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.

翻译：本文采用解析方法研究了磁场存在下物理参数对环形截面多孔介质中三阶非牛顿纳米流体传热与流动的影响。纳米流体粘度分为三种模型：恒定模型和随温度变化的可变模型，其中可变类别采用雷诺模型和沃格尔模型确定粘度对流场的影响。通过Akbari-Ganji方法（AGM）建立了速度、温度和纳米颗粒浓度的解析解，该方法与数值解（四阶龙格-库塔法）高度吻合。用于提取非线性方程无量纲变量结果的物理参数包括压力梯度、布朗运动参数、热泳参数、磁场强度和格拉晓夫数。研究表明：压力梯度和热泳参数的增大以及布朗运动参数的减小会导致速度剖面升高；同时，格拉晓夫数的增加和磁流体动力学参数的降低也会使速度剖面上升。此外，热泳参数增大或布朗运动参数减小均会增强纳米颗粒浓度。采用沃格尔模型描述粘度时观测到速度最大值。