EFFECTS OF RADIAL TEMPERATURE-GRADIENT ON THE STABILITY OF A NARROW-GAP ANNULUS FLOW

An eigenvalue problem of the stability of Couette flow between two concentric cylinders in relative motion in the presence of a positive (T2 > T1) and a negative (T2 < T1) radial temperature gradient is solved numerically, where T1, T2 are the temperatures of the inner and outer cylinders, respectively. The numerical values of the critical wave number ac and the critical Taylor number Tc are calculated for ± μ (= Ω2 Ω1, where Ω2 is the angular speed of the outer cylinder and Ω1 is the angular speed of the inner cylinder) and ±N (ratio of the Rayleigh and Taylor numbers). The radial eigenfunction and the cell patterns are shown graphically for different values of ± μ and ±N. It is observed that the flow is more stable in the presence of a negative temperature gradient for both ±μ. The stabilising effect is more promising when the two cylinders are counterrotating. The magnitude of ac also increases steeply in the presence of counterrotating cylinders and a negative radial temperature gradient (T2 < T1). © 1990.