Application of the Homotopy Perturbation Method (HPM) and the Homotopy Analysis Method (HAM) to the Problem of the Thermal Explosion in a Radiation Gas with Polydisperse Fuel Spray
- *Corresponding Author:
- Ophir Nave
Department of Mathematics
Ben-Gurion University of the Negev
PO Box 653, Beer-Sheva, 84105, Israel
E-mail: [email protected]
Received Date: April 20, 2012; Accepted Date: June 20, 2012; Published Date: June 23, 2012
Citation: Nave O, Lehavi Y, Gol’dshtein V, Ajadi S (2012) Application of the Homotopy Perturbation Method (HPM) and the Homotopy Analysis Method (HAM) to the Problem of the Thermal Explosion in a Radiation Gas with Polydisperse Fuel Spray. J Appl Computat Math 1:115. doi: 10.4172/2168-9679.1000115
Copyright: © 2012 Nave O, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
The aim of this work is to apply the homotopy perturbation method and homotopy analysis method to the problem of thermal explosion in a flammable gas mixture with the addition of volatile fuel droplets. The system of equations that describes the effects of heating, evaporation, and combustion of fuel in a polydisperse spray is simplified. Both convective and radiative heating of droplets is taken into account in the model. The model for the radiative heating of droplets takes into account the semitransparency of the droplets. The results of the analysis have been applied to the modeling of the thermal explosion in diesel engines. We applied the Homotopy Perturbation Method and the Homotopy Analysis Method to the new model and we found the region of the convergence of the considered solutions of the relevant physical parameters. The results demonstrate that these methods are very effective for solving nonlinear problems in science and engineering.