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In the current study, an efficient, reliable and relatively novel analytical method is applied to describe the temperature behavior of an unsteady nanofluid flow containing water as the base fluid and graphene oxide particles as the nanoparticles between moving parallel plates. The first phase of this investigation involves turning the governing equations including partial differential equations (PDE) into ordinary differential equations (ODE) using similarity solution. Subsequently, a system of differential equations is solved applying Akbari-Ganji method (AGM) and reliable functions are obtained for temperature and velocity distributions. The effect of viscous dissipation in the derived equations is considered and comprehensively discussed. In order to examine the accuracy and precision of the current analytical results, the equations are also solved by using appropriate numerical solution. By comparing the results, a proper agreement with low error rate is observed between the analytical and numerical results. Finally, by definition of a viscous dissipation ratio parameter, the amount of heat due to shear stress is calculated for several nanoparticles and Eckert numbers. According to the results, viscous dissipation ratio of titanium oxide nanoparticles is greater than that of the other considered nanoparticles.

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The random modeling combustion of lycopodium particles has been researched by many authors. In this paper, we extend this model and we also generate a different method by analyzing the effect of random distributed sources of combustible mixture. The flame structure is assumed to consist of a preheat-vaporization zone, a reaction zone and finally a post flame zone. We divide the preheat zone to different parts. We assumed that there is different distribution of particles in sections which are really random. Meanwhile, it is presumed that the fuel particles vaporize first to yield gaseous fuel. In other words, most of the fuel particles are vaporized at the end of the preheat zone. It is assumed that the Zel'dovich number is large; therefore, the reaction term in preheat zone is negligible. In this work, the effect of random distribution of particles in the preheat zone on combustion characteristics such as burning velocity, flame temperature for different particle radius is obtained.