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Analytical and Numerical Method in the Free Convection Flow of Pure Water Non-Newtonian Nano fluid between Two Parallel Perpendicular Flat Plates

Gholinia M, Ganji DD, Poorfallah M and Gholinia S

In this research, free convection of a non-Newtonian silver-water nanofluid between two infinite parallel perpendicular flat plates is investigated. The Maxwell Garnetts (MG) nanofluid model is used in this work. The basic partial differential equations are reduced to the ordinary differential equations which are solved analytically using Homotopy Perturbation Method (HPM). The impact of various physical parameters such as nanoparticle volume fraction (φ), dimensionless non-Newtonian viscosity (δ) and Eckert number (Ec) on the velocity and dimensionless temperature profiles is studied. The comparison of the results of HPM, Akbari-Ganji’s Method (AGM), Collocation Method (CM), the fourth-order Runge-Kutta numerical Method (NUM) and FlexPDE software results shows excellent complying in solving this problem. Also, this research shows that AGM and HPM are powerful methods to solve non-linear differential equations, such as the problem raised in this research.