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

Journal of Applied & Computational Mathematics

article

Ophir Nave¹  Yaron Lehavi²  Vladimir Gol’dshtein¹  Suraj Ajadi³ 

[1] Department of Mathematics, Ben-Gurion University of the Negev;Jerusalem College of Technology ,(JCT), Department of Physics David Yellin;Faculty of Science, Department of Mathematics

关键词: Homotopy perturbation method (HPM);    Homotopy analysis method (HAM);    Nonlinear differential equations;    Thermal explosion;    Polydisperse fuel spray;   

DOI  :  10.4172/2168-9679.1000115

来源: Hilaris Publisher

【 摘 要 】

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.

【 授权许可】

Unknown