Stability of MHD Couette flow in a narrow gap annulus

A numerical solution to the MHD stability problem for dissipative Couette flow in a narrow gap is presented under following conditions: (i) the inner cylinder rotating with the outer one stationary, (ii) co-rotating cylinders, (iii) counter-rotating cylinders, (iv) an axially applied magnetic field, and (v) conducting and non-conducting walls.Results for the critical wave number and the critical Taylor number are presented and are compared with those of Chandrasekhar (1953). The agreement is very good. The amplitude of the radial velocity and the cell-pattern are shown on graphs for both the conducting and non-conducting walls and for different values of ± (=₂/₁, ₂-the angular velocity of the outer cylinder, ₁-the angular velocity of the inner cylinder) and Q the magnetic field parameter which is the square of the Hartman number. The effects of ± and Q on the stability of the flow are discussed. It is seen that the effect of the magnetic field is to inhibit the onset of instability, it being more so in the presence of conducting walls than in the presence of non-conducting walls.