Heat Transfer by Conduction and Radiation in a One-Dimensional Absorbing, Emitting and Anisotropically-Scattering Medium

Abstract

Heat transfer by simultaneous conduction and radiation in an absorbing, emitting and anisotropically-scattering material is investigated theoretically. Consideration is given to a one-dimensional system bounded by two parallel gray, diffuse and isothermal walls. Assuming a physical model of linear-anisotropic scattering, the resulting integral-differential equation is solved by a successive approximation technique similar to the method of undetermined parameters. The solution method is demonstrated to be relatively simple and yields solution converging qucikly to the exact results. Results show that for the present one-dimensional system, the common approach of treating the total heat transfer as a simple addition of separate independent contributions from conduction and radiation is quite inaccurate for certain cases. This approach is thus ineffective in illustrating the general effect of scattering. Both the scattering albedo and the forward-backward scattering parameters are shown to have some interesting effects on the total heat transfer and the medium’s temperature. The magnitude of these effects depends on the surface emissivity of the two boundaries.