Variational calculation of the effective emissivity for a random bed (Q1324649)

Rigorous variational upper bounds are formulated for the effective emissivity of an isothermal semi-infinite slab with an arbitrary void- solid distribution. Explicit calculations are given for a model pore structure, a semi-infinite slab cut from a bed of randomly placed freely overlapping solid spheres all of the same radius. The variational upper bound and a recently obtained lower, truncated multiple scattering summation bound provide a rigorous squeeze on the effective emissivity curves, which tightens with decreasing void fraction. These reciprocal bounds are compared with cell model and two-flux bed emissivities as well as available experimental data.