The Cheng-Minkowycz problem of natural convection past a vertical plate, in a porous medium saturated by a nanofluid, is studied analytically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. For the porous medium the Darcy model is employed. A similarity solution is presented. This solution depends on a Lewis number Le, a buoyancy-ratio number Nr, a Brownian motion number Nb. and a thermophoresis number Nt. The dependency of the Nusslelt number on these four parameters is investigated. (C) 2009 Elsevier Ltd. All rights reserved.