Theoretical solution is derived for annular laminar flows with MHD interaction driven by a rotating co-axial cylinder. The effects on the flow field and rotational torque are clarified by changing the radius ratio and the strength of MHD interaction. As increasing the radius ratio, azimuthal flow velocity increases and approaches the plane Couette flow profile for weak MHD interaction. The azimuthal flow velocity, however, decreases as increasing MHD interaction, and the reverse flow emerges in large radial locations. As increasing the MHD interaction, the rotational torque increases. A larger radius ratio leads to the larger sensitivity of the change in rotational torque.
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