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Axisymmetric stagnation point flow in magnetohydrodynamics

Axisymmetric stagnation point flow in magnetohydrodynamics SummaryThis paper contains a theoretical treatment of the axisymmetric stagnation point problem in magnetohydrodynamics. Two distinct arrangements of the magnetic field are considered, with the lines of force lying in the plane of, and perpendicular to the streamlines, respectively. The boundary conditions are examined carefully and the solutions are completed by joining them to meaningful distributions of magnetic field in the solid region. Exact solutions can be obtained by numerical methods, but it is more illuminating to consider approximations valid for very large and very small diffusion numbers (ratio of kinematic viscosity to magnetic diffusivity). Distinct boundary layers of current and vorticity occur in these limiting cases, which can be treated separately. For flows with the first arrangement of the magnetic field, and in which the field does not vanish at infinity, it is deduced that the solution refers to a forward stagnation point when the Alfvén number is less than unity, and to a rear stagnation point when the Alfvén number exceeds unity. An interesting choking effect is found in flows with the second arrangement of the magnetic field when the diffusion number is small, and the Alfvén number exceeds unity; it is believed that this effect could be demonstrated in the laboratory. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Scientific Research, Section B Springer Journals

Axisymmetric stagnation point flow in magnetohydrodynamics

Axford, W. I.
Applied Scientific Research, Section B , Volume 9 (3) – Jun 1, 1961
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References (15)

Publisher
Springer Journals
Copyright
Copyright © Martinus Nijhoff 1961
ISSN
0365-7140
DOI
10.1007/bf02922226
Publisher site
See Article on Publisher Site

Abstract

SummaryThis paper contains a theoretical treatment of the axisymmetric stagnation point problem in magnetohydrodynamics. Two distinct arrangements of the magnetic field are considered, with the lines of force lying in the plane of, and perpendicular to the streamlines, respectively. The boundary conditions are examined carefully and the solutions are completed by joining them to meaningful distributions of magnetic field in the solid region. Exact solutions can be obtained by numerical methods, but it is more illuminating to consider approximations valid for very large and very small diffusion numbers (ratio of kinematic viscosity to magnetic diffusivity). Distinct boundary layers of current and vorticity occur in these limiting cases, which can be treated separately. For flows with the first arrangement of the magnetic field, and in which the field does not vanish at infinity, it is deduced that the solution refers to a forward stagnation point when the Alfvén number is less than unity, and to a rear stagnation point when the Alfvén number exceeds unity. An interesting choking effect is found in flows with the second arrangement of the magnetic field when the diffusion number is small, and the Alfvén number exceeds unity; it is believed that this effect could be demonstrated in the laboratory.

Journal

Applied Scientific Research, Section B – Springer Journals

Published: Jun 1, 1961

Keywords: Magnetic Field; Boundary Layer; Vorticity; Stagnation Point; Current Layer

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