Abstract
An electrically conducting fluid is driven by a stretching sheet, in the presence of a magnetic field that is strong enough to produce significant Hall current. The sheet is porous, allowing mass transfer through suction or injection. The limiting behavior of the flow is studied, as the magnetic field strength grows indefinitely. The flow variables are properly scaled, and uniformly valid asymptotic expansions of the velocity components are obtained through parameter straining. The leading order approximations show sinusoidal behavior that is decaying exponentially, as we move away from the surface. The two-term expansions of the surface shear stress components, as well as the far field inflow speed, compare well with the corresponding finite difference solutions; even at moderate magnetic fields.
Highlights
The flow due to a moving surface is an important field of fluid mechanics
Crane [1] obtained an exact solution for the two-dimensional flow of a Newtonian fluid due to a linearly stretching sheet
A uniform magnetic field is applied in the z-direction
Summary
The flow due to a moving surface is an important field of fluid mechanics. It has several applications; for example, in production of glass and paper sheets, drawing of plastic films, and extrusion of metals and polymers. The velocity components in this case has simple forms; tending to their limits monotonically in an exponential manner as we move away from the surface. The simplicity of this solution invited several authors to consider different related problems, which exhibit the same behavior; e.g. When the magnetic field is strong enough to produce significant Hall current, the problem changes considerably. Finite difference solutions are obtained and show qualitative adherence to the predicted limiting behavior even for moderate magnetic fields. The two term expansions show excellent agreement with the numerical results
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