Effect of Radial Temperature Gradient on the Stability of Magnetohydrodynamic Dean Flow in an Annular Channel at High Magnetic Parameter

Abstract

The effect of a radial temperature gradient on the stability of Dean flow of an electrically conducting fluid in an annular channel is investigated. A strong constant magnetic field is imposed in the axial direction. Finitedifference method is used to solve the eigenvalue problem. For given values of gap width d, between the cylinders, and magnetic parameter Q, electrically nonconducting (NC) walls are found to be more destabilizing than perfectly conducting (PC) walls when the temperature parameter N < 0. This trend persists even for small positive values of N but when N (>0) exceeds a critical value depending on Q, PC walls are slightly more destabilizing than NC walls. The critical value of the radii ratio خ· (0 < خ·â€‰< 1) beyond which the first unstable mode becomes nonaxisymmetric is determined for various values of N and Q.