Comparison of the Homotopy Perturbation Method (HPM) and Method of Integral Manifolds (MIM) on a Thermal Explosion of Polydisperse Fuel Spray System

The aim of this work is to carry out a comparative analysis of a more recent homotopy perturbation method and the method of integral manifolds for solving the problem of thermal explosion in a combustible mixture containing vaporizing fuel droplets of different radii, i.e., polydisperse fuel spray. The model under consideration, known as parcel approximation, is a system of nonlinear ordinary differential equations. Our results include a comparative analysis between the following models: (1) the parcel model, which is solved numerically, by applying the method of integral manifolds for zero-order and third-order approximation and by applying the homotopy perturbation method, and (2) the continuous model, which is solved by Runge--Kutta methods. We compare these methods applied to experimental fuel spray data such as $n$-Butanol, $n$-Decane, and $n$-Heptane. Although these methods are in agreement with each other, application of the homotopy perturbation method to these systems of equations shows rapid con...

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