  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.
