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A linear stability analysis has been presented for hydromagnetic
dissipative Couette flow, a viscous electrically conducting fluid
between rotating concentric cylinders in the presence of a uniform axial
magnetic field and constant heat flux at the outer cylinder. The
narrow-gap equations with respect to axisymmetric disturbances are
derived and solved by a direct numerical procedure. Both types of
boundary conditions, conducting and non-conducting walls are considered.
A parametric study covering on the basis of m,
the ratio of the angular velocity of the outer cylinder to that of inner
cylinder, Q, the Hartmann number which represents the strength of the
axial magnetic field, and N, the ratio of the Rayleigh number and Taylor
number representing the supply of heat to the outer cylinder at constant
rate is presented. The three cases of m < 0
(counter rotating),
m > 0 (co-rotating) and m = 0
(stationary outer cylinder) are considered wherein the magnetic Prandtl
number is assumed to be small. Results show that the stability
characteristics depend mainly on the conductivity on the cylinders and
not on the heat supplied to the outer cylinder. As a departure from
earlier results corresponding to isothermal as well as hydromagnetic
flow, it is found that the critical wave number is strictly a monotonic
decreasing function of Q for conducting walls. Also, the presence of
constant heat flux leads to a fall in the critical wave number for
counter rotating cylinders, which states that for large values of -m,
there occur transition from axisymmetric to non-axisymmetric disturbance
whether the flow is hydrodynamic or hydromagnetic and this transition
from axisymmetric to non-axisymmetric disturbance occur earlier as the
strength of the magnetic field increases.
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