A linear stability analysis for the onset of Marangoni convection in a horizontal layer of a nanofluid heated from below is investigated. The model used 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 boundaries of the layer are assumed to be impenetrable to nanoparticles with their distribution being determined from a conservation condition. The linear analysis uses spectral methods based on the expansion of eigenfunctions as Chebyshev series. Stability boundaries for temperature and volume fraction Marangoni numbers are obtained for nanofluids on either distilled water or ethanol with either alumina or multi-walled carbon nanotubules as nanoparticles. (C) 2016 Elsevier Ltd. All rights reserved.