A finite-volume scheme for radiative heat transfer in semitransparent media

Radiation in semi-transparent media occurs in a variety of industrial applications. In the HVAC area, the selective transmission of thermal radiation through windows governs the heat load of rooms. In fiber drawing applications, the rate of quenching of the semi-transparent glass fiber is critically dependent on the radiant exchange with the hot furnace. In ceramics processing, the high index of refraction leads to strong internal reflection effects, and greatly influences the thermal field. It would be useful to develop numerical methods for computing this type of radiation heat transfer in the complex geometries encountered in most industrial applications. Here, a procedure for computing radiation in semi-transparent media is presented. A conservative cell-based finite volume method is developed for unstructured meshes composed of arbitrary polyhedra. The angular domain is discretized into a finite number of control angles over which radiant energy is conserved. At Fresnel interfaces, numerical procedures are developed to conservatively transfer radiant energy from one angular direction to another as a result of reflection and refraction, while accounting for control angle overhang. Similar procedures are also employed at specular surfaces and symmetry boundaries. The method is tested against analytical solutions and shown to perform satisfactorily.