Transient coupled heat transfer in a rectangular medium with black surfaces

The main objective of this paper is to extend to two-dimensional (2-D) medium the ray tracing-node analyzing method, which has already been successfully used to solve one-dimensional (1-D) problem of coupled heat transfer in a semitransparent medium. For simplicity, an infinitely long rectangular semitransparent medium with four black opaque surfaces is chosen as our studying object. A control volume method in the implicit scheme is adopted for discretizing the partial transient energy equation. In combination with spectral band model, the radiative heat source term is calculated using the radiative transfer coefficients (RTCs), which are deduced by the ray tracing method. The Partankar's linearization method is used to linearize the radiative source term and the opaque boundary condition, and the linearized equations are solved by the ADI method. Effects of absorption coefficient, refractive index and conductivity on transient cooling process in the 2-D gray rectangular medium are investigated under the condition that the radiation and convection processes cool one side of the rectangular medium while heat the remaining three sides.