This paper deals with the construction of a computational approach based on B-spline functions for solving a nonlinear boundary value problem describing the electrohydrodynamic 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 Hand the strength of the nonlinearity beta, 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 + beta)(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/( H root 1+ beta), 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 + beta)(from below) for rvalues 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. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.
