On the Normal-mode Expansion Technique for Radiative Transfer in a Scattering, Absorbing and Emitting Slab with Specularly Reflecting Boundaries

The normal-mode expansion technique has been used to solve the uncoupled radiative heat transfer problem for an absorbing, emitting, isotropically scattering, nonisothermal, gray medium confined between specularly reflecting, gray parallel boundaries held at uniform but different temperatures. Solutions are given for the intensity of radiation, the incident radiation and the net radiation heat flux for a prescribed inhomogeneous source term, represented by a polynomial expansion, in the medium. In addition the solution due to an arbitrary inhomogeneous source term is available from the Green’s function developed for the considered problem. NOMENCLATURE albedo, the ratio of the scattering to the extinction coefficient ; incident radiation ; radiation flux ; inhomogeneous source term ; temperatures of the boundary surfaces ; Case’s X-function ; emissivities of the boundary surfaces ; direction cosine ; optical variable ; optical thickness between the boundaries.