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

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 beta 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 T-2 - T-1 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 beta and N. It is also found that for given values of eta (the ratio of the radii of inner and outer cylinders) and beta, 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. (C) 2012 Elsevier Ltd. All rights reserved.