On the insertion of a thin gas layer in micro cylindrical Couette flows involving power-law liquids

Abstract

Consideration is given to the fluid flow and heat transfer repercussions for introducing a thin (micro) gas layer into a cylindrical Couette flow assembly dealing with a power law liquid (lubricant). The trio influence of the thin gas layer on (1) the torque required for activating the lubrication process, (2) on the maximum temperature of the shaft (inner cylinder) and (3) on Nusselt number of the two-phase flow configuration are studied analytically. The results demonstrate that the thin gas layer normally contributes to reduce in the torque to set the fluid in motion and to downscale the maximum temperature at the shaft, especially for the sub-category of shear thickening liquids. However, in the sub-category of shear thinning liquids, the above-mentioned positive roles attributed to the micro gas layer hold true only for a limited number of flow configurations depending on several factors such as the Knudsen number, the accommodation coefficients and the rheological parameters of the liquid. It is further corroborated that the thin gas layer stabilizes or destabilizes the flow, depending on the magnitude of the power index number characterizing the liquid.