Stability of Frictionally-Heated Flow

Extended results relative to the existence of a critical stress (a finite shear stress or pressure gradient above which fully-developed steady solutions do not exist) in Couette and Poiseuille motions are reported. The results apply to liquids under general thermal boundary conditions including a conduction-convection balance at the boundaries. A bound which gives a close a priori estimate of the value of the critical stress is developed. Stability characteristics of frictionally-heated Couette flow in the inviscid limit are specified. Below the critical stress the steady solutions are double-valued. The stress parameter first increases, then decreases, with increasing temperature. To the previously reported temperature instability on the second branch can be added a corresponding (inviscid) instability of the motion. On the first branch of the double-valued solution the flow is stable despite the presence of a single vorticity maximum at the channel center.