Heat Transfer in a Gray Planar Medium With Linear Anisotropic Scattering

Abstract

Radiative transfer in an absorbing and linearly-anisotropic scattering gray medium is analyzed. The medium is confined between plane parallel, gray, diffuse walls and contains uniform heat generation. The problem is formulated in terms of coupled integral equations with the intensity-moments as the unknown variables. The set of equations is solved both numerically and in closed form. The closed-form solution consists of exact limiting solutions and approximate general solutions obtained by the kernel-substitution method. The case of combined radiation and conduction is also treated. The results reveal clearly the effects of anisotropic scattering on important characteristics such as heat flux and incident radiant energy per unit area. The approximate closed-form solutions which predict quite well these effects are very simple and convenient to use for engineering calculations.