Natural element method for coupled radiative and conductive heat transfer

Natural element method has been employed to solve two-dimensional coupled radiative and conductive heat transfer problems. Natural element method (NEM) is a kind of meshless method based on natural neighbor interpolation. Unlike most other meshless methods, the shape function used in NEM has interpolation property and its support domain is anisotropy. In the framework of NEM, the natural neighbor interpolations are employed to constructed shape function, such as Sibson interpolant and Laplace interpolant. Laplace interpolant is introduced in this paper, and the convergence property of it is investigated. The Galerkin weighted residual method is employed to discrete both the radiative heat transfer and energy equation. By using NEM, the coupled heat transfer problems in rectangular and cylindrical ring enclosures are solved. Correctness of the results is validated by comparison with those in the literature.