Instability in Annular Sliding Couette Flow with Variable-Viscosity and Viscous Dissipation

The study focuses on investigating the combined effect of viscous heating and viscous dissipation in annular sliding Couette flow (ASCF) between two coaxial circular cylinders, where the inner cylinder undergoes axial motion while the outer cylinder is at rest. Viscosity varies exponentially with temperature and is modelled using two different laws; Arrhenius-type law and Nahme-type law. Temporal linear stability analysis is employed to explore instability characteristics. The stability of ASCF is influenced by parameters including the Reynolds number, radius ratio (the ratio of the inner cylinder radius to the outer cylinder radius), Brinkman number, activation energy parameter, and Prandtl number. Existing literature (Deguchi & Nagata, J. Fluid Mech., vol. 678, 2011, pp. 156–178) establishes the stability of sliding annular Couette flows with uniform viscosity for all radius ratio values exceeding 0.1415. However, the current analysis reported that a small deviation in the fluid’s viscosity induces flow instability for all values of the radius ratio. Additionally, the analysis highlights the destabilizing impact of the radius ratio on the flow instability. The Arrhenius-type model demonstrates greater stability compared to the Nahme-type model. An increase in the Brinkman number and activation energy parameter makes the system more unstable.