Conductive-radiative heat transfer in an inhomogeneous slab with directional reflecting boundaries

Conductive-radiative heat transfer through an inhomogeneous, anisotropic scattering, turbid plane-parallel medium is considered. The medium is taken to be of diffuse and specular reflecting boundaries. The specular reflecting coefficients of the boundaries are considered to be angular dependent. The variational technique is used to solve the radiative problem while an iterative method is taken to include the nonlinearity effect of the temperature distribution of the medium from the conductive energy equation. The dimensionless temperature distribution and conductive, radiative and total net fluxes through the medium are calculated. The calculations for matched boundaries and a homogeneous, isotropic scattering slab are calculated and compared with other calculations to show good agreement. The calculations are carried out for mismatched boundaries, with homogeneous and inhomogeneous media. The results are given for isotropic and forward linear anisotropic scattering slabs.