Semi-analytic algorithms for the electrohydrodynamic flow equation

In this paper, we consider the nonlinear boundary value problem for the electrohydrodynamic (EHD) flow of a fluid inan ion-drag configuration in a circular cylindrical conduit. This phenomenon is governed by a nonlinear second-orderdifferential equation. The degree of nonlinearity is determined by a nondimensional parameter α. We present twosemi-analytic algorithms to solve the EHD flow equation for various values of relevant parameters based on optimalhomotopy asymptotic method (OHAM) and optimal homotopy analysis method. In 1999, Paullet has shown that forlarge α, the solutions are qualitatively different from those calculated by Mckee in 1997. Both of our solutions obtainedby OHAM and optimal homotopy analysis method are qualitatively similar with Paullet’s solutions.

Keywords:

Optimal homotopy asymptotic method (OHAM) , Optimal homotopy analysis method , Electrohydrodynamic flow , Square residual error , Gauss quadrature