Simulations of coupled radiative and convective heat transfer in 2D and 3D semitransparent medium by the moving least square method

The aim of the paper is to use the moving least square meshless method to study the coupled problem between radiation and natural convection in semitransparent medium of 2D and 3D geometries. The flow is incompressible, laminar, and governed in the vorticity-stream function formulation (2D) and vorticity-vector potential formulation (3D) of Navier-Stokes equations. We use the discrete ordinate method to solve the radiative transfer equation. We study the influence of optical thickness, albedo, heat source, and geometry shape to the flow patterns and temperature distributions. The examples (square, cylindrical ring, and cubic) are taken to compare to the references to check the performance of the proposed method. The results show that the moving least square meshless method is capable to deal with the coupled radiation and natural convection with stability and accuracy.