Effect of Radial Temperature Gradient on Stability of Hydromagnetic Couette Flow in Narrow-Gap Annulus with Constant Heat Flux at Outer Cylinder

Abstract

In this paper, the stability of the Couette flow of a viscous incompressible and electrically conducting fluid between two electrically non-conducting concentric rotating cylinders is studied by taking into account the following conditions (i) a radial temperature gradient (ii) a constant heat flux at outer cylinder (iii) an axially applied constant magnetic field (iv) the inner cylinder rotating with the outer one stationary (v) co-rotating cylinders (vi) and counter-rotating cylinders. The approximate solution of the eigenvalue problem is obtained by using the Galerkin’s method, when the gap between the cylinders is narrow. The numerical values of the critical wave number and the critical Taylor number are computed from the obtained approximate expression. It is found that the numerical values of the critical wave number and the critical Taylor number obtained by taking three terms in the Galerkin method agree very well with earlier results obtained by the shooting method. The amplitude of the radial velocity and the cell-pattern are also shown on the graphs for different values of the ratio of the angular velocities. The effects of ratios of angular velocities, radial temperature gradient and magnetic field on the stability of flows are discussed. It is found that the effect of the magnetic field is to inhibit the onset of instability but the effect of heat flux on the outer cylinder is to increase the onset of instability. These effects are more when the cylinders are rotating in anti clockwise sense.