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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.

Semi-analytical Investigation of Momentum and Heat Transfer of a Non-Newtonian Fluid Flow for Specific Turbine Cooling Application Using AGM