The present study deals with analytical investigation of temperature of a single burning iron particle.Three mathematical methods including AGM(Akbari-Ganji’s method),CM(Collocation method)and GM(Galerkin Method)are ...The present study deals with analytical investigation of temperature of a single burning iron particle.Three mathematical methods including AGM(Akbari-Ganji’s method),CM(Collocation method)and GM(Galerkin Method)are applied to solving non-linear differential governing equation and effectiveness of these methods is examined as well.For further investigation,forth order Runge-Kutta approach,a numerical method,is used to validate the obtained analytical results.In the present study,the developed mathematical model takes into account the effects of thermal radiation,convective heat transfer and particle density variations during combustion process.Due to particles’small size and high thermal conductivity,the system is assumed to be lumped in which the particle temperature does not change within the body and all of its regions are at the same temperature.The temperature distributions obtained by analytical methods have satisfactory agreement with numerical outputs.Finally,the results indicate that AGM is a more appropriate method than GM and CM due to its lower mean relative error and less run time.展开更多
文摘The present study deals with analytical investigation of temperature of a single burning iron particle.Three mathematical methods including AGM(Akbari-Ganji’s method),CM(Collocation method)and GM(Galerkin Method)are applied to solving non-linear differential governing equation and effectiveness of these methods is examined as well.For further investigation,forth order Runge-Kutta approach,a numerical method,is used to validate the obtained analytical results.In the present study,the developed mathematical model takes into account the effects of thermal radiation,convective heat transfer and particle density variations during combustion process.Due to particles’small size and high thermal conductivity,the system is assumed to be lumped in which the particle temperature does not change within the body and all of its regions are at the same temperature.The temperature distributions obtained by analytical methods have satisfactory agreement with numerical outputs.Finally,the results indicate that AGM is a more appropriate method than GM and CM due to its lower mean relative error and less run time.
