Multiple solutions and hysteresis in steady parallel viscous flows

Abstract

A study is made of flows of viscous fluids when viscosity varies with temperature according to an Arrhenius law, and when viscous dissipation is taken into account. It is shown that for fluids with highly temperature‐sensitive viscosity the graph of shear rate against shear stress is an S‐shaped curve, with either one or three values of shear rate for given shear stress. In this situation hysteresis can occur if steady unidirectional flow is maintained. The velocity and temperature profiles are calculated, and the manner in which the temperature‐sensitivity parameter affects the conclusions is discussed. The calculations serve as criteria for evaluating the importance of viscous‐heating effects in applications.