A high accuracy numerical approach for electro-hydrodynamic flow of a fluid in an ion-drag configuration in a circular cylindrical conduit

Abstract

This paper deals with the construction of a computational approach based on B-spline functions for solving a nonlinear boundary value problem describing the electro-hydrodynamic flow (EHF) of a fluid in a circular cylindrical conduit. The radial dependence of the velocity field emerging in the EHF is computed. We study the effects of two relevant parameters, namely the Hartmann electric number H and the strength of the nonlinearity β, on the velocity field. Computational results show that the method is of sixth-order accuracy. It is shown that the Hartmann electric number (HEN) and the strength of the nonlinearity both have a profound impact on the velocity profile of EHF and that these effects can be understood from analytical considerations. In particular, quantitative results include: The velocity, taking its maximum at the center of the conduit, does not exceed the value 1/(1+β) (this confirms a previous result). At large HEN, a boundary layer develops near the outer radial boundary of the conduit (r=1). Its thickness is proportional to 1/(H1+β), being determined by both the HEN and the nonlinearity. Moreover, when a boundary layer is present, the flow velocity has a plug-like profile approaching the plateau value 1/(1+β) (from below) for r values smaller than those of the boundary layer. If both the nonlinearity and the HEN are too small for a boundary layer to develop, then the flow profile is essentially parabolic and describable via a modified Bessel function. The CPU time for our method is provided.