Marangoni convection in water-alumina nanofluids: Dependence on the nanoparticle size

A linear stability analysis for the onset of Marangoni convection in a horizontal layer of distilled water/alumina nanofluid heated from below is investigated using a model which incorporates the effects of Brownian and thermophoreticdiffusions. The analysis uses realistic constitutive models for thermal conductivity and dynamic viscosity which include a dependence on average size of nanoparticles in addition to the volume fraction of nanoparticles and temperature. The lower boundary of the layer is a rigid surface at fixed temperature while the upper boundary behaves as a non-deformable free surface cooled by convection to an exterior region at a fixed temperature. Both boundaries are assumed to be impenetrable to nanoparticles so that their distribution is determined from a conservation condition. The numerical results are obtained using the method of expansion of Chebyshev polynomials. Stability boundary curves are investigated for nanoparticle sizes ranging from 15  nm to 100  nm. Nanofluids with nanoparticle of smaller average size are found to be more stable than those with larger sized nanoparticles.