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This work uses the mathematical machinery of Renewal/Ruin (surplus risk)theory to derive preliminary explicit estimations for the radiative propertiesof dilute and disperse porous media otherwise only computable accurately withMonte Carlo Ray Tracing (MCRT) simulations. Although random walk and Levyprocesses have been extensively used for modeling diffuse processes in varioustransport problems and porous media modeling, relevance to radiation heattransfer is scarce, as opposed to other problems such as probe diffusion andpermeability modeling. Furthermore, closed form derivations that lead totangible variance reduction in MCRT are widely missing. The particular angle ofsurplus risk theory provides a richer apparatus to derive directly relatedquantities. To the best of the authors' knowledge, the current work is the onlywork relating the surplus risk theory derivations to explicit computations ofray tracing results in porous media. The paper contains mathematicalderivations of the radiation heat transfer estimates using the extractedmachinery along with proofs and numerical validation using MCRT.

Precise Derivations of Radiative Properties of Porous Media Using Renewal Theory