Combustion process for iron particles burning in the gaseous oxidizing medium is investigated using the Boubaker polynomial expansion scheme (BPES) and the differential transformation method (DTM). Effects of thermal radiation from the external surface of burning particle and alterations of density of iron particle with temperature are considered. The solutions obtained using BPES technique and DTM are compared with those of the fourth-order Runge-Kutta numerical method. Results reveal that BPES is more accurate and reliable method than DTM. Also the effects of some physical parameters that appeared in mathematical section on temperature variations of particles as a function of time are studied. 1. Introduction Combustion of metallic particles is one of the most challenging issues in industries that manufacture, process, generate, or use combustible dusts, and an accurate knowledge of their explosion hazards is essential. Many studies have been done for estimating and modeling the particle and dust combustion. Haghiri and Bidbadi [1] investigated the dynamic behavior of particles across flame propagation through a two-phase mixture consisting of micro-iron particles and air. They assumed three zones for flame structure: preheat, reaction, and postflame (burned). Liu et al. [2] analyzed the flame propagation through hybrid mixture of coal dust and methane in a combustion chamber. A one-dimensional, steady-state theoretical analysis of flame propagation mechanism through microiron dust particles based on dust particles’ behavior with special remark on the thermophoretic force in small Knudsen numbers is presented by Bidabadi et al. [3]. Haghiri and Bidabadi [4] performed a mathematical model to analyze the structure of flame propagating through a two-phase mixture consisting of organic fuel particles and air. In contrast to previous analytical studies, they take thermal radiation effect into consideration, which has not been attempted before. Recently, Bidbadi and Mafi [5] solved the nonlinear energy equation that resulted from particle combustion modeling by using homotopy perturbation method (HPM), and they presented equations for calculating the convective heat transfer coefficient and burning time for iron particles. Because HPM needs perturbation and a small parameter, it can be solved by other high-accuracy analytical methods where in the present study two of them are presented and compared with fourth-order Runge-Kutta numerical method. Polynomial expansion methods are extensively used in many mathematical and engineering fields to yield meaningful
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