In this paper, combustion process for iron particles burning in the gaseous oxidizing medium due to radiation is investigated by three weighted residual methods (WRMs) called Galerkin method (GM), least square method (LSM) and collocation method (CM). The effect of thermal radiation from the external surface of burning particle and variations of density of iron particle with temperature are considered. The solutions obtained by WRMs techniques are compared with those of the fourth order Runge–Kutta numerical method. Results show that LSM has the most accurate results among other WRMs. Also, results show that by increasing the heat realized parameter (Ψ), combustion temperature increased and it faster reaches to its constant value.