Solution of directional emissivity from isothermal dispersions by source function expansion technique

A source function expansion in terms of Legendre polynomials is used in a study of the directional emissivity of an absorbing, isotropically scattering slab. Dimensionless radiative transfer and boundary equations are defined and the reflectance distribution is expressed by Fresnel's Law. The source function expansion is then developed for solving an integral equation for the intensity of the reflected radiation. Sample results are provided for the emissivity of a slab with free boundaries, the effects of albedo, optical thickness and the refractive index on the directional emissivity from a slab with reflecting boundaries, and the variation of directional emissivity with changes in the refractive index. It is noted that the directional emittance decreases with increasing albedo.