Nongray Particulate Radiation in an Isothermal Cylindrical Medium

Abstract

The radial radiative heat flux and its divergence are determined both exactly and approximately for homogeneous suspensions of small particles. Scattering is assumed to be small compared to absorption and the absorption coefficient is taken to be inversely proportional to wavelength. The exact solution is reduced to an infinite series of single integrals. The optically thin and the next higher order behavior appear in closed form as the first two terms in the series. Two approximate solutions are also developed. One is in good agreement with the exact solution while the other is not. Finally, a closed form approximate relation is derived for the dimensionless heat flux at the surface. This expression, which also gives the emissivity or absorptivity of the medium, is in excellent agreement with the exact result.