Effects of radial temperature gradient on the stability of flow of a viscous incompressible fluid between two rotating cylinders

Stability of the flow of a viscous incompressible fluid in a narrow gap between two concentric cylinders rotating in opposite directions is studied. Exact values of critical Taylor number for the first and second modes are derived by a numerical procedure and these are compared with the known results. It is observed that the value of the critical Taylor number T_crit decreases with increasing the values of a parameter $\text{N (N =}\text{Ra}\text{T}\text{,}\text{Ra = Rayleigh number, T = Taylor number}\text{)}$, and the rate of decrease in the value of T_crit is more when the two cylinders rotate in the opposite directions.