Self-oscillating mode in an anomalous thermoviscous liquid flow

It is known that the flow of liquids with a nonmonotonic dependence of viscosity on temperature (abnormally thermoviscous liquids) in the presence of temperature gradients, for example, when a heated liquid flows into a cooled channel, is accompanied by the formation of a high-viscosity region localized in the flow, which determines the features of its flow. In this paper, the conditions for the occurrence of self-oscillating regimes of flow rate variation during the flow of anomalously thermoviscous liquids in annular channels under the action of a constant pressure drop and under given conditions of heat transfer on the inner and outer walls of the annular channel are determined. It has been found that self-oscillations in the flow rate of an anomalously thermoviscous liquid can occur when flowing in an annular channel, on the walls of which there is an abrupt decrease in the intensity of heat transfer. The region of existence of the self-oscillation mode is determined by the values of the pressure drop and the geometric parameter equal to the ratio of the width of the annular gap to the radius of the inner cylinder. In addition, weakly damped flow rate oscillations with a very small damping decrement were also observed at the boundaries of this region.