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

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.