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 convergence of the sequence constructed to the solutions that are obtained by numerical simulations.