An analytic approximation of wire coating analysis for third-grade magneto-hydrodynamic flow

摘要

In this article, homotopy perturbation method (HPM) is applied to solve non-linear problems for third-grade fluid. The fluid is electrically conducting in the presence of a uniform applied magnetic field, and wire coating by withdrawal from a bath of third-grade fluid is investigated. Although traditional HPM is divergent for higher-order approximation to obtain enough accuracy in this work, a new method on boundary conditions is proposed to solve this boundary value problem by HPM and convergence of the solution is clearly discussed. Results reveal that this method is very effective and simple to overcome the divergence of the HPM solution. The influence of the non-Newtonian parameter on the velocity, volume flowrate, radius of coated wire, shear stress at the surface of the wire, and the force required to pull the wire is seen and discussed.