Natural element method for solving radiative transfer with or without conduction in three-dimensional complex geometries

Abstract

A meshless method called as the natural element method (NEM) is developed for solving radiative heat transfer problem in 3D complex enclosures filled with an absorbing, emitting and scattering medium. The boundary surfaces are supposed to be opaque, diffuse as well as gray. The shape functions used in NEM are constructed by the natural neighbor interpolations, which are strictly interpolant and the essential boundary conditions can be imposed directly. The NEM solutions dealing with the radiative heat transfer with or without conduction are validated by comparison with some cases reported by the literature. Furthermore, the radiative heat transfer in cubic enclosures with or without an inner hollow sphere, cylinder and elliptical cylinder is also examined to demonstrate the applicability of the present method towards various three-dimensional geometries. For pure radiative transfer, both the cases of radiative non-equilibrium and radiative equilibrium are investigated. For combined conduction and radiation heat transfer, effects of various parameters such as the conduction–radiation parameter, the scattering albedo, the extinction coefficient, and the boundary emissivity are analyzed on the temperature distributions.