Radiation and Conduction in an Isotropic Scattering Rectangular Medium With One Semitransparent and Diffusely Reflecting Boundary

Abstract

Using the ray tracing-node analyzing method, the 2D transient coupled radiative and conductive heat transfer in a rectangular semitransparent medium is investigated. The rectangular medium has one semitransparent and diffuse boundary (the other three boundaries are black) and is isotropically scattering. The transient differential energy equation is discretized by the fully implicit finite difference method, and the radiative source term of the energy equation is expressed by the radiative transfer coefficients (RTCs). The integrality and reciprocity relationships of the RTCs without considering scattering for the 2D physical model are discovered, which are much different from those for the 1D case. When solving the isotropic scattering RTCs, the RTCs without considering scattering are normalized at first, and then the normalized RTCs are used to trace the energy scattered by control volumes. Finally, the isotropic scattering RTCs are solved by reverse calculation. The Patankar’s linearization method is used to linearize the radiative source term and the opaque boundary conditions, and the boundary conditions are dealt with an additional source term method. The alternating direction implicit method is applied to solve the nominal linearized equations. The effects of scattering albedo, extinction coefficient, refractive index, etc., on transient coupled heat transfer are studied. The study shows that when the extinction coefficient is so small, the increase in scattering albedo can intensify the cooling of the three black surfaces of the rectangular medium.