A two-dimensional, non-isothermal model is presented for a small passive direct methanol fuel cell (DMFC) in vertical operation. The effect of natural convection at the anode in the fuel reservoir is considered. The coupled heat and mass transport of the whole cell, along with the electrochemical reactions occurring in the passive DMFC are modeled. The comprehensive model is solved numerically by the finite element method and validated against the experiment results reported in this paper. The numerical results show that when in vertical operation, the cell temperature increases gradually from the bottom of the cell to the top of the cell, resulting from natural convection at the anode. A higher cell temperature will lead to stronger natural convection in the fuel reservoir, which will in turn lead to a larger temperature difference across the cell. The results also indicate that the rate of methanol crossover increases with increasing methanol concentration from 1 M to 4 M. When incrementally increasing the current densities, the rate of methanol crossover decreased at low methanol concentration of 1 M-2 M but increased at high methanol concentration of 3 M-4 M. (C) 2013 Elsevier Ltd. All rights reserved.