  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.
