Centrifugal instability of nanofluids with radial temperature and concentration non-uniformity between co-axial rotating cylinders

Abstract

Different methods of nanofluid preparation and further preserving of their properties have been developed so far. One of them is a so called centrifugal method. During the nanofluid preparation in centrifugal devices, centrifugal instability of different nature may arise, which must be taken into account. Therefore, this paper focuses on a theoretical study of instability of Taylor–Couette flows of nanofluids in a curved channel formed by two concentric cylindrical surfaces. The flow is driven by rotation of the inner cylindrical surface. The collocation method is used to find numerically critical values of the Taylor number, which plays the role of the instability criteria. Effects of the following parameters on the critical values of the Taylor number were studied: the ratio of the radii of the concave and convex walls, the dimensionless parameters that describe the temperature gradient, the relative density of the nanoparticles, the ratio of Brownian diffusion and thermophoretic diffusion, as well as the Prandtl and the Schmidt numbers. It was demonstrated that an increase in the relative density, the ratio of Brownian diffusion and thermophoretic diffusion and Schmidt numbers incurs loss of the flow stability under both positive and negative temperature gradients. In the same time, increasing Prandtl numbers stabilize flow under the negative temperature gradient and destabilize it in the conditions of the positive temperature gradient. The theoretical results obtained in the paper help understand mechanisms of centrifugal instability in nanofluids and thereby optimize the functionality of centrifugal devices used to prepare nanofluids.