Effects of Radial Temperature Gradient on the Stability of a Viscous Flow between Two Rotating Porous Cylinders with a Narrow Gap

Abstract

The linear stability of viscous fluid flow between two rotating concentric porous cylinders at temperature θ 1 (of the inner cylinder) and θ 2 (of the outer cylinder) is studied in a narrow gap case. The numerical values of the critical wave number a c and the critical Taylor number T c are listed in a table for different values of μ (-0 only the inner cylinder rotating), μ (≷0, both cylinders co-rotating or counter-rotating) ratio of angular velocities Ω 2 /Ω 1 , and for different values of ±N, ±S where N is a radial temperature gradient parameter based on the temperature difference θ 2 - θ 1 >/ 0) or injection (<0) velocity. The effects of these parameters on the stability of flows are discussed.