Effects of radial temperature gradient on the stability of a narrow-gap annulus flow

Abstract

An eigenvalue problem of the stability of Couette flow between two concentric cylinders in relative motion in the presence of a positive ( T 2 > T 1) and a negative ( T 2 < T 1) radial temperature gradient is solved numerically, where T 1, T 2 are the temperatures of the inner and outer cylinders, respectively. The numerical values of the critical wave number a c and the critical Taylor number T c are calculated for ± μ (= Ω 2 Ω 1 , where Ω 2 is the angular speed of the outer cylinder and Ω 1 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 a c also increases steeply in the presence of counterrotating cylinders and a negative radial temperature gradient ( T 2 < T 1).