Meshless local Petrov–Galerkin approach for coupled radiative and conductive heat transfer

A meshless local Petrov–Galerkin approach is employed for solving the coupled radiative and conductive heat transfer in absorbing, emitting and scattering media. The meshless local Petrov–Galerkin approach with upwind scheme for radiative transfer is based on the discrete ordinate equations. The moving least square approximation is used to construct the shape function. Three particular test cases for coupled radiative and conductive heat transfer are examined to verify this new approximate method. The dimensionless temperatures and the dimensionless heat fluxes are obtained. The results are compared with the other benchmark approximate solutions. By comparison, the results show that the meshless local Petrov–Galerkin approach has a good accuracy in solving the coupled radiative and conductive heat transfer in absorbing, emitting and scattering media.