Analysis of radiative transfer in cylindrical enclosures using the finite volume method

Radiative heat transfer in a cylindrical enclosure with or without a concentric cylinder containing absorbing-, emitting-, and isotropically- or anisotropically-scattering media is studied by using the finite volume method (FVM) for radiation. Since the unit direction vector is defined with respect to the Cartesian base vectors, the intrinsic difficulty in treating an angular derivative encountered in the discrete ordinates method (DOM) does not arise in the FVM. For the special case of an axisymmetric cylinder, a mapping, which transforms the dependence of intensity on two-spatial and two-angular to three-spatial and one-angular variables, was adopted. The scattering phase function is approximated by a finite series of Legendre polynomials. Several solutions are obtained in axisymmetric as well as three-dimensional cylindrical geometries with participating media and compared with others obtained by different methods, which are unique in this work. The computational efficiency of the FVM is discussed by comparison with the DOM. The problem of control angle overlaps is also examined in the last example by changing the angular grid systems.