A STUDY OF SOME TIME-DEPENDENT FLOWS IN MAGNETOHYDRODYNAMICS
A STUDY OF SOME TIME-DEPENDENT FLOWS IN MAGNETOHYDRODYNAMICS
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Date
2012-04
Authors
CLEMENT, ADEDAYO APERE
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Abstract
The motion of an electrically conducting fluid in two types of geometries is
studied; namely a channel formed by two parallel plates and an annulus formed
by two concentric cylinders. The fluid flow is assumed to be unsteady, laminar
and incompressible with a magnetic field applied perpendicular to the flow
direction. It is also assumed that no applied or polarization voltage exists.
We have considered different physical situations and factored the effect of
Hall and ion-slip currents in some cases. The system of partial differential
equations describing the different flow problems has been formulated and
unified closed form expressions are obtained for both cases of the applied
magnetic field being fixed to either the fluid or the moving wall where applicable.
The Laplace transform techniques are used to reduce the system of partial
differential equations to ordinary differential equations; the resulting boundary
value problems are then solved analytically. However, the Riemann-sum
approximation method is used to invert the Laplace domain to the time domain
where direct inversion is difficult. The corresponding steady state equations are
derived where appropriate and solved analytically to double check the results.
Also, the implicit finite difference method is used to verify the Riemann-sum
approximation method. MATLAB programmes are written to compute and
generate the graphs for the velocities and the skin frictions. A parametric study
depicting the effect of the various dimensionless parameters on the velocity and
skin friction is conducted. These parameters include the Ekman number E, the
Hall parameter /3„ ion-slip parameter /3„ the suction/injection parameter S, the
Hartmann number Ha and time r\ amongst others. The effects of changing the
parameters mentioned above are observed either to increase, to decrease or to
have no effect on the velocity profiles and the skin friction.
Description
A DISSERTATION SUBMITTED TO THE SCHOOL OF
POSTGRADUATE STUDIES AHMADU BELLO UNIVERSITY
ZARIA, NIGERIA IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE AWARD OF
DOCTOR OF PHILOSOPHY IN MATHEMATICS
DEPARTMENT OF MATHEMATICS
FACULTY OF SCIENCE
AHMADU BELLO UNIVERSITY
ZARIA, NIGERIA
Keywords
TIME-DEPENDENT ,, FLOWS,, MAGNETOHYDRODYNAMICS