scattering albedo and refractive index on transient temperature distribution are investigated.