• A Sithapathi

Articles written in Proceedings – Section A

• Laminar boundary layers along an infinite porous plate in the presence of a transverse magnetic field

Exact solutions of the Navier-Stokes equations are derived by a Laplace-transform technique for two-dimensional, incompressible flow of an electrically conducting fluid past on infinite porous plate. It is assumed that the flow is independent of the distance parallel to the plate and that the velocity component normal to the plate is constant. A general formula is derived for the velocity distribution in terms of the given external velocity. The skin friction is obtained and some special cases are considered.

• A note on Hydromagnetic oscillatory flow along an infinite flat plate with variable suction

The two-dimensional, incompressible flow past an infinite plate of a weakly conducting fluid in the presence of a transverse magnetic field is discussed when the suction velocity normal to the plate as well as the external flow velocity vary periodically with time. Expressions for the velocity and the skin-friction in the boundary layer have been obtained in a non-dimensional form.

• On MHD flow along an infinite flat wall with constant suction

Exact solutions of the Navier-Stokes equations are derived by a Laplace-transform technique for two-dimensional, incompressible flow of an electrically conducting fluid past an infinite porous plate under the action of a transverse magnetic field subject to the conditions: (i) the magnetic Prandtl number Pm is unity, and (ii) the Alfven velocity is less than the suction velocity. It is assumed that the flow is independent of the distance parallel to the plate and that the velocity component normal to the plate is constant. General formulae are derived for the velocity distribution and the magnetic field in terms of the given external velocity. The skin-friction is obtained and some special cases are considered.

• Flow of fluids with microstructure between parallel plates—I

The basic equations for fluids with microstructure are applied to the steady flow between two parallel plates under the action of a constant pressure gradient. The flow is governed by a microstructure parameter α*. The classical flow is recovered when α* → ∞, while maximum effects of microstructure correspond to α* → 0. For a Poiseuille flow, the microstructure fluid exhibits resistance to motion greater than or equal to that of the classical flow. For a Couette flow it is shown that for a given applied velocity to the moving plate, the shearing stress at the plate is greater than or equal to that corresponding to the classical flow situation. For a Generalised Couette flow, it is shown that for a given pressure gradient in the direction of flow, the flow is retarded; while for an adverse pressure gradient the back flow is controlled.

• Unsteady flow of fluids with microstructure between parallel plates—II

Two types of unsteady flow between two parallel plates of a fluid with microstructure have been considered. (i) Initially the fluid is at rest and the motion is caused by a sudden change of pressure gradient from zero to a constant value. It is shown that for a given time asα* decreases from infinity to zero, the velocity in the flow decreases. (ii) One plate is fixed and the other is accelerated with a velocity ν = Utn (U andn being positive constants). The flow pattern is discussed in both cases in detail.

• Flow of a fluid with microstructure past an accelerated plate—III

The generalised Rayleigh’s problem for fluids with microstructure has been considered. Closed expressions for the velocity and the spin have been obtained for an impulsively moving plate and uniformly accelerated plate. Interesting conclusions have been drawn for any finite value of the microstructure parameter.

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