Dean instability of nanofluids with radial temperature and concentration non-uniformity

Abstract

The paper focuses on an investigation into instability of Dean flows of nanofluids in curved channels restricted by two concentric cylinders. The flow is caused by a constant azimuthal pressure gradient. Critical values of the Dean number, which serves as the instability criterion, were found numerically by the collocation method. Functional dependencies of the critical Dean number on the ratio between the radii of the concave and convex walls (0.1…0.99), as well as dimensionless parameters describing the temperature gradient (−3…6), the relative density of the nanoparticles (0…4), the ratio of the Brownian and thermophoretic diffusion (0.1…0.9), Prandtl (0.1…10) and Schmidt (10…100) number were revealed. It was shown that an increase in the relative density of the nanoparticles, the ratio of the Brownian and thermophoretic diffusion, and Schmidt number causes instability under conditions of either positive or negative temperature gradients. An increase in the Prandtl number enforces flow stability for the negative temperature gradient and deteriorates stability for the positive temperature gradient. In light of the complexity of the physical problem in the present paper, only axisymmetric perturbations are considered as the first step to be further developed in future investigations.

A review on the flow instability of nanofluids

“…Avramenko et al [18] investigated the instability of Dean flow in a curved channel between two cylinders produced by a pressure gradient in the azimuthal direction. The critical Dean number De cr related to flow instability was found numerically using the collocation method.…”

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