Viscous heating effects in fluids with temperature-dependent viscosity: triggering of secondary flows

Viscous heating can play an important role in the dynamics of fluids with strongly temperature-dependent viscosities because of the coupling between the energy and momentum equations. The heat generated by viscous friction produces a local temperature increase near the tube walls with a consequent decrease of the viscosity and a strong stratification in the viscosity profile. The problem of viscous heating in fluids was investigated and reviewed by Costa & Macedonio (2003) because of its important implications in the study of magma flows. Because of the strong coupling between viscosity and temperature, the temperature rise due to the viscous heating may trigger instabilities in the velocity field, which cannot be predicted by a simple isothermal Newtonian model. When viscous heating produces a pronounced peak in the temperature profile near the walls, a triggering of instabilities and a transition to secondary flows can occur because of the stratification in the viscosity profile. In this paper we focus on the thermal and mechanical effects caused by viscous heating. We will present the linear stability equations and we will show, as in certain regimes, these effects can trigger and sustain a particular class of secondary rotational flows which appear organised in coherent structures similar to roller vortices. This phenomenon can play a very important role in the dynamics of magma flows in conduits and lava flows in channels and, to our knowledge, it is the first time that it has been investigated by a direct numerical simulation.