Application of homotopy perturbation method to the MHD pipe flow of a fourth grade fluid

This paper applies He's homotopy perturbation method (HPM) to analyze the strongly nonlinear magneto-hydrodynamic (MHD) flow of a fourth grade fluid through a circular pipe. In this method, a homotopy is constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. The results reveal that HPM is very effective, convenient and quite accurate to both linear and nonlinear problems. It is predicted that HPM can be widely applied in engineering. Some illustrations are presented to show the reliability and simplicity of the method.