Calculation of electrohydrodynamic flow in a circular cylindrical conduit. (English) Zbl 0883.76093
Summary: The electrohydrodynamic flow of a fluid in an “ion drag” configuration in a circular cylindrical conduit is governed by a nonlinear second-order ordinary differential equation. The degree of nonlinearity in this equation is determined by a non-dimensional parameter \(\alpha\), and the equation can be approximated by two different linear equations for very small or very large values of \(\alpha\), respectively. Perturbation solutions of the fluid velocities for \(\alpha\ll 1\) and \(\alpha\gg 1\) are developed. A Gauss-Newton finite-difference solver combined with the continuation method and a Runge-Kutta shooting method are used to provide numerical results for the fluid velocity over a large range of values of \(\alpha\). Both numerical and analytical results are compared in order to establish the range of validity for the perturbation solutions.
MSC:
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
Keywords:
ion drag configuration; non-dimensional parameter; Gauss-Newton finite-difference solver; continuation method; Runge-Kutta shooting method; perturbation solutionsReferences:
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