Effect of radial temperature gradient on the stability of Taylor–Dean flow between two arbitrarily spaced concentric rotating cylinders

Abstract

The effect of a radial temperature gradient on the stability of Taylor–Dean flow of an incompressible viscous fluid between two arbitrarily spaced concentric rotating circular cylinders driven by a constant azimuthal pressure gradient is studied. Here the ratio of representative pumping and rotation velocities β is varied from −6.1613 to 1.00 and both positive and negative values of the temperature gradient parameter N are considered, where N depends on the temperature differences T2−T1 between the outer and inner cylinders. The linearized stability equations form an eigenvalue problem which is solved by using a classical Runge–Kutta scheme combined with a shooting technique, termed unit disturbance method. It is found that as the gap width between the cylinders increases, the critical Taylor number progressively increases for given values of β and N. It is also found that for given values of η (the ratio of the radii of inner and outer cylinders) and β, the flow becomes more and more unstable with increase in N(>0). In the present work, emphasis is given on the point as to whether the two neutral stability curves cross at some point for given value of N for which the flow is completely stable.