Finite Volume Method for Radiation Heat Transfer in Graded Index Medium

Abstract

Because a ray goes along a curved path determined by the Fermat principle, curved ray tracing is very difficult and complex in a graded index medium. To avoid the complicated and time-consuming computation of curved ray trajectories, a finite volume formulation is developed to solve the radiative-transfer problem in a multidimensional absorbing-emitting-scattering semitransparent graded index medium. Three test problems in radiative transfer are taken as examples to verify this finite volume formulation. The predicted temperature distributions and apparent directional emissivity are determined by the proposed method and compared with data in the references. The results show that the finite volume formulation presented in this paper has a good accuracy in solving the radiative transfer problem in a multidimensional absorbing-emitting-scattering semitransparent graded index medium. Nomenclature A = surface area of cell, m 2 b = asymmetry factor of scattering D = direction cosine integrated over control solid angle Erms = rms error of apparent directional emissivity, defined in Eq. (27) ei = unit outward normal vector at the ith surface of cell volume H = height of medium, m I = radiative intensity, W/m 3 sr Ib = blackbody radiative intensity, W/m 3 sr