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AXIALLY SYMMETRIC STAGNATION POINT FLOW WITH HEAT TRANSFER IN MAGNETOHYDRODYNAMICS
( Department of Theoretical Mechanics, University of Bristol )
The steady axially symmetric stagnation point flow of an incompressible electrically conducting viscous fluid in the presence of a magnetic field normal to the wall is investigated. The wall is assumed to be thermally insulated and all physical properties of the fluid such as viscosity, electrical conductivity, and magnetic permeability, etc., are assumed to be independent of the temperature and the strength of the magnetic field. Solution of the equations of magnetohydrodynamics leads to the conclusion of the existence of three regions of flow: (i) a layer of fluid near the wall in which viscosity is important, called the magneto-viscous layer having thickness of order (v/a)½, (ii) a buffer-layer in which viscosity is unimportant, called the magneto-inviscid layer and having thickness of order 1/(8
µe)½, and (iii) a region of potential flow in which the velocity field is directly proportional in magnitude to the magnetic field. Here 
is a parameter of dimensions (time)–1, such that the radial component of external velocity is ar.
A numerical solution of the basic equations has been obtained for the special case of ß = 
/2v = 106 and P = 0.72, in the form of a series expansion in terms of the magnetic parameter 
. In particular it appears that the presence of the magnetic field produces, in the vicinity of the stagnation point, a considerable reduction in the local shear stress and the eigentemperature at the wall. The new results obtained are intended to supplement the results of Neuringer and Mcllroy (1), Rossow (2), and Meyer (3) who have investigated the corresponding problem of the two-dimensional stagnation point flow.