Magnetohydrodynamic flow in channels of variable cross-section with strong transverse magnetic fields

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Abstract
This paper is an analysis of the steady incompressible, two-dimensional flow of conducting fluids through ducts of arbitrarily varying cross-section under the action of a strong, uniform, transverse, magnetic field. More precisely, the flow is such that the velocity is given by , where b [Gt ] ft−fb, and the magnetic field by B0 = (0, B0, O). It is assumed that the magnetic field is strong enough to satisfy the conditions that the interaction parameter, N(=M2/R) [Gt ] 1, where M is the Hartmann number and R is the Reynolds number, and also that M [Gt ] 1 and Rm [Lt ] 1, where Rm is the magnetic Reynolds number.We examine the flow in three separate regions: the ‘core’ region in which the pressure gradient is balanced by electromagnetic forces;Hartmann boundary layers where electromagnetic forces are balanced by viscous forces;thin layers parallel to the magnetic field in which electromagnetic forces, inertial forces, and the pressure gradient balance each other. These layers which have thickness occur where the slope of the duct wall changes abruptly.By expanding the solution as a series in descending powers of N we calculate the velocity distribution for regions (i) and (ii) for finite values of N attainable in the laboratory.

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