Natural element method for radiative heat transfer in two-dimensional semitransparent medium

The natural element method (NEM) is employed for solving radiative heat transfer problem in a two-dimensional enclosure containing an absorbing, emitting and isotropically scattering medium. Medium boundaries are considered to be opaque, diffuse as well as gray. The NEM referred to as natural neighbor Galerkin method is a new technique in the field of computational mechanics and can be considered as a meshless numerical method. Unlike most of other meshless methods such as element-free Galerkin method or those based on radial basis functions, the shape functions used in NEM, which are based on the Voronoi tesselation of a set of nodes, are strictly interpolant and the essential boundary conditions can be imposed by directly substituting the corresponding terms in the system of equations. Three types of radiative heat transfer problems are addressed. For pure radiation, studies are made for three representative benchmark problems dealing with radiative equilibrium and non-radiative equilibrium. For coupled heat transfer, transient conduction and radiation problem in a rectangular geometry, steady conduction and radiation problem in a gray cylindrical ring are solved. For these problems considered, tests are presented for various parameters, such as the aspect ratio, conduction-radiation parameter, optical thickness, scattering albedo and surface emissivity. Results for NEM are compared with those for finite element method (FEM) generated by the authors and those reported in the literatures. By comparison, it is shown that NEM is efficient, accurate and stable, and can be used for solving radiative heat transfer problem in 2-D semitransparent media.