In this paper, effect of physical parameters in presence of magnetic field on heat transfer and flow of third grade non-Newtonian Nanofluid in a porous medium with annular cross sectional analytically has been investigated. The viscosity of Nanofluid categorized in 3 model include constant model and variable models with temperature that in variable category Reynolds Model and Vogel's Model has been used to determine the effect of viscosity in flow filed. analytically solution for velocity, temperature, and nanoparticle concentration are developed by Akbari-Ganji's Method (AGM) that has high proximity with numerical solution (Runge-Kutta 4th-order). Physical parameters that used for extract result for non dimensional variables of nonlinear equations are pressure gradient, Brownian motion parameter, thermophoresis parameter, magnetic field intensity and Grashof number. The results show that the increase in the pressure gradient and Thermophoresis parameter and decrease in the Brownian motion parameter cause the rise in the velocity profile. Also the increase in the Grashof number and decrease in MHD parameter cause the rise in the velocity profile. Furthermore, either increase in Thermophoresis or decrease in Brownian motion parameters results in enhancement in nanoparticle concentration. The highest value of velocity is observed when the Vogel's Model is used for viscosity.

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