No abstract

In this paper, micropolar fluid flow and heat transfer in a permeable channel have been investigated. The main aim of this study is based on solving the nonlinear differential equation of heat and mass transfer of the mentioned problem by utilizing a new and innovative method in semianalytical field which is called Akbari-Ganji's Method (AGM). Results have been compared with numerical method (Runge-Kutte 4th) in order to achieve conclusions based on not only accuracy and efficiency of the solutions but also simplicity of the taken procedures which would have remarkable effects on the time devoted for solving processes.Results are presented for different values of parameters such as: Reynolds number, micro rotation/angular velocity and Peclet number in which the effects of these parameters are discussed on the flow, heat transfer and concentration characteristics. Also relation between Reynolds and Peclet numbers with Nusselts and Sherwood numbers would found for both suction and injection Furthermore, due to the accuracy and convergence of obtained solutions, it will be demonstrating that AGM could be applied through other nonlinear problems even with high nonlinearity. Ó 2017 University of Bahrain. Publishing services by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

In this paper, attempts have been made to solve nonlinear vibrational equation such as Van Der Pol Oscillator by utilizing a semi analytical Akbari-Ganji's Method (AGM). It is noticeable that there are some valuable advantages in this way of solving differential equations and also the answer of various sets of complicated differential equations can be achieved in this manner which in the other methods it would be difficult to obtain.Based on the comparison between AGM and numerical methods, AGM can be successfully applied for a broad range of nonlinear equations. One of the important reasons of selecting AGM for solving differential equations in miscellaneous fields not only in vibrations but also in different fields of sciences for instance fluid mechanics, solid mechanics, chemical engineering, etc. The main benefit of this method in comparison with the other approaches are as follows, normally according to the order of differential equations, we need boundary conditions so in the case of the number of boundary conditions is less than the order of the differential equation, AGM can create additional new boundary conditions in regard to the own differential equation and its derivatives. Results illustrate that method is efficient and has enough accuracy in comparison with other semi analytical and numerical methods because of the simplicity of this method. Moreover results demonstrate that AGM could be applicable through other methods in nonlinear problems with high nonlinearity. Furthermore convergence problems for solving nonlinear equations by using AGM appear small.

In this paper, a new and innovative semi-analytical method called Akbari-Ganji's method (AGM) has been applied to solve nonlinear equations of the semicircular oscillator. The major concern is to achieve an accurate solution that has an efficient approximation according to the Runge-Kutta numerical method. The results are presented for different values of parameters to demonstrate the applicability of this method. It was found that the proposed solution is very accurate and efficient for the discussed problem. It is worthwhile to mention that not only do convergence problems for solving nonlinear equations by using AGM appear small, but the results also demonstrate that the AGM could be applied to nonlinear problems with high nonlinearity.

In this paper, a non-Newtonian fluid flow in an axisymmetric channel with porous wall for specific turbine cooling application has been considered. The purpose of this article is based on solving the nonlinear differential equations of momentum and heat transfer of the mentioned problem by utilizing a new and innovative method in semi-analytical field which is called Akbari-Ganji's method. Meanwhile, relationships between power law index, Reynolds, Prandtl and Nusselt numbers have been investigated. Results have been compared with numerical method (Runge-Kutte 4th) to achieve conclusions based on not only accuracy of the solution but also simplicity of their procedures which would have remarkable effects on the time devoted for solving process. Moreover, results are presented for various values of constant parameters and different steps of trial function due to the aim of comparison and prove that proposed solution is very accurate, simple and also have efficient convergence.