## A Mathematical Model for Magnetohydrodynamic Convection Flow in a Rotating Horizontal Channel with Inclined Magnetic Field, Magnetic Induction and Hall Current Effects

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##### Date

2011-06##### Author

Ghosh, Swapan K.

Bég, Osman A.

Aziz, Abdul

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Show full item record##### Abstract

Closed-form and asymptotic solutions are derived for the steady, fully-developed hydromagnetic free and
forced convection flow in a rotating horizontal parallel-plate channel under the action of an inclined magnetic
field and constant pressure gradient along the longitudinal axis of the channel. The magnetic field is
strong enough to generate Hall current effects and the magnetic Reynolds number of sufficient magnitude
that induced magnetic field effects are also present. Secondary flow is present owing to the Hall current effect.
The channel plates are also taken to be electrically-conducting. The conservation equations are formulated
in an (x, y, z) coordinate system and non-dimensionalized using appropriate transformations. The resulting
non-dimensional coupled ordinary differential equations for primary and secondary velocity components
and primary and secondary induced magnetic field components and transformed boundary conditions
are shown to be controlled by the dimensionless pressure gradient parameter (px), Hartmann number (M
2
),
Grashof number (G), Hall current parameter (m), rotational parameter (K
2
), magnetic field inclination (q),
and the electrical conductance ratios of the upper (f1) and lower (f2) plates. Solutions are derived using the
method of complex variables. Asymptotic solutions are also presented for very high rotation parameter and
Hartmann number of order equal to unity, for which Ekman-Hartmann boundary layers are identified at the
plates. A parametric study of the evolution of velocity and induced magnetic field distributions is undertaken.
It is shown that generally increasing Hall current effect (m) serves to accentuate the secondary (cross) flow
but oppose the primary flow. An increase in rotational parameter (K
2
) is also found to counteract primary
flow intensity. An elevation in the Grashof number i.e. free convection parameter (G) is shown to aid the
secondary induced magnetic field component (Hz); however there is a decrease in magnitudes of the primary
induced magnetic field component (Hx) with increasing Grashof number. Increasing inclination of the applied
magnetic field (q, is also found to oppose the primary flow (u1) but conversely to strongly assist the
secondary flow (w1). Both critical primary (Gcx) and secondary (Gcz) Grashof numbers are shown to be reduced
with increasing inclination of the magnetic field (q), increasing Hall parameter (m) and rotational parameter
(K
2
). Applications of the study arise in rotating MHD induction power generators and also astrophysical
flows