Modelling the stability of Marangoni convection in a layer of nanofluid

A linear stability analysis is undertaken for the onset of Marangoni convection in a horizontal layer of a nanofluid heated from below. The model employed for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The lower boundary of the layer is assumed to be a rigid surface at fixed temperature while the top boundary is assumed to be a non-deformable free surface cooled by convection to an exterior region at a fixed temperature. The lower boundary of the layer is assumed to be impenetrable to nanoparticles with their distribution being determined from a conservation condition. Material properties of the nanofluid are modelled by the non-constant constitutive expressions developed by Kanafer and Vafai based on experimental evidence. The steady state solution across the layer is shown to be well approximated by a linear distribution of temperature and an exponential distribution of nanoparticle volume fraction. Constitutive properties are assumed to be non-constant functions of temperature and the volume fraction of nanoparticles. New behavior is introduced which in turn leads to significantly different stability boundaries from those predicted by historical analyses.