Abstract

RUN-UP FLOW OF AN ELECTRICALLY CONDUCTING FLUID IN THE PRESENCE OF TRANSVERSE MAGNETIC FIELD IN ANNULUS

Jibril, H. M., Jha, B. K. & Yusuf, K. L.

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Abstract In this paper, the run-up flow of an incompressible, viscous electrically conducting fluid in an annulus formed by two infinitely long concentric cylinders is considered. The flow is initially induced by a constant pressure gradient parallel to the direction of the fluid flow, when steady state is attained, the pressure gradient is suddenly withdrawn while the inner cylinder is impulsively started in the direction of the fluid flow and the outer cylinder continues to be at rest. For that, the governing equations are simplified by using reasonable dimensionless parameters. Laplace transform technique is then employed to obtain the solutions of the velocity in Laplace domain. Consequently, Riemann-sum approximation is then used to invert the obtained solutions into the corresponding time domain, and the skin friction on both cylinders are calculated. More so, expressions are obtained for the velocities for both cases of the applied magnetic field being fixed relative to either the fluid or the moving inner cylinder. As a result, the influence of the various parameters such as the Hartmann number, pressure gradient on the velocity and skin friction is discussed by the use of graphs. It is found that the fluid velocity increases with increase in time t and subsequently decreases. It is also discovered that the fluid velocity increases with the increase in pressure gradient G. In addition, a reversal of flow is observed when the orientation of the pressure gradient is reversed. The fluid velocity is seen to decrease with the increase in M when the magnetic lines of force are fixed relative to the fluid and increases when fixed relative to the moving inner cylinder. The results provided useful information to engineers to improve efficiency and performance of machines. Keywords: Run-up flow, MHD, Couette flow, Poissuielle flow, Annulus, Pressure gradient, Riemann-sum, Transverse magnetic field, and Impulsive motion.

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