Magnetohydrodynamic flows of conducting liquids in divergent-convergent channels

We show that the full set of magnetohydrodynamic (MHD) equations, for resistive and viscous incompressible fluids, allows in cylindrical coordinates an exact reduction to a pair of coupled, nonlinear, ordinary differential equations (ODE) for two scalar potentials. The ODEs represent self-similar MH...

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Autores principales:	Gnavi, Graciela Delia, Gratton, Fausto Tulio Livio
Publicado:	2003
Materias:	Channel flow Flow control Liquid metals Navier Stokes equations Ordinary differential equations Partial differential equations Reynolds number Divergent-convergent channels Magnetohydrodynamic flows Magnetohydrodynamics
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03928764_v21_n1_p99_Gnavi http://hdl.handle.net/20.500.12110/paper_03928764_v21_n1_p99_Gnavi
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_03928764_v21_n1_p99_Gnavi
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spelling	paper:paper_03928764_v21_n1_p99_Gnavi2023-06-08T15:41:00Z Magnetohydrodynamic flows of conducting liquids in divergent-convergent channels Gnavi, Graciela Delia Gratton, Fausto Tulio Livio Channel flow Flow control Liquid metals Navier Stokes equations Ordinary differential equations Partial differential equations Reynolds number Divergent-convergent channels Magnetohydrodynamic flows Magnetohydrodynamics We show that the full set of magnetohydrodynamic (MHD) equations, for resistive and viscous incompressible fluids, allows in cylindrical coordinates an exact reduction to a pair of coupled, nonlinear, ordinary differential equations (ODE) for two scalar potentials. The ODEs represent self-similar MHD flows in channels, bounded by non-parallel plane walls, intersecting on the z-axis, akin to the Jeffery-Hamel flows of non-conducting fluids. We consider the case in which an external current, flows along the z-axis, and exerts a body force that controls the flow. Only one nonlinear ODE governs the solution in this case. Besides the Reynolds number (Re) and the angle of the walls, two other non dimensional parameters determine the solutions, the magnetic Reynolds number (Rm), and the Hartmann number (Ha). We give a preliminary study of the properties of the high resistivity regime, in which the Hartmann number becomes important. The main result is that for Ha larger than 2 the flow reversal near the walls, which is a typical feature of channels with Ha=0 and Re∼O(1) or larger, tends to disappear. Moderate values of Ha∼6 are sufficient to suppress flow reversal up to Re∼25 for angular widths of the channel as large as 240°. The configuration may be of interest for applications to flow control of liquid metals, and industrial treatment of molten metals. Fil:Gnavi, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Gratton, F.T. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2003 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03928764_v21_n1_p99_Gnavi http://hdl.handle.net/20.500.12110/paper_03928764_v21_n1_p99_Gnavi
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Channel flow Flow control Liquid metals Navier Stokes equations Ordinary differential equations Partial differential equations Reynolds number Divergent-convergent channels Magnetohydrodynamic flows Magnetohydrodynamics
spellingShingle	Channel flow Flow control Liquid metals Navier Stokes equations Ordinary differential equations Partial differential equations Reynolds number Divergent-convergent channels Magnetohydrodynamic flows Magnetohydrodynamics Gnavi, Graciela Delia Gratton, Fausto Tulio Livio Magnetohydrodynamic flows of conducting liquids in divergent-convergent channels
topic_facet	Channel flow Flow control Liquid metals Navier Stokes equations Ordinary differential equations Partial differential equations Reynolds number Divergent-convergent channels Magnetohydrodynamic flows Magnetohydrodynamics
description	We show that the full set of magnetohydrodynamic (MHD) equations, for resistive and viscous incompressible fluids, allows in cylindrical coordinates an exact reduction to a pair of coupled, nonlinear, ordinary differential equations (ODE) for two scalar potentials. The ODEs represent self-similar MHD flows in channels, bounded by non-parallel plane walls, intersecting on the z-axis, akin to the Jeffery-Hamel flows of non-conducting fluids. We consider the case in which an external current, flows along the z-axis, and exerts a body force that controls the flow. Only one nonlinear ODE governs the solution in this case. Besides the Reynolds number (Re) and the angle of the walls, two other non dimensional parameters determine the solutions, the magnetic Reynolds number (Rm), and the Hartmann number (Ha). We give a preliminary study of the properties of the high resistivity regime, in which the Hartmann number becomes important. The main result is that for Ha larger than 2 the flow reversal near the walls, which is a typical feature of channels with Ha=0 and Re∼O(1) or larger, tends to disappear. Moderate values of Ha∼6 are sufficient to suppress flow reversal up to Re∼25 for angular widths of the channel as large as 240°. The configuration may be of interest for applications to flow control of liquid metals, and industrial treatment of molten metals.
author	Gnavi, Graciela Delia Gratton, Fausto Tulio Livio
author_facet	Gnavi, Graciela Delia Gratton, Fausto Tulio Livio
author_sort	Gnavi, Graciela Delia
title	Magnetohydrodynamic flows of conducting liquids in divergent-convergent channels
title_short	Magnetohydrodynamic flows of conducting liquids in divergent-convergent channels
title_full	Magnetohydrodynamic flows of conducting liquids in divergent-convergent channels
title_fullStr	Magnetohydrodynamic flows of conducting liquids in divergent-convergent channels
title_full_unstemmed	Magnetohydrodynamic flows of conducting liquids in divergent-convergent channels
title_sort	magnetohydrodynamic flows of conducting liquids in divergent-convergent channels
publishDate	2003
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03928764_v21_n1_p99_Gnavi http://hdl.handle.net/20.500.12110/paper_03928764_v21_n1_p99_Gnavi
work_keys_str_mv	AT gnavigracieladelia magnetohydrodynamicflowsofconductingliquidsindivergentconvergentchannels AT grattonfaustotuliolivio magnetohydrodynamicflowsofconductingliquidsindivergentconvergentchannels
_version_	1768544089357156352

Magnetohydrodynamic flows of conducting liquids in divergent-convergent channels

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