Effect of radial temperature gradient on the Stability of flow in an annulus with constant Heat flux at the inner cylinder: wide-gap Problem

Abstract

An exact numerical solution is given to the eigenvalue problem of stability of Couette flow in a wide-gap region bounded by two concentric cylinders in the presence of constant heat flux at the inner cylinder. Numerical values of a c (the critical wave number) and T c (the critical Taylor) are calculated for different values of ±μ(=Ω 2/Ω 1) and η (=R 1/R 2) where Ω 1, Ω 2 are the angular velocities of the inner and outer cylinders of radii R 1, R 2 respectively. It is observed that the presence of radial temperature gradient enhances the stability of the flow, and with a decrease in the gap-width, the flow becomes less stable. In the presence of counter-rotating flow, the flow becomes more stable due to the presence of a radial temperature gradient.