The present study deals with analytical investigation of temperature of a single burning iron particle. Three mathematical methods including AGM (Akbari-Ganji’s method), CM (Collocation method) and GM (Galerkin Method) are applied to solving non-linear differential governing equation and effectiveness of these methods is examined as well. For further investigation, forth order Runge-Kutta approach, a numerical method, is used to validate the obtained analytical results. In the present study, the developed mathematical model takes into account the effects of thermal radiation, convective heat transfer and particle density variations during combustion process. Due to particles’ small size and high thermal conductivity, the system is assumed to be lumped in which the particle temperature does not change within the body and all of its regions are at the same temperature. The temperature distributions obtained by analytical methods have satisfactory agreement with numerical outputs. Finally, the results indicate that AGM is a more appropriate method than GM and CM due to its lower mean relative error and less run time.

本研究涉及单个燃烧的铁颗粒的温度的分析研究。分别采用AGM（Akbari-Ganji法），CM（配位法）和GM（Galerkin法）三种数学方法求解非线性微分控制方程，并检验了这些方法的有效性。为了进一步研究，使用了一种数值方法Runge-Kutta方法来验证所获得的分析结果。在本研究中，开发的数学模型考虑了燃烧过程中热辐射，对流传热和颗粒密度变化的影响。由于颗粒尺寸小且导热系数高，假定系统是集总的，其中粒子温度在体内不发生变化，并且其所有区域都处于同一温度。通过分析方法获得的温度分布与数值输出具有令人满意的一致性。最后，结果表明，AGM比GM和CM更合适，因为它的平均相对误差较低，运行时间较短。