Radiation heat transport in disordered media

Radiation heat transport through the internal void spaces of particle beds, fiber beds, packed beds, reactors and porous media with opaque, diffusely reflecting, gray body surfaces and large solid dimensions (pi d/lambda(th) > 100) is considered. A variational principle formulated for the effective radiation conductivity, based on the local particle surface radiosity, differential view factor and solid temperature, permits a rigorous solution of the dependent, long range multiple scattering problem. The conductivity results, applied to a bed of randomly overlapping spheres, agree exactly with pseudohomogeneous results in both the isotropic and anisotropic scattering limits and shed rigorous light on the anisotropic phase function expansion theory. Explicit calculations, performed for several other standard packings, e.g. fiber beds, exhibit a parallel upper and series lower bound over the various particle shapes and dispersion structures. Results show that an empirical equation first suggested by Vortmeyer (German Chem. Engng, 3, (1980) 124-137), but generalized herein from one P to four P-0, P-1, P-2, P-3 coefficients, which vary substantially with the various industrial packings, will provide a suitable generalization of the emissivity factor of k(rad) for engineering conductivity modeling of radiation heat transport. Copyright (C) 1996 Elsevier Science Ltd