In this research various nonlinear fluid models have been introduced and the balloon movement in the porous arteries, including third-order non-Newtonian fluid, is described under the influence of the magnetic field. In order to solve the nonlinear equations governing the desired artery, an analytical method of approximation collocation and least squares are proposed. The effect of various parameters such as Brownian motion, thermophoresis and pressure gradient are shown on the distribution of velocity and fluid temperature. According to the studies, Increase the thermophoresis parameter and Brownian motion are increases the temperature. Also, by increasing the values of the electromagnetic parameter, fluid velocity decreases. Although many papers have investigated the flow of intra-arterial blood in the presence of MHD, it is clear that the governing equations of these articles unfortunately reveal obvious errors by extracting the governing equations. In this paper, the equations have been revised and corrected. It can also be seen by increasing the thermophoresis and Brownian parameters, increases the temperature of the nanofluid, but reduces velocity of the nanofluid and also increase the porosity parameter, the velocity of fluid flow between the balloon and the vessel wall decreases. Manuscript profile