Viscous heating in the cone-and-plate viscometer—II: Newtonian fluids with temperature-dependent viscosity and thermal conductivity

Abstract

Analytical solutions are given for the velocity and temperature profiles in a Newtonian fluid between two infinite parallel planes, one of which is moving fast enough that viscous dissipation heating effects are important. The temperature dependence of the viscosity and the thermal conductivity are taken into account. In one set of solutions both plates are maintained at the same temperature, and in another set of solutions there is zero heat flux through the moving plate. These results are then applied to the cone-and-plate viscometer, to show how the torque vs. angular speed curves deviate from linear behaviour because of the temperature dependence of the transport properties. The analytical expressions are compared with experimental flow curves, which seem to indicate that the viscous heating effects are slightly larger than the theoretical expressions would predict.