Analytical Investigation of Jeffery-hamel Fow with High Magnetic Field and Nano Particle by RVIM

Abstract

Many researchers have been interested in application of mathematical methods to find analytical solutions of nonlinear equations and for this purpose, new methods have been developed. One of the newest analytical methods to solve nonlinear equations is Reconstruction of variational Iteration Method (RVIM) which is an accurate and a rapid convergence method in finding the approximate solution for nonlinear equations. By applying Laplace Transform, RVIM overcomes the difficulty of the perturbation techniques and other variational methods in case of using small parameters and Lagrange multipliers, respectively. In this study RVIM is applied for the effects of magnetic field and nano particle on the Jeffery-Hamel flow. The traditional Navier-Stokes equation of fluid mechanics and Maxwell’s electromagnetism governing equations are reduced to nonlinear ordinary differential equations to model the problem. The flow field inside the divergent channel is studied for various values of Hartmann number and angle of channel. Finally the effect of nano particle volume fraction in the absence of magnetic field is investigated, too. The validity of RVIM method is ascertained by comparing our results with numerical (Runge Kutta method) results.