We develop an extension of our previous thermal instability analysis of a nanofluid-saturated porous layer. The extension is based on a new boundary condition for the nanoparticle fraction, which is physically more realistic. In the previous model we imposed both temperature and nanoparticle volume fractions at the boundaries of the layer. It is now assumed that the value of the temperature can be imposed on the boundaries, but the nanoparticle fraction adjusts so that the nanoparticle flux is zero on the boundaries. The new boundary condition on the nanoparticle volume fraction is made possible by accounting for the contributions of the effect of thermophoresis to the nanoparticle flux. It is shown that, with the new boundary conditions, oscillatory convection cannot occur. The effect of the nanoparticles on non-oscillatory convection is destabilizing. (C) 2013 Elsevier Ltd. All rights reserved.