Stability of Taylor–Couette Magnetoconvection With Radial Temperature Gradient and Constant Heat Flux at the Outer Cylinder

An analysis is made of the linear stability of wide-gap hydromagnetic (MHD) dissipative Couette flow of an incompressible electrically conducting fluid between two rotating concentric circular cylinders in the presence of a uniform axial magnetic field. A constant heat flux is applied at the outer cylinder and the inner cylinder is kept at a constant temperature. Both types of boundary conditions viz; perfectly electrically conducting and electrically nonconducting walls are examined. The three cases of $μ<0$ (counter-rotating), $μ>0$ (co-rotating), and $μ=0$ (stationary outer cylinder) are considered. Assuming very small magnetic Prandtl number $Pm$⁠, the wide-gap perturbation equations are derived and solved by a direct numerical procedure. It is found that for given values of the radius ratio $η$ and the heat flux parameter $N$⁠, the critical Taylor number $Tc$ at the onset of instability increases with increase in Hartmann number $Q$ for both conducting and nonconducting walls thus establishing the stabilizing influence of the magnetic field. Further it is found that insulating walls are more destabilizing than the conducting walls. It is observed that for given values of $η$ and $Q$⁠, the critical Taylor number $Tc$ decreases with increase in $N$⁠. The analysis further reveals that for $μ=0$ and perfectly conducting walls, the critical wave number $ac$ is not a monotonic function of $Q$ but first increases, reaches a maximum and then decreases with further increase in $Q$⁠. It is also observed that while $ac$ is a monotonic decreasing function of $μ$ for $N=0$⁠, in the presence of heat flux $(N=1)$⁠, $ac$ has a maximum at a negative value of $μ$ (counter-rotating cylinders).