On the solutions of electrohydrodynamic flow in a circular cylindrical conduit

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

This article considers the nonlinear boundary value problem (BVP) for the electrohydrodynamic flow of a fluid in an ion drag configuration in a circular cylindrical conduit. We present rigorous results concerning the existence and uniqueness of a solution to this BVP for all relevant values of the parameters. We also show that the solution is monotonically decreasing and derive bounds on it in terms of the parameters. In [1] MCKEE et al. develop perturbation solutions in terms of the parameter governing the nonlinearity of the problem, a. This is done for both large and small values of a. For large a the solutions calculated here are qualitatively different from those calculated in [1]. This stems from the fact that for a large the solutions are O(1/α), not O(1) as proposed in the perturbation expansion used in [1].

Original languageEnglish (US)
Pages (from-to)357-360
Number of pages4
JournalZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Volume79
Issue number5
DOIs
StatePublished - Jan 1 1999

Fingerprint

Electrohydrodynamics
Boundary value problems
Perturbation Solution
Perturbation Expansion
Nonlinear Boundary Value Problems
Drag
Existence and Uniqueness
Boundary Value Problem
Nonlinearity
Fluid
Configuration
Fluids
Ions

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Applied Mathematics

Cite this

@article{2d342d4f94894ae6b28e713c4790777f,
title = "On the solutions of electrohydrodynamic flow in a circular cylindrical conduit",
abstract = "This article considers the nonlinear boundary value problem (BVP) for the electrohydrodynamic flow of a fluid in an ion drag configuration in a circular cylindrical conduit. We present rigorous results concerning the existence and uniqueness of a solution to this BVP for all relevant values of the parameters. We also show that the solution is monotonically decreasing and derive bounds on it in terms of the parameters. In [1] MCKEE et al. develop perturbation solutions in terms of the parameter governing the nonlinearity of the problem, a. This is done for both large and small values of a. For large a the solutions calculated here are qualitatively different from those calculated in [1]. This stems from the fact that for a large the solutions are O(1/α), not O(1) as proposed in the perturbation expansion used in [1].",
author = "Paullet, {Joseph E.}",
year = "1999",
month = "1",
day = "1",
doi = "10.1002/(SICI)1521-4001(199905)79:5<357::AID-ZAMM357>3.0.CO;2-B",
language = "English (US)",
volume = "79",
pages = "357--360",
journal = "ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik",
issn = "0044-2267",
publisher = "Wiley-VCH Verlag",
number = "5",

}

TY - JOUR

T1 - On the solutions of electrohydrodynamic flow in a circular cylindrical conduit

AU - Paullet, Joseph E.

PY - 1999/1/1

Y1 - 1999/1/1

N2 - This article considers the nonlinear boundary value problem (BVP) for the electrohydrodynamic flow of a fluid in an ion drag configuration in a circular cylindrical conduit. We present rigorous results concerning the existence and uniqueness of a solution to this BVP for all relevant values of the parameters. We also show that the solution is monotonically decreasing and derive bounds on it in terms of the parameters. In [1] MCKEE et al. develop perturbation solutions in terms of the parameter governing the nonlinearity of the problem, a. This is done for both large and small values of a. For large a the solutions calculated here are qualitatively different from those calculated in [1]. This stems from the fact that for a large the solutions are O(1/α), not O(1) as proposed in the perturbation expansion used in [1].

AB - This article considers the nonlinear boundary value problem (BVP) for the electrohydrodynamic flow of a fluid in an ion drag configuration in a circular cylindrical conduit. We present rigorous results concerning the existence and uniqueness of a solution to this BVP for all relevant values of the parameters. We also show that the solution is monotonically decreasing and derive bounds on it in terms of the parameters. In [1] MCKEE et al. develop perturbation solutions in terms of the parameter governing the nonlinearity of the problem, a. This is done for both large and small values of a. For large a the solutions calculated here are qualitatively different from those calculated in [1]. This stems from the fact that for a large the solutions are O(1/α), not O(1) as proposed in the perturbation expansion used in [1].

UR - http://www.scopus.com/inward/record.url?scp=33748263250&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33748263250&partnerID=8YFLogxK

U2 - 10.1002/(SICI)1521-4001(199905)79:5<357::AID-ZAMM357>3.0.CO;2-B

DO - 10.1002/(SICI)1521-4001(199905)79:5<357::AID-ZAMM357>3.0.CO;2-B

M3 - Article

VL - 79

SP - 357

EP - 360

JO - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

JF - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

SN - 0044-2267

IS - 5

ER -