A parametric study of radiative transfer with anisotropic scattering in a one-dimensional system.

Radiative heat transfer in an absorbing, emitting, anisotropically scattering, one-dimensional medium is analyzed. Unlike many of the existing works, the present analysis does not require a known temperature distribution within the medium. Assuming a model of linear anisotropic scattering, the transfer equation and the energy equation are solved simultaneously by utilizing a recently developed successive approximation technique. Closed-form approximate solutions and accurate higher-order results are both presented. Calculations show that the relative importance of the anisotropic scattering effect generally decreases with decreasing wall emissivity and decreasing optical thickness. For radiative equilibrium without internal heat generation, it is demonstrated that the anisotropic-scattering heat-transfer results can be approximated quite adequately by the isotropic-scattering result with the introduction of the concept of an effective optical thickness. For media with internal heat generation, an interesting effect of the scattering albedo is observed. It is established that, in the limit of a large scattering albedo, the temperature of the medium approaches a constant value that is independent of anisotropic-scattering effects and wall emissivity. The exact limiting expressions for the temperature and apparent emissivity of an isothermal slab are found.