Stability of flows heated by friction

Simple flows can be used to measure viscosities. If the viscosity is high enough and depends on temperature, frictional heating presents a technical difficulty. Yet in many viscometric flows formulas predicting the temperature and the velocity distribution are available. The resulting flow may or may not be stable to small perturbations. If it is unstable it will not be seen in an experiment. Our aim is to show that stability depends on how the experiment is controlled, whether by holding a kinematic or a dynamic variable fixed, eg., wall speed or wall stress. In a plane Couette flow, controlled by the wall speed, stability to long wave length perturbations is established for all points of the base curve. In both a rotational Couette flow and a Poiseulle flow stability obtains at least part way along the upper branch.