Abstract

In the present paper we applied two well- known analytical method to the problem of thermal explosion of monodisperse and polydisperse fuel spray. The methods are the method of integral manifold (MIM) and the homotopy analysis method (HAM). The MIM method used as a basic tools for the analysis of SPS system of ordinary differential equations which means that the physical/ mathematical model should contain a small parameter in the governing equations. The HAM is always valid no matter whether there exist small physical parameters or not in contrast to the classical perturbation methods which requires the existence of a small parameter in the system (in general this is not the case). According to the theory of HAM, the convergence and the rate of solution series are dependent on the convergent control parameter h. This means that this parameter gives one a convenient way to adjust and to control the convergent region of the solutions.

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