The effect of radial temperature gradient and axial magnetic field on the stability of couette flow: The narrow gap problem

Abstract

A numerical solution to the MHD stability problem for dissipative Couette flow in a narrow gap is presented under the following conditions: (i) the inner cylinder rotating with the outer cylinder stationary, (ii) corotating cylinders, (iii) counter-rotating cylinders, (iv) an axially applied magnetic field, (v) conducting and nonconducting walls, and (vi) the presence of a radial temperature gradient. Results for the critical wave number ac, and the critical Taylor number Tc, are presented. The variation of Tc is shown on graphs for both the conducting and nonconducting walls and for different values of ±μ (= Ω2/Ω1, where Ω2 is the angular velocity of the outer cylinder, and Ω1 is the angular velocity of the inner cylinder), the magnetic field parameter Q, which is the square of the Hartmann number and ± N (= Ra/Ta, where Ra is the Rayleigh number). The effects of ±μ, N and Q on the stability of flow are discussed. It is seen that the effect of the magnetic field is to inhibit the onset of instability, this being more so in the presence of conducting walls and a negative temperature gradient.