Based on the continuity hypothesis of fluid, 1-D mathematical models of ions' transport in the rectangular nanofluidic channels are established by using the Poisson-Boltzmann (PB) equation and the modified Navier-Stokes (N-S) equations. The deduced equations are solved with MATLAB software. The results show that the distribution of the electric potential and the flow field could be predicted by the parameters, such as conductivity, surface charge density, solution concentration and channel height. The relationships between the parameters and the flow characteristics of the solution are also discussed. The research will help to the accurate manipulation of the solution in the nanofluidic channels. (C) 2011 Elsevier B.V. All rights reserved.