In this research, a fully developed steady flow of a third-grade fluid in a pipe under an externally applied magnetic field withconvection on wall is investigated. The governing equations including momentum and energy in the form of partial differentialequations are reduced to ordinary differential equations which are solved numerically by using a finite element method(FEM) as part of the FlexPDE software package. For validity, the results are compared with the 4th order Runge-Kutta method.The effect of different physical parameters such as the non-Newtonian parameter, the Biot number, the Hartmann number,the Eckert number on the dimensionless velocity profiles, the dimensionless velocity gradient profiles, the dimensionlesstemperature profiles, and the dimensionless gradient temperature... profiles have been discussed. It is concluded that byincreasing the non-Newtonian parameter and Hartman number the dimensionless velocity, the velocity gradient, the temperatureand temperature gradient profiles reduce and thus the heat transfer of fluid flow, the shear stress and the skin frictionon the pipe wall decrease. Increasing the Biot number caused a decrease of the temperature and a more uniform dimensionlesstemperature profile of the fluid within the pipe. Besides, with a decrease of the Prandtl number, the dimensionlesstemperature decreases inside the pipe. In fact, the dimensionless temperature profile becomes flat. For this reason, thedimensionless temperature gradient decreases on the pipe wall which causes the reduction of the heat transfer rate on thepipe wall. Further, by increasing the Eckert number, the dimensionless temperature of the fluid within the pipe and the heattransfer from the fluid to the pipe wall increases. Applying the FlexPDE software for solving governing equations numericallyseems to lead to appropriate and reasonable results.