Axial flow effects on the stability of circular Couette flow with viscous heating

We consider flow between concentric circular cylinders driven jointly by a constant axial pressure gradient and rotation of one or both cylinder walls. In this work we account for viscous heating effects with a temperature-dependent viscosity, and have computed critical values with a radius ratio η≡Ri∕Ro=0.827 and rotation rate ratio κ≡Ωo∕Ωi=0 as used in the recent zero axial flow experiments of White and Muller [J. Fluid Mech. 462, 133 (2002)], where Ri and Ro are the inner and outer cylinder radii, respectively, and Ωi and Ωo are the corresponding (signed) angular velocities. The effects of gravity are neglected, whereas conductivity, the volumetric coefficient of thermal expansion, density, and constant pressure specific heat are taken to be constant. The analysis extends previous results with no axial flow, and accounts for arbitrary disturbances of infinitesimal amplitude. Results show that over the entire range of axial flow rates considered, stability boundaries differ significantly from those foun...

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