The analysis of natural convection flow with radiation for a medium inside an triangular enclosure using natural element method

In this paper the natural element method is employed for study conductive, convective and radiative heat transfer for laminar flow in a triangular enclosure. The natural element method referred to as natural neighbor Galerkin method is a new technique in the field of computational mechanics and considered as a meshless numerical method. The shape functions used in natural element method, which are based on the Voronoi diagram of a set of nodes, are attentively interpolant and the essential boundary conditions can be imposed by directly substituting the corresponding terms in the system of equations. In this paper for solving radiative transfer equation used P_1 approximation. Effects of different parameters such as Rayleigh number for non-radiation and Planck number and mean temperature for radiation are considered. revealed that increasing the Rayleigh number, increases the strength of free convection regime and consequently increases the value of convective heat transfer rate. It is also revealed that decreasing the Planck number and mean temperature, increases the strength of Radiation regime and consequently increases the value of radiative heat transfer rate. Results for natural element method are compared with the another studys reported in the literatures. By comparison, it is shown that natural element method is efficient, accurate and stable, and can be used for heat transfer and fluid flow.