Gray radiation transport in multi-dimensional stochastic binary media with material temperature coupling

Models for radiation transport through stochastic binary media are tested in two and three dimensions. Theoretical models for stochastic media transport usually assume Markovian processes and exponential chord length statistics that are not fully realizable in multi-dimensions. Therefore, the previous validation studies done using one-dimensional (1D) transport are not necessarily applicable to multi-dimensions. The work presented here analyzes pure radiation transport and radiation when it is coupled to material energy balance. The sensitivity to chord length statistics is found to be different for these two cases. The assumptions made to linearize the transport equation are discussed and results for both linear and nonlinear transport are shown. For the coupled radiation and material problem in 2D and 3D, the mean radiation field differs significantly from previous analyses done in 1D. The differences between 1D and multi-dimensions are discussed. Modeling of the mean radiation field in the parameter range explored can be achieved with a simple formula for the mean opacity when the opacities are constant in space and time. Temperature-dependent opacities in stochastic media require different formulas for the effective opacity.