Radiative Heat Transfer Using Isotropic Scaling Approximation: Application to Fibrous Medium

The applicability of the isotropic scaling approximation to heat transfer analysis in fibrous medium is discussed. The isotropic scaling model allows the transformation of an anisotropic scattering problem to an isotropic one. The scaled parameters are derived for general anisotropic scattering and for radiative properties dependent of the incidence radiation. Three different isotropic scaling approaches are considered: Directional isotropic scaling, mean isotropic scaling, and P1 isotropic scaling; corresponding to isotropic scaling parameters function of incident radiation, arithmetic mean over all incident direction of radiative properties, and mean on weighted radiative properties, respectively. The discrete ordinate method is used to solve the radiative transfer equation through fibrous medium. The fibers in the medium are randomly oriented either in space or parallel to the boundaries. Numerical results presented for a pure radiation problem show good accuracy on radiative heat flux between the exact solution and solution obtained with both P1 and directional isotropic scaling while using mean isotropic scaling is unsuitable. Using isotropic scaling approximation to model radiative heat transfer is faster than the exact solution and required few quadratures to converge.