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Calculation of Electrohydrodynamic Flow in a Circular Cylindrical Conduit
Author(s) -
McKee S.,
Watson R.,
Cuminato J. A.,
Caldwell J.,
Chen M. S.
Publication year - 1997
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19970770612
Subject(s) - drag , mathematics , mechanics , electrohydrodynamics , shooting method , mathematical analysis , differential equation , physics , classical mechanics , boundary value problem , quantum mechanics , electric field
The electrohydrodynamic flow of a fluid in an “ion drag” configuration in a circular cylindrical conduit is governed by a non‐linear second‐order ordinary differential equation. The degree of non‐linearity in this equation is determined by a nondimensional parameter α and the equation can be approximated by two different linear equations for very small or very large values of α respectively. Perturbation solutions of the fluid velocities for α ≪ 1 and α ≫ 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 α. Both numerical and analytical results are compared in order to establish the range of validity for the perturbation solutions.