Convection in nanofluids with a particle-concentration-dependent thermal conductivity

TL;DR

This paper models thermal convection in nanofluids considering how particle concentration affects thermal conductivity, revealing how boundary conductivity differences influence convection onset and oscillatory behavior.

Contribution

It introduces a continuum model accounting for concentration-dependent thermal conductivity, analyzing its impact on convection onset and oscillations in nanofluids.

Findings

Convection onset shifts with boundary conductivity differences.

Oscillatory convection occurs beyond a critical conductivity difference.

Range of oscillatory behavior extends with increased conductivity disparity.

Abstract

Thermal convection in nanofluids is investigated by means of a continuum model for binary-fluid mixtures, with a thermal conductivity depending on the local concentration of colloidal particles. The applied temperature difference between the upper and the lower boundary leads via the Soret effect to a variation of the colloid concentration and therefore to a spatially varying heat conductivity. An increasing difference between the heat conductivity of the mixture near the colder and the warmer boundary results in a shift of the onset of convection to higher values of the Rayleigh number for positive values of the separation ratio psi>0 and to smaller values in the range psi<0. Beyond some critical difference of the thermal conductivity between the two boundaries, we find an oscillatory onset of convection not only for psi<0, but also within a finite range of psi>0. This range can be extended by increasing the difference in the thermal conductivity and it is bounded by two codimension-2 bifurcations.